Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(36.8882785570\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(26.5679\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 | ||||||||
\(3\) | 26.5679 | 1.70433 | 0.852166 | − | 0.523272i | \(-0.175289\pi\) | ||||
0.852166 | + | 0.523272i | \(0.175289\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −106.272 | −1.20514 | ||||||||
\(7\) | 257.945 | 1.98967 | 0.994836 | − | 0.101499i | \(-0.0323637\pi\) | ||||
0.994836 | + | 0.101499i | \(0.0323637\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 462.854 | 1.90475 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 382.346 | 0.952740 | 0.476370 | − | 0.879245i | \(-0.341952\pi\) | ||||
0.476370 | + | 0.879245i | \(0.341952\pi\) | |||||||
\(12\) | 425.087 | 0.852166 | ||||||||
\(13\) | 152.988 | 0.251072 | 0.125536 | − | 0.992089i | \(-0.459935\pi\) | ||||
0.125536 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(14\) | −1031.78 | −1.40691 | ||||||||
\(15\) | 664.198 | 0.762200 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 437.640 | 0.367278 | 0.183639 | − | 0.982994i | \(-0.441212\pi\) | ||||
0.183639 | + | 0.982994i | \(0.441212\pi\) | |||||||
\(18\) | −1851.41 | −1.34686 | ||||||||
\(19\) | −2052.16 | −1.30415 | −0.652074 | − | 0.758156i | \(-0.726101\pi\) | ||||
−0.652074 | + | 0.758156i | \(0.726101\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 6853.05 | 3.39106 | ||||||||
\(22\) | −1529.38 | −0.673689 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | −1700.35 | −0.602572 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −611.951 | −0.177535 | ||||||||
\(27\) | 5841.05 | 1.54199 | ||||||||
\(28\) | 4127.11 | 0.994836 | ||||||||
\(29\) | 2360.37 | 0.521177 | 0.260588 | − | 0.965450i | \(-0.416083\pi\) | ||||
0.260588 | + | 0.965450i | \(0.416083\pi\) | |||||||
\(30\) | −2656.79 | −0.538957 | ||||||||
\(31\) | −4283.89 | −0.800634 | −0.400317 | − | 0.916377i | \(-0.631100\pi\) | ||||
−0.400317 | + | 0.916377i | \(0.631100\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 10158.1 | 1.62379 | ||||||||
\(34\) | −1750.56 | −0.259705 | ||||||||
\(35\) | 6448.62 | 0.889808 | ||||||||
\(36\) | 7405.66 | 0.952374 | ||||||||
\(37\) | −12212.3 | −1.46654 | −0.733271 | − | 0.679936i | \(-0.762008\pi\) | ||||
−0.733271 | + | 0.679936i | \(0.762008\pi\) | |||||||
\(38\) | 8208.63 | 0.922171 | ||||||||
\(39\) | 4064.56 | 0.427910 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −16759.8 | −1.55707 | −0.778536 | − | 0.627600i | \(-0.784037\pi\) | ||||
−0.778536 | + | 0.627600i | \(0.784037\pi\) | |||||||
\(42\) | −27412.2 | −2.39784 | ||||||||
\(43\) | −4911.50 | −0.405082 | −0.202541 | − | 0.979274i | \(-0.564920\pi\) | ||||
−0.202541 | + | 0.979274i | \(0.564920\pi\) | |||||||
\(44\) | 6117.53 | 0.476370 | ||||||||
\(45\) | 11571.3 | 0.851829 | ||||||||
\(46\) | 2116.00 | 0.147442 | ||||||||
\(47\) | −21338.3 | −1.40902 | −0.704508 | − | 0.709696i | \(-0.748832\pi\) | ||||
−0.704508 | + | 0.709696i | \(0.748832\pi\) | |||||||
\(48\) | 6801.38 | 0.426083 | ||||||||
\(49\) | 49728.4 | 2.95879 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 11627.2 | 0.625964 | ||||||||
\(52\) | 2447.80 | 0.125536 | ||||||||
\(53\) | −36998.9 | −1.80925 | −0.904625 | − | 0.426208i | \(-0.859849\pi\) | ||||
−0.904625 | + | 0.426208i | \(0.859849\pi\) | |||||||
\(54\) | −23364.2 | −1.09035 | ||||||||
\(55\) | 9558.64 | 0.426078 | ||||||||
\(56\) | −16508.5 | −0.703455 | ||||||||
\(57\) | −54521.5 | −2.22270 | ||||||||
\(58\) | −9441.48 | −0.368528 | ||||||||
\(59\) | −29669.6 | −1.10964 | −0.554819 | − | 0.831971i | \(-0.687213\pi\) | ||||
−0.554819 | + | 0.831971i | \(0.687213\pi\) | |||||||
\(60\) | 10627.2 | 0.381100 | ||||||||
\(61\) | 29601.2 | 1.01856 | 0.509278 | − | 0.860602i | \(-0.329913\pi\) | ||||
0.509278 | + | 0.860602i | \(0.329913\pi\) | |||||||
\(62\) | 17135.6 | 0.566134 | ||||||||
\(63\) | 119391. | 3.78982 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 3824.69 | 0.112283 | ||||||||
\(66\) | −40632.5 | −1.14819 | ||||||||
\(67\) | 25795.4 | 0.702030 | 0.351015 | − | 0.936370i | \(-0.385837\pi\) | ||||
0.351015 | + | 0.936370i | \(0.385837\pi\) | |||||||
\(68\) | 7002.25 | 0.183639 | ||||||||
\(69\) | −14054.4 | −0.355378 | ||||||||
\(70\) | −25794.5 | −0.629189 | ||||||||
\(71\) | 27128.9 | 0.638684 | 0.319342 | − | 0.947640i | \(-0.396538\pi\) | ||||
0.319342 | + | 0.947640i | \(0.396538\pi\) | |||||||
\(72\) | −29622.6 | −0.673430 | ||||||||
\(73\) | −49568.3 | −1.08867 | −0.544336 | − | 0.838867i | \(-0.683218\pi\) | ||||
−0.544336 | + | 0.838867i | \(0.683218\pi\) | |||||||
\(74\) | 48849.4 | 1.03700 | ||||||||
\(75\) | 16604.9 | 0.340866 | ||||||||
\(76\) | −32834.5 | −0.652074 | ||||||||
\(77\) | 98624.0 | 1.89564 | ||||||||
\(78\) | −16258.3 | −0.302578 | ||||||||
\(79\) | 73611.6 | 1.32702 | 0.663512 | − | 0.748166i | \(-0.269065\pi\) | ||||
0.663512 | + | 0.748166i | \(0.269065\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 42711.1 | 0.723316 | ||||||||
\(82\) | 67039.1 | 1.10102 | ||||||||
\(83\) | 54599.4 | 0.869946 | 0.434973 | − | 0.900443i | \(-0.356758\pi\) | ||||
0.434973 | + | 0.900443i | \(0.356758\pi\) | |||||||
\(84\) | 109649. | 1.69553 | ||||||||
\(85\) | 10941.0 | 0.164252 | ||||||||
\(86\) | 19646.0 | 0.286436 | ||||||||
\(87\) | 62710.1 | 0.888258 | ||||||||
\(88\) | −24470.1 | −0.336845 | ||||||||
\(89\) | 24120.5 | 0.322783 | 0.161392 | − | 0.986890i | \(-0.448402\pi\) | ||||
0.161392 | + | 0.986890i | \(0.448402\pi\) | |||||||
\(90\) | −46285.4 | −0.602334 | ||||||||
\(91\) | 39462.4 | 0.499551 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | −113814. | −1.36455 | ||||||||
\(94\) | 85353.4 | 0.996325 | ||||||||
\(95\) | −51303.9 | −0.583232 | ||||||||
\(96\) | −27205.5 | −0.301286 | ||||||||
\(97\) | 103363. | 1.11541 | 0.557705 | − | 0.830039i | \(-0.311682\pi\) | ||||
0.557705 | + | 0.830039i | \(0.311682\pi\) | |||||||
\(98\) | −198914. | −2.09218 | ||||||||
\(99\) | 176970. | 1.81473 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 45095.7 | 0.439877 | 0.219939 | − | 0.975514i | \(-0.429414\pi\) | ||||
0.219939 | + | 0.975514i | \(0.429414\pi\) | |||||||
\(102\) | −46508.8 | −0.442623 | ||||||||
\(103\) | 89880.9 | 0.834784 | 0.417392 | − | 0.908727i | \(-0.362944\pi\) | ||||
0.417392 | + | 0.908727i | \(0.362944\pi\) | |||||||
\(104\) | −9791.22 | −0.0887674 | ||||||||
\(105\) | 171326. | 1.51653 | ||||||||
\(106\) | 147995. | 1.27933 | ||||||||
\(107\) | −127029. | −1.07262 | −0.536309 | − | 0.844022i | \(-0.680182\pi\) | ||||
−0.536309 | + | 0.844022i | \(0.680182\pi\) | |||||||
\(108\) | 93456.8 | 0.770995 | ||||||||
\(109\) | −10406.1 | −0.0838919 | −0.0419459 | − | 0.999120i | \(-0.513356\pi\) | ||||
−0.0419459 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(110\) | −38234.6 | −0.301283 | ||||||||
\(111\) | −324456. | −2.49948 | ||||||||
\(112\) | 66033.8 | 0.497418 | ||||||||
\(113\) | 3869.90 | 0.0285104 | 0.0142552 | − | 0.999898i | \(-0.495462\pi\) | ||||
0.0142552 | + | 0.999898i | \(0.495462\pi\) | |||||||
\(114\) | 218086. | 1.57169 | ||||||||
\(115\) | −13225.0 | −0.0932505 | ||||||||
\(116\) | 37765.9 | 0.260588 | ||||||||
\(117\) | 70810.9 | 0.478229 | ||||||||
\(118\) | 118678. | 0.784633 | ||||||||
\(119\) | 112887. | 0.730763 | ||||||||
\(120\) | −42508.7 | −0.269479 | ||||||||
\(121\) | −14862.7 | −0.0922858 | ||||||||
\(122\) | −118405. | −0.720228 | ||||||||
\(123\) | −445272. | −2.65377 | ||||||||
\(124\) | −68542.2 | −0.400317 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −477562. | −2.67981 | ||||||||
\(127\) | 98019.0 | 0.539263 | 0.269632 | − | 0.962964i | \(-0.413098\pi\) | ||||
0.269632 | + | 0.962964i | \(0.413098\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −130488. | −0.690394 | ||||||||
\(130\) | −15298.8 | −0.0793959 | ||||||||
\(131\) | −118385. | −0.602723 | −0.301361 | − | 0.953510i | \(-0.597441\pi\) | ||||
−0.301361 | + | 0.953510i | \(0.597441\pi\) | |||||||
\(132\) | 162530. | 0.811893 | ||||||||
\(133\) | −529343. | −2.59482 | ||||||||
\(134\) | −103182. | −0.496410 | ||||||||
\(135\) | 146026. | 0.689599 | ||||||||
\(136\) | −28009.0 | −0.129852 | ||||||||
\(137\) | −12515.2 | −0.0569688 | −0.0284844 | − | 0.999594i | \(-0.509068\pi\) | ||||
−0.0284844 | + | 0.999594i | \(0.509068\pi\) | |||||||
\(138\) | 56217.7 | 0.251290 | ||||||||
\(139\) | 350905. | 1.54047 | 0.770235 | − | 0.637760i | \(-0.220139\pi\) | ||||
0.770235 | + | 0.637760i | \(0.220139\pi\) | |||||||
\(140\) | 103178. | 0.444904 | ||||||||
\(141\) | −566915. | −2.40143 | ||||||||
\(142\) | −108516. | −0.451618 | ||||||||
\(143\) | 58494.2 | 0.239206 | ||||||||
\(144\) | 118491. | 0.476187 | ||||||||
\(145\) | 59009.3 | 0.233077 | ||||||||
\(146\) | 198273. | 0.769808 | ||||||||
\(147\) | 1.32118e6 | 5.04276 | ||||||||
\(148\) | −195398. | −0.733271 | ||||||||
\(149\) | 6379.53 | 0.0235409 | 0.0117704 | − | 0.999931i | \(-0.496253\pi\) | ||||
0.0117704 | + | 0.999931i | \(0.496253\pi\) | |||||||
\(150\) | −66419.8 | −0.241029 | ||||||||
\(151\) | −516891. | −1.84483 | −0.922416 | − | 0.386197i | \(-0.873789\pi\) | ||||
−0.922416 | + | 0.386197i | \(0.873789\pi\) | |||||||
\(152\) | 131338. | 0.461086 | ||||||||
\(153\) | 202563. | 0.699572 | ||||||||
\(154\) | −394496. | −1.34042 | ||||||||
\(155\) | −107097. | −0.358054 | ||||||||
\(156\) | 65033.0 | 0.213955 | ||||||||
\(157\) | 187263. | 0.606321 | 0.303161 | − | 0.952939i | \(-0.401958\pi\) | ||||
0.303161 | + | 0.952939i | \(0.401958\pi\) | |||||||
\(158\) | −294447. | −0.938348 | ||||||||
\(159\) | −982982. | −3.08356 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −136453. | −0.414875 | ||||||||
\(162\) | −170844. | −0.511461 | ||||||||
\(163\) | 616742. | 1.81817 | 0.909086 | − | 0.416609i | \(-0.136782\pi\) | ||||
0.909086 | + | 0.416609i | \(0.136782\pi\) | |||||||
\(164\) | −268156. | −0.778536 | ||||||||
\(165\) | 253953. | 0.726179 | ||||||||
\(166\) | −218397. | −0.615145 | ||||||||
\(167\) | −261863. | −0.726579 | −0.363290 | − | 0.931676i | \(-0.618346\pi\) | ||||
−0.363290 | + | 0.931676i | \(0.618346\pi\) | |||||||
\(168\) | −438595. | −1.19892 | ||||||||
\(169\) | −347888. | −0.936963 | ||||||||
\(170\) | −43764.0 | −0.116144 | ||||||||
\(171\) | −949848. | −2.48407 | ||||||||
\(172\) | −78583.9 | −0.202541 | ||||||||
\(173\) | −452537. | −1.14958 | −0.574790 | − | 0.818301i | \(-0.694916\pi\) | ||||
−0.574790 | + | 0.818301i | \(0.694916\pi\) | |||||||
\(174\) | −250840. | −0.628094 | ||||||||
\(175\) | 161215. | 0.397934 | ||||||||
\(176\) | 97880.5 | 0.238185 | ||||||||
\(177\) | −788259. | −1.89119 | ||||||||
\(178\) | −96482.0 | −0.228242 | ||||||||
\(179\) | 391812. | 0.913998 | 0.456999 | − | 0.889467i | \(-0.348924\pi\) | ||||
0.456999 | + | 0.889467i | \(0.348924\pi\) | |||||||
\(180\) | 185141. | 0.425914 | ||||||||
\(181\) | −709815. | −1.61046 | −0.805228 | − | 0.592965i | \(-0.797957\pi\) | ||||
−0.805228 | + | 0.592965i | \(0.797957\pi\) | |||||||
\(182\) | −157849. | −0.353236 | ||||||||
\(183\) | 786442. | 1.73596 | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | −305309. | −0.655858 | ||||||||
\(186\) | 455256. | 0.964880 | ||||||||
\(187\) | 167330. | 0.349921 | ||||||||
\(188\) | −341413. | −0.704508 | ||||||||
\(189\) | 1.50667e6 | 3.06805 | ||||||||
\(190\) | 205216. | 0.412408 | ||||||||
\(191\) | 158111. | 0.313602 | 0.156801 | − | 0.987630i | \(-0.449882\pi\) | ||||
0.156801 | + | 0.987630i | \(0.449882\pi\) | |||||||
\(192\) | 108822. | 0.213041 | ||||||||
\(193\) | 326743. | 0.631413 | 0.315707 | − | 0.948857i | \(-0.397758\pi\) | ||||
0.315707 | + | 0.948857i | \(0.397758\pi\) | |||||||
\(194\) | −413451. | −0.788714 | ||||||||
\(195\) | 101614. | 0.191367 | ||||||||
\(196\) | 795655. | 1.47940 | ||||||||
\(197\) | 94961.8 | 0.174335 | 0.0871673 | − | 0.996194i | \(-0.472219\pi\) | ||||
0.0871673 | + | 0.996194i | \(0.472219\pi\) | |||||||
\(198\) | −707881. | −1.28321 | ||||||||
\(199\) | −159731. | −0.285928 | −0.142964 | − | 0.989728i | \(-0.545663\pi\) | ||||
−0.142964 | + | 0.989728i | \(0.545663\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 685330. | 1.19649 | ||||||||
\(202\) | −180383. | −0.311040 | ||||||||
\(203\) | 608845. | 1.03697 | ||||||||
\(204\) | 186035. | 0.312982 | ||||||||
\(205\) | −418994. | −0.696344 | ||||||||
\(206\) | −359523. | −0.590281 | ||||||||
\(207\) | −244850. | −0.397167 | ||||||||
\(208\) | 39164.9 | 0.0627680 | ||||||||
\(209\) | −784634. | −1.24251 | ||||||||
\(210\) | −685305. | −1.07235 | ||||||||
\(211\) | 1.03326e6 | 1.59774 | 0.798868 | − | 0.601506i | \(-0.205433\pi\) | ||||
0.798868 | + | 0.601506i | \(0.205433\pi\) | |||||||
\(212\) | −591982. | −0.904625 | ||||||||
\(213\) | 720758. | 1.08853 | ||||||||
\(214\) | 508118. | 0.758455 | ||||||||
\(215\) | −122787. | −0.181158 | ||||||||
\(216\) | −373827. | −0.545176 | ||||||||
\(217\) | −1.10501e6 | −1.59300 | ||||||||
\(218\) | 41624.2 | 0.0593205 | ||||||||
\(219\) | −1.31693e6 | −1.85546 | ||||||||
\(220\) | 152938. | 0.213039 | ||||||||
\(221\) | 66953.6 | 0.0922133 | ||||||||
\(222\) | 1.29783e6 | 1.76740 | ||||||||
\(223\) | 566494. | 0.762839 | 0.381420 | − | 0.924402i | \(-0.375435\pi\) | ||||
0.381420 | + | 0.924402i | \(0.375435\pi\) | |||||||
\(224\) | −264135. | −0.351728 | ||||||||
\(225\) | 289284. | 0.380950 | ||||||||
\(226\) | −15479.6 | −0.0201599 | ||||||||
\(227\) | 1.00552e6 | 1.29517 | 0.647587 | − | 0.761992i | \(-0.275778\pi\) | ||||
0.647587 | + | 0.761992i | \(0.275778\pi\) | |||||||
\(228\) | −872344. | −1.11135 | ||||||||
\(229\) | 1.00056e6 | 1.26082 | 0.630412 | − | 0.776260i | \(-0.282886\pi\) | ||||
0.630412 | + | 0.776260i | \(0.282886\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | 2.62023e6 | 3.23080 | ||||||||
\(232\) | −151064. | −0.184264 | ||||||||
\(233\) | −1.02845e6 | −1.24106 | −0.620532 | − | 0.784181i | \(-0.713083\pi\) | ||||
−0.620532 | + | 0.784181i | \(0.713083\pi\) | |||||||
\(234\) | −283244. | −0.338159 | ||||||||
\(235\) | −533458. | −0.630131 | ||||||||
\(236\) | −474713. | −0.554819 | ||||||||
\(237\) | 1.95571e6 | 2.26169 | ||||||||
\(238\) | −451548. | −0.516727 | ||||||||
\(239\) | 701099. | 0.793934 | 0.396967 | − | 0.917833i | \(-0.370063\pi\) | ||||
0.396967 | + | 0.917833i | \(0.370063\pi\) | |||||||
\(240\) | 170035. | 0.190550 | ||||||||
\(241\) | −504212. | −0.559204 | −0.279602 | − | 0.960116i | \(-0.590203\pi\) | ||||
−0.279602 | + | 0.960116i | \(0.590203\pi\) | |||||||
\(242\) | 59450.9 | 0.0652559 | ||||||||
\(243\) | −284632. | −0.309220 | ||||||||
\(244\) | 473619. | 0.509278 | ||||||||
\(245\) | 1.24321e6 | 1.32321 | ||||||||
\(246\) | 1.78109e6 | 1.87650 | ||||||||
\(247\) | −313955. | −0.327435 | ||||||||
\(248\) | 274169. | 0.283067 | ||||||||
\(249\) | 1.45059e6 | 1.48268 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −1.23699e6 | −1.23932 | −0.619659 | − | 0.784871i | \(-0.712729\pi\) | ||||
−0.619659 | + | 0.784871i | \(0.712729\pi\) | |||||||
\(252\) | 1.91025e6 | 1.89491 | ||||||||
\(253\) | −202261. | −0.198660 | ||||||||
\(254\) | −392076. | −0.381317 | ||||||||
\(255\) | 290680. | 0.279940 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 191965. | 0.181296 | 0.0906482 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906482 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(258\) | 521953. | 0.488182 | ||||||||
\(259\) | −3.15011e6 | −2.91794 | ||||||||
\(260\) | 61195.1 | 0.0561414 | ||||||||
\(261\) | 1.09251e6 | 0.992710 | ||||||||
\(262\) | 473539. | 0.426189 | ||||||||
\(263\) | −857405. | −0.764358 | −0.382179 | − | 0.924088i | \(-0.624826\pi\) | ||||
−0.382179 | + | 0.924088i | \(0.624826\pi\) | |||||||
\(264\) | −650120. | −0.574095 | ||||||||
\(265\) | −924972. | −0.809122 | ||||||||
\(266\) | 2.11737e6 | 1.83482 | ||||||||
\(267\) | 640831. | 0.550130 | ||||||||
\(268\) | 412727. | 0.351015 | ||||||||
\(269\) | 423229. | 0.356611 | 0.178305 | − | 0.983975i | \(-0.442938\pi\) | ||||
0.178305 | + | 0.983975i | \(0.442938\pi\) | |||||||
\(270\) | −584105. | −0.487620 | ||||||||
\(271\) | −2.21758e6 | −1.83424 | −0.917119 | − | 0.398613i | \(-0.869492\pi\) | ||||
−0.917119 | + | 0.398613i | \(0.869492\pi\) | |||||||
\(272\) | 112036. | 0.0918196 | ||||||||
\(273\) | 1.04843e6 | 0.851400 | ||||||||
\(274\) | 50060.8 | 0.0402830 | ||||||||
\(275\) | 238966. | 0.190548 | ||||||||
\(276\) | −224871. | −0.177689 | ||||||||
\(277\) | 770934. | 0.603695 | 0.301848 | − | 0.953356i | \(-0.402397\pi\) | ||||
0.301848 | + | 0.953356i | \(0.402397\pi\) | |||||||
\(278\) | −1.40362e6 | −1.08928 | ||||||||
\(279\) | −1.98281e6 | −1.52501 | ||||||||
\(280\) | −412711. | −0.314595 | ||||||||
\(281\) | −2.54824e6 | −1.92519 | −0.962597 | − | 0.270939i | \(-0.912666\pi\) | ||||
−0.962597 | + | 0.270939i | \(0.912666\pi\) | |||||||
\(282\) | 2.26766e6 | 1.69807 | ||||||||
\(283\) | 378353. | 0.280822 | 0.140411 | − | 0.990093i | \(-0.455158\pi\) | ||||
0.140411 | + | 0.990093i | \(0.455158\pi\) | |||||||
\(284\) | 434062. | 0.319342 | ||||||||
\(285\) | −1.36304e6 | −0.994022 | ||||||||
\(286\) | −233977. | −0.169144 | ||||||||
\(287\) | −4.32309e6 | −3.09806 | ||||||||
\(288\) | −473962. | −0.336715 | ||||||||
\(289\) | −1.22833e6 | −0.865107 | ||||||||
\(290\) | −236037. | −0.164811 | ||||||||
\(291\) | 2.74613e6 | 1.90103 | ||||||||
\(292\) | −793093. | −0.544336 | ||||||||
\(293\) | −1.31258e6 | −0.893215 | −0.446608 | − | 0.894730i | \(-0.647368\pi\) | ||||
−0.446608 | + | 0.894730i | \(0.647368\pi\) | |||||||
\(294\) | −5.28472e6 | −3.56577 | ||||||||
\(295\) | −741740. | −0.496245 | ||||||||
\(296\) | 781590. | 0.518501 | ||||||||
\(297\) | 2.23330e6 | 1.46912 | ||||||||
\(298\) | −25518.1 | −0.0166459 | ||||||||
\(299\) | −80930.5 | −0.0523521 | ||||||||
\(300\) | 265679. | 0.170433 | ||||||||
\(301\) | −1.26689e6 | −0.805980 | ||||||||
\(302\) | 2.06757e6 | 1.30449 | ||||||||
\(303\) | 1.19810e6 | 0.749697 | ||||||||
\(304\) | −525352. | −0.326037 | ||||||||
\(305\) | 740030. | 0.455512 | ||||||||
\(306\) | −810254. | −0.494672 | ||||||||
\(307\) | −2.74167e6 | −1.66023 | −0.830117 | − | 0.557589i | \(-0.811727\pi\) | ||||
−0.830117 | + | 0.557589i | \(0.811727\pi\) | |||||||
\(308\) | 1.57798e6 | 0.947820 | ||||||||
\(309\) | 2.38795e6 | 1.42275 | ||||||||
\(310\) | 428389. | 0.253183 | ||||||||
\(311\) | 457160. | 0.268020 | 0.134010 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134010 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(312\) | −260132. | −0.151289 | ||||||||
\(313\) | 2.30247e6 | 1.32841 | 0.664206 | − | 0.747549i | \(-0.268770\pi\) | ||||
0.664206 | + | 0.747549i | \(0.268770\pi\) | |||||||
\(314\) | −749052. | −0.428734 | ||||||||
\(315\) | 2.98477e6 | 1.69486 | ||||||||
\(316\) | 1.17779e6 | 0.663512 | ||||||||
\(317\) | 605094. | 0.338201 | 0.169100 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169100 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(318\) | 3.93193e6 | 2.18041 | ||||||||
\(319\) | 902478. | 0.496546 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | −3.37491e6 | −1.82810 | ||||||||
\(322\) | 545811. | 0.293361 | ||||||||
\(323\) | −898107. | −0.478985 | ||||||||
\(324\) | 683377. | 0.361658 | ||||||||
\(325\) | 95617.3 | 0.0502144 | ||||||||
\(326\) | −2.46697e6 | −1.28564 | ||||||||
\(327\) | −276467. | −0.142980 | ||||||||
\(328\) | 1.07263e6 | 0.550508 | ||||||||
\(329\) | −5.50411e6 | −2.80348 | ||||||||
\(330\) | −1.01581e6 | −0.513486 | ||||||||
\(331\) | 733658. | 0.368064 | 0.184032 | − | 0.982920i | \(-0.441085\pi\) | ||||
0.184032 | + | 0.982920i | \(0.441085\pi\) | |||||||
\(332\) | 873590. | 0.434973 | ||||||||
\(333\) | −5.65253e6 | −2.79339 | ||||||||
\(334\) | 1.04745e6 | 0.513769 | ||||||||
\(335\) | 644885. | 0.313957 | ||||||||
\(336\) | 1.75438e6 | 0.847765 | ||||||||
\(337\) | 1.62914e6 | 0.781417 | 0.390709 | − | 0.920514i | \(-0.372230\pi\) | ||||
0.390709 | + | 0.920514i | \(0.372230\pi\) | |||||||
\(338\) | 1.39155e6 | 0.662533 | ||||||||
\(339\) | 102815. | 0.0485912 | ||||||||
\(340\) | 175056. | 0.0821259 | ||||||||
\(341\) | −1.63793e6 | −0.762796 | ||||||||
\(342\) | 3.79939e6 | 1.75650 | ||||||||
\(343\) | 8.49190e6 | 3.89735 | ||||||||
\(344\) | 314336. | 0.143218 | ||||||||
\(345\) | −351361. | −0.158930 | ||||||||
\(346\) | 1.81015e6 | 0.812875 | ||||||||
\(347\) | 3.37477e6 | 1.50460 | 0.752300 | − | 0.658821i | \(-0.228945\pi\) | ||||
0.752300 | + | 0.658821i | \(0.228945\pi\) | |||||||
\(348\) | 1.00336e6 | 0.444129 | ||||||||
\(349\) | 537073. | 0.236031 | 0.118016 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118016 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(350\) | −644862. | −0.281382 | ||||||||
\(351\) | 893609. | 0.387151 | ||||||||
\(352\) | −391522. | −0.168422 | ||||||||
\(353\) | 1.16518e6 | 0.497685 | 0.248842 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248842 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(354\) | 3.15303e6 | 1.33727 | ||||||||
\(355\) | 678222. | 0.285628 | ||||||||
\(356\) | 385928. | 0.161392 | ||||||||
\(357\) | 2.99917e6 | 1.24546 | ||||||||
\(358\) | −1.56725e6 | −0.646294 | ||||||||
\(359\) | 2.18962e6 | 0.896668 | 0.448334 | − | 0.893866i | \(-0.352017\pi\) | ||||
0.448334 | + | 0.893866i | \(0.352017\pi\) | |||||||
\(360\) | −740566. | −0.301167 | ||||||||
\(361\) | 1.73525e6 | 0.700800 | ||||||||
\(362\) | 2.83926e6 | 1.13876 | ||||||||
\(363\) | −394871. | −0.157286 | ||||||||
\(364\) | 631398. | 0.249775 | ||||||||
\(365\) | −1.23921e6 | −0.486869 | ||||||||
\(366\) | −3.14577e6 | −1.22751 | ||||||||
\(367\) | 4.62473e6 | 1.79234 | 0.896172 | − | 0.443707i | \(-0.146337\pi\) | ||||
0.896172 | + | 0.443707i | \(0.146337\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | −7.75732e6 | −2.96583 | ||||||||
\(370\) | 1.22123e6 | 0.463762 | ||||||||
\(371\) | −9.54366e6 | −3.59981 | ||||||||
\(372\) | −1.82102e6 | −0.682273 | ||||||||
\(373\) | 4.31479e6 | 1.60579 | 0.802893 | − | 0.596123i | \(-0.203293\pi\) | ||||
0.802893 | + | 0.596123i | \(0.203293\pi\) | |||||||
\(374\) | −669320. | −0.247431 | ||||||||
\(375\) | 415124. | 0.152440 | ||||||||
\(376\) | 1.36565e6 | 0.498162 | ||||||||
\(377\) | 361108. | 0.130853 | ||||||||
\(378\) | −6.02667e6 | −2.16944 | ||||||||
\(379\) | −2.49537e6 | −0.892352 | −0.446176 | − | 0.894945i | \(-0.647214\pi\) | ||||
−0.446176 | + | 0.894945i | \(0.647214\pi\) | |||||||
\(380\) | −820863. | −0.291616 | ||||||||
\(381\) | 2.60416e6 | 0.919084 | ||||||||
\(382\) | −632444. | −0.221750 | ||||||||
\(383\) | −1.49289e6 | −0.520034 | −0.260017 | − | 0.965604i | \(-0.583728\pi\) | ||||
−0.260017 | + | 0.965604i | \(0.583728\pi\) | |||||||
\(384\) | −435289. | −0.150643 | ||||||||
\(385\) | 2.46560e6 | 0.847756 | ||||||||
\(386\) | −1.30697e6 | −0.446476 | ||||||||
\(387\) | −2.27330e6 | −0.771578 | ||||||||
\(388\) | 1.65380e6 | 0.557705 | ||||||||
\(389\) | 5.36234e6 | 1.79672 | 0.898360 | − | 0.439260i | \(-0.144759\pi\) | ||||
0.898360 | + | 0.439260i | \(0.144759\pi\) | |||||||
\(390\) | −406456. | −0.135317 | ||||||||
\(391\) | −231512. | −0.0765828 | ||||||||
\(392\) | −3.18262e6 | −1.04609 | ||||||||
\(393\) | −3.14524e6 | −1.02724 | ||||||||
\(394\) | −379847. | −0.123273 | ||||||||
\(395\) | 1.84029e6 | 0.593463 | ||||||||
\(396\) | 2.83152e6 | 0.907365 | ||||||||
\(397\) | −1.83492e6 | −0.584307 | −0.292153 | − | 0.956371i | \(-0.594372\pi\) | ||||
−0.292153 | + | 0.956371i | \(0.594372\pi\) | |||||||
\(398\) | 638923. | 0.202181 | ||||||||
\(399\) | −1.40635e7 | −4.42244 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 877209. | 0.272422 | 0.136211 | − | 0.990680i | \(-0.456508\pi\) | ||||
0.136211 | + | 0.990680i | \(0.456508\pi\) | |||||||
\(402\) | −2.74132e6 | −0.846047 | ||||||||
\(403\) | −655383. | −0.201017 | ||||||||
\(404\) | 721531. | 0.219939 | ||||||||
\(405\) | 1.06778e6 | 0.323477 | ||||||||
\(406\) | −2.43538e6 | −0.733249 | ||||||||
\(407\) | −4.66934e6 | −1.39723 | ||||||||
\(408\) | −744140. | −0.221312 | ||||||||
\(409\) | 2.45886e6 | 0.726819 | 0.363409 | − | 0.931630i | \(-0.381613\pi\) | ||||
0.363409 | + | 0.931630i | \(0.381613\pi\) | |||||||
\(410\) | 1.67598e6 | 0.492389 | ||||||||
\(411\) | −332503. | −0.0970937 | ||||||||
\(412\) | 1.43809e6 | 0.417392 | ||||||||
\(413\) | −7.65311e6 | −2.20782 | ||||||||
\(414\) | 979398. | 0.280840 | ||||||||
\(415\) | 1.36498e6 | 0.389052 | ||||||||
\(416\) | −156659. | −0.0443837 | ||||||||
\(417\) | 9.32282e6 | 2.62547 | ||||||||
\(418\) | 3.13853e6 | 0.878590 | ||||||||
\(419\) | −5.08361e6 | −1.41461 | −0.707305 | − | 0.706908i | \(-0.750089\pi\) | ||||
−0.707305 | + | 0.706908i | \(0.750089\pi\) | |||||||
\(420\) | 2.74122e6 | 0.758264 | ||||||||
\(421\) | 1.91427e6 | 0.526378 | 0.263189 | − | 0.964744i | \(-0.415226\pi\) | ||||
0.263189 | + | 0.964744i | \(0.415226\pi\) | |||||||
\(422\) | −4.13306e6 | −1.12977 | ||||||||
\(423\) | −9.87653e6 | −2.68382 | ||||||||
\(424\) | 2.36793e6 | 0.639667 | ||||||||
\(425\) | 273525. | 0.0734556 | ||||||||
\(426\) | −2.88303e6 | −0.769707 | ||||||||
\(427\) | 7.63547e6 | 2.02659 | ||||||||
\(428\) | −2.03247e6 | −0.536309 | ||||||||
\(429\) | 1.55407e6 | 0.407687 | ||||||||
\(430\) | 491150. | 0.128098 | ||||||||
\(431\) | −1.01147e6 | −0.262278 | −0.131139 | − | 0.991364i | \(-0.541863\pi\) | ||||
−0.131139 | + | 0.991364i | \(0.541863\pi\) | |||||||
\(432\) | 1.49531e6 | 0.385498 | ||||||||
\(433\) | 1.13027e6 | 0.289709 | 0.144855 | − | 0.989453i | \(-0.453729\pi\) | ||||
0.144855 | + | 0.989453i | \(0.453729\pi\) | |||||||
\(434\) | 4.42002e6 | 1.12642 | ||||||||
\(435\) | 1.56775e6 | 0.397241 | ||||||||
\(436\) | −166497. | −0.0419459 | ||||||||
\(437\) | 1.08559e6 | 0.271933 | ||||||||
\(438\) | 5.26771e6 | 1.31201 | ||||||||
\(439\) | −3.62722e6 | −0.898282 | −0.449141 | − | 0.893461i | \(-0.648270\pi\) | ||||
−0.449141 | + | 0.893461i | \(0.648270\pi\) | |||||||
\(440\) | −611753. | −0.150641 | ||||||||
\(441\) | 2.30170e7 | 5.63575 | ||||||||
\(442\) | −267815. | −0.0652046 | ||||||||
\(443\) | 2.60561e6 | 0.630812 | 0.315406 | − | 0.948957i | \(-0.397859\pi\) | ||||
0.315406 | + | 0.948957i | \(0.397859\pi\) | |||||||
\(444\) | −5.19130e6 | −1.24974 | ||||||||
\(445\) | 603013. | 0.144353 | ||||||||
\(446\) | −2.26598e6 | −0.539409 | ||||||||
\(447\) | 169491. | 0.0401215 | ||||||||
\(448\) | 1.05654e6 | 0.248709 | ||||||||
\(449\) | −636675. | −0.149040 | −0.0745198 | − | 0.997220i | \(-0.523742\pi\) | ||||
−0.0745198 | + | 0.997220i | \(0.523742\pi\) | |||||||
\(450\) | −1.15713e6 | −0.269372 | ||||||||
\(451\) | −6.40803e6 | −1.48348 | ||||||||
\(452\) | 61918.3 | 0.0142552 | ||||||||
\(453\) | −1.37327e7 | −3.14421 | ||||||||
\(454\) | −4.02210e6 | −0.915826 | ||||||||
\(455\) | 986559. | 0.223406 | ||||||||
\(456\) | 3.48938e6 | 0.785843 | ||||||||
\(457\) | −2.44658e6 | −0.547986 | −0.273993 | − | 0.961732i | \(-0.588345\pi\) | ||||
−0.273993 | + | 0.961732i | \(0.588345\pi\) | |||||||
\(458\) | −4.00224e6 | −0.891538 | ||||||||
\(459\) | 2.55628e6 | 0.566339 | ||||||||
\(460\) | −211600. | −0.0466252 | ||||||||
\(461\) | 8.31672e6 | 1.82263 | 0.911317 | − | 0.411705i | \(-0.135066\pi\) | ||||
0.911317 | + | 0.411705i | \(0.135066\pi\) | |||||||
\(462\) | −1.04809e7 | −2.28452 | ||||||||
\(463\) | 3.27620e6 | 0.710260 | 0.355130 | − | 0.934817i | \(-0.384437\pi\) | ||||
0.355130 | + | 0.934817i | \(0.384437\pi\) | |||||||
\(464\) | 604255. | 0.130294 | ||||||||
\(465\) | −2.84535e6 | −0.610244 | ||||||||
\(466\) | 4.11381e6 | 0.877564 | ||||||||
\(467\) | −8.51659e6 | −1.80706 | −0.903532 | − | 0.428521i | \(-0.859035\pi\) | ||||
−0.903532 | + | 0.428521i | \(0.859035\pi\) | |||||||
\(468\) | 1.13297e6 | 0.239114 | ||||||||
\(469\) | 6.65379e6 | 1.39681 | ||||||||
\(470\) | 2.13383e6 | 0.445570 | ||||||||
\(471\) | 4.97519e6 | 1.03337 | ||||||||
\(472\) | 1.89885e6 | 0.392316 | ||||||||
\(473\) | −1.87789e6 | −0.385938 | ||||||||
\(474\) | −7.82283e6 | −1.59926 | ||||||||
\(475\) | −1.28260e6 | −0.260829 | ||||||||
\(476\) | 1.80619e6 | 0.365381 | ||||||||
\(477\) | −1.71251e7 | −3.44617 | ||||||||
\(478\) | −2.80439e6 | −0.561396 | ||||||||
\(479\) | 1.70961e6 | 0.340454 | 0.170227 | − | 0.985405i | \(-0.445550\pi\) | ||||
0.170227 | + | 0.985405i | \(0.445550\pi\) | |||||||
\(480\) | −680138. | −0.134739 | ||||||||
\(481\) | −1.86834e6 | −0.368208 | ||||||||
\(482\) | 2.01685e6 | 0.395417 | ||||||||
\(483\) | −3.62526e6 | −0.707085 | ||||||||
\(484\) | −237803. | −0.0461429 | ||||||||
\(485\) | 2.58407e6 | 0.498827 | ||||||||
\(486\) | 1.13853e6 | 0.218652 | ||||||||
\(487\) | 7.87548e6 | 1.50472 | 0.752358 | − | 0.658754i | \(-0.228916\pi\) | ||||
0.752358 | + | 0.658754i | \(0.228916\pi\) | |||||||
\(488\) | −1.89448e6 | −0.360114 | ||||||||
\(489\) | 1.63856e7 | 3.09877 | ||||||||
\(490\) | −4.97284e6 | −0.935652 | ||||||||
\(491\) | 99613.8 | 0.0186473 | 0.00932365 | − | 0.999957i | \(-0.497032\pi\) | ||||
0.00932365 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(492\) | −7.12435e6 | −1.32688 | ||||||||
\(493\) | 1.03299e6 | 0.191417 | ||||||||
\(494\) | 1.25582e6 | 0.231531 | ||||||||
\(495\) | 4.42425e6 | 0.811572 | ||||||||
\(496\) | −1.09668e6 | −0.200159 | ||||||||
\(497\) | 6.99775e6 | 1.27077 | ||||||||
\(498\) | −5.80236e6 | −1.04841 | ||||||||
\(499\) | −4.03670e6 | −0.725730 | −0.362865 | − | 0.931842i | \(-0.618201\pi\) | ||||
−0.362865 | + | 0.931842i | \(0.618201\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | −6.95715e6 | −1.23833 | ||||||||
\(502\) | 4.94797e6 | 0.876331 | ||||||||
\(503\) | −5.09894e6 | −0.898586 | −0.449293 | − | 0.893385i | \(-0.648324\pi\) | ||||
−0.449293 | + | 0.893385i | \(0.648324\pi\) | |||||||
\(504\) | −7.64100e6 | −1.33990 | ||||||||
\(505\) | 1.12739e6 | 0.196719 | ||||||||
\(506\) | 809044. | 0.140474 | ||||||||
\(507\) | −9.24265e6 | −1.59690 | ||||||||
\(508\) | 1.56830e6 | 0.269632 | ||||||||
\(509\) | 3.39724e6 | 0.581208 | 0.290604 | − | 0.956843i | \(-0.406144\pi\) | ||||
0.290604 | + | 0.956843i | \(0.406144\pi\) | |||||||
\(510\) | −1.16272e6 | −0.197947 | ||||||||
\(511\) | −1.27859e7 | −2.16610 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −1.19868e7 | −2.01098 | ||||||||
\(514\) | −767860. | −0.128196 | ||||||||
\(515\) | 2.24702e6 | 0.373327 | ||||||||
\(516\) | −2.08781e6 | −0.345197 | ||||||||
\(517\) | −8.15862e6 | −1.34243 | ||||||||
\(518\) | 1.26004e7 | 2.06329 | ||||||||
\(519\) | −1.20230e7 | −1.95926 | ||||||||
\(520\) | −244780. | −0.0396980 | ||||||||
\(521\) | −6.06716e6 | −0.979245 | −0.489622 | − | 0.871935i | \(-0.662865\pi\) | ||||
−0.489622 | + | 0.871935i | \(0.662865\pi\) | |||||||
\(522\) | −4.37002e6 | −0.701952 | ||||||||
\(523\) | −2.33142e6 | −0.372706 | −0.186353 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186353 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(524\) | −1.89416e6 | −0.301361 | ||||||||
\(525\) | 4.28316e6 | 0.678212 | ||||||||
\(526\) | 3.42962e6 | 0.540483 | ||||||||
\(527\) | −1.87480e6 | −0.294055 | ||||||||
\(528\) | 2.60048e6 | 0.405946 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 3.69989e6 | 0.572135 | ||||||||
\(531\) | −1.37327e7 | −2.11358 | ||||||||
\(532\) | −8.46949e6 | −1.29741 | ||||||||
\(533\) | −2.56404e6 | −0.390937 | ||||||||
\(534\) | −2.56332e6 | −0.389001 | ||||||||
\(535\) | −3.17574e6 | −0.479689 | ||||||||
\(536\) | −1.65091e6 | −0.248205 | ||||||||
\(537\) | 1.04096e7 | 1.55776 | ||||||||
\(538\) | −1.69292e6 | −0.252162 | ||||||||
\(539\) | 1.90135e7 | 2.81896 | ||||||||
\(540\) | 2.33642e6 | 0.344799 | ||||||||
\(541\) | 206989. | 0.0304056 | 0.0152028 | − | 0.999884i | \(-0.495161\pi\) | ||||
0.0152028 | + | 0.999884i | \(0.495161\pi\) | |||||||
\(542\) | 8.87032e6 | 1.29700 | ||||||||
\(543\) | −1.88583e7 | −2.74475 | ||||||||
\(544\) | −448144. | −0.0649262 | ||||||||
\(545\) | −260151. | −0.0375176 | ||||||||
\(546\) | −4.19373e6 | −0.602031 | ||||||||
\(547\) | 9.25725e6 | 1.32286 | 0.661430 | − | 0.750007i | \(-0.269950\pi\) | ||||
0.661430 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(548\) | −200243. | −0.0284844 | ||||||||
\(549\) | 1.37010e7 | 1.94009 | ||||||||
\(550\) | −955864. | −0.134738 | ||||||||
\(551\) | −4.84385e6 | −0.679691 | ||||||||
\(552\) | 899483. | 0.125645 | ||||||||
\(553\) | 1.89877e7 | 2.64034 | ||||||||
\(554\) | −3.08374e6 | −0.426877 | ||||||||
\(555\) | −8.11141e6 | −1.11780 | ||||||||
\(556\) | 5.61449e6 | 0.770235 | ||||||||
\(557\) | 9.55108e6 | 1.30441 | 0.652206 | − | 0.758042i | \(-0.273844\pi\) | ||||
0.652206 | + | 0.758042i | \(0.273844\pi\) | |||||||
\(558\) | 7.93126e6 | 1.07834 | ||||||||
\(559\) | −751399. | −0.101705 | ||||||||
\(560\) | 1.65085e6 | 0.222452 | ||||||||
\(561\) | 4.44561e6 | 0.596381 | ||||||||
\(562\) | 1.01930e7 | 1.36132 | ||||||||
\(563\) | −1.21668e7 | −1.61772 | −0.808862 | − | 0.587999i | \(-0.799916\pi\) | ||||
−0.808862 | + | 0.587999i | \(0.799916\pi\) | |||||||
\(564\) | −9.07064e6 | −1.20072 | ||||||||
\(565\) | 96747.4 | 0.0127502 | ||||||||
\(566\) | −1.51341e6 | −0.198571 | ||||||||
\(567\) | 1.10171e7 | 1.43916 | ||||||||
\(568\) | −1.73625e6 | −0.225809 | ||||||||
\(569\) | 3.88469e6 | 0.503009 | 0.251505 | − | 0.967856i | \(-0.419075\pi\) | ||||
0.251505 | + | 0.967856i | \(0.419075\pi\) | |||||||
\(570\) | 5.45215e6 | 0.702879 | ||||||||
\(571\) | 148768. | 0.0190950 | 0.00954748 | − | 0.999954i | \(-0.496961\pi\) | ||||
0.00954748 | + | 0.999954i | \(0.496961\pi\) | |||||||
\(572\) | 935907. | 0.119603 | ||||||||
\(573\) | 4.20068e6 | 0.534482 | ||||||||
\(574\) | 1.72924e7 | 2.19066 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | 1.89585e6 | 0.238093 | ||||||||
\(577\) | 7.60448e6 | 0.950890 | 0.475445 | − | 0.879746i | \(-0.342287\pi\) | ||||
0.475445 | + | 0.879746i | \(0.342287\pi\) | |||||||
\(578\) | 4.91331e6 | 0.611723 | ||||||||
\(579\) | 8.68089e6 | 1.07614 | ||||||||
\(580\) | 944148. | 0.116539 | ||||||||
\(581\) | 1.40836e7 | 1.73091 | ||||||||
\(582\) | −1.09845e7 | −1.34423 | ||||||||
\(583\) | −1.41464e7 | −1.72375 | ||||||||
\(584\) | 3.17237e6 | 0.384904 | ||||||||
\(585\) | 1.77027e6 | 0.213870 | ||||||||
\(586\) | 5.25031e6 | 0.631599 | ||||||||
\(587\) | 1.43808e7 | 1.72262 | 0.861309 | − | 0.508082i | \(-0.169645\pi\) | ||||
0.861309 | + | 0.508082i | \(0.169645\pi\) | |||||||
\(588\) | 2.11389e7 | 2.52138 | ||||||||
\(589\) | 8.79121e6 | 1.04414 | ||||||||
\(590\) | 2.96696e6 | 0.350898 | ||||||||
\(591\) | 2.52294e6 | 0.297124 | ||||||||
\(592\) | −3.12636e6 | −0.366636 | ||||||||
\(593\) | −1.16050e7 | −1.35522 | −0.677610 | − | 0.735421i | \(-0.736984\pi\) | ||||
−0.677610 | + | 0.735421i | \(0.736984\pi\) | |||||||
\(594\) | −8.93320e6 | −1.03882 | ||||||||
\(595\) | 2.82217e6 | 0.326807 | ||||||||
\(596\) | 102072. | 0.0117704 | ||||||||
\(597\) | −4.24371e6 | −0.487316 | ||||||||
\(598\) | 323722. | 0.0370185 | ||||||||
\(599\) | 1.04099e7 | 1.18544 | 0.592720 | − | 0.805409i | \(-0.298054\pi\) | ||||
0.592720 | + | 0.805409i | \(0.298054\pi\) | |||||||
\(600\) | −1.06272e6 | −0.120514 | ||||||||
\(601\) | 7.62102e6 | 0.860651 | 0.430326 | − | 0.902674i | \(-0.358399\pi\) | ||||
0.430326 | + | 0.902674i | \(0.358399\pi\) | |||||||
\(602\) | 5.06758e6 | 0.569914 | ||||||||
\(603\) | 1.19395e7 | 1.33719 | ||||||||
\(604\) | −8.27026e6 | −0.922416 | ||||||||
\(605\) | −371568. | −0.0412715 | ||||||||
\(606\) | −4.79239e6 | −0.530116 | ||||||||
\(607\) | 36429.8 | 0.00401314 | 0.00200657 | − | 0.999998i | \(-0.499361\pi\) | ||||
0.00200657 | + | 0.999998i | \(0.499361\pi\) | |||||||
\(608\) | 2.10141e6 | 0.230543 | ||||||||
\(609\) | 1.61757e7 | 1.76734 | ||||||||
\(610\) | −2.96012e6 | −0.322096 | ||||||||
\(611\) | −3.26450e6 | −0.353764 | ||||||||
\(612\) | 3.24102e6 | 0.349786 | ||||||||
\(613\) | −5.16547e6 | −0.555212 | −0.277606 | − | 0.960695i | \(-0.589541\pi\) | ||||
−0.277606 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(614\) | 1.09667e7 | 1.17396 | ||||||||
\(615\) | −1.11318e7 | −1.18680 | ||||||||
\(616\) | −6.31194e6 | −0.670210 | ||||||||
\(617\) | −1.64300e7 | −1.73750 | −0.868752 | − | 0.495248i | \(-0.835077\pi\) | ||||
−0.868752 | + | 0.495248i | \(0.835077\pi\) | |||||||
\(618\) | −9.55178e6 | −1.00604 | ||||||||
\(619\) | −1.33143e7 | −1.39666 | −0.698329 | − | 0.715777i | \(-0.746073\pi\) | ||||
−0.698329 | + | 0.715777i | \(0.746073\pi\) | |||||||
\(620\) | −1.71356e6 | −0.179027 | ||||||||
\(621\) | −3.08992e6 | −0.321527 | ||||||||
\(622\) | −1.82864e6 | −0.189519 | ||||||||
\(623\) | 6.22175e6 | 0.642233 | ||||||||
\(624\) | 1.04053e6 | 0.106978 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −9.20988e6 | −0.939330 | ||||||||
\(627\) | −2.08461e7 | −2.11766 | ||||||||
\(628\) | 2.99621e6 | 0.303161 | ||||||||
\(629\) | −5.34462e6 | −0.538629 | ||||||||
\(630\) | −1.19391e7 | −1.19845 | ||||||||
\(631\) | 911454. | 0.0911300 | 0.0455650 | − | 0.998961i | \(-0.485491\pi\) | ||||
0.0455650 | + | 0.998961i | \(0.485491\pi\) | |||||||
\(632\) | −4.71114e6 | −0.469174 | ||||||||
\(633\) | 2.74517e7 | 2.72307 | ||||||||
\(634\) | −2.42037e6 | −0.239144 | ||||||||
\(635\) | 2.45047e6 | 0.241166 | ||||||||
\(636\) | −1.57277e7 | −1.54178 | ||||||||
\(637\) | 7.60784e6 | 0.742870 | ||||||||
\(638\) | −3.60991e6 | −0.351111 | ||||||||
\(639\) | 1.25567e7 | 1.21653 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 1.88172e6 | 0.180888 | 0.0904438 | − | 0.995902i | \(-0.471171\pi\) | ||||
0.0904438 | + | 0.995902i | \(0.471171\pi\) | |||||||
\(642\) | 1.34996e7 | 1.29266 | ||||||||
\(643\) | −1.48647e7 | −1.41784 | −0.708922 | − | 0.705287i | \(-0.750818\pi\) | ||||
−0.708922 | + | 0.705287i | \(0.750818\pi\) | |||||||
\(644\) | −2.18324e6 | −0.207438 | ||||||||
\(645\) | −3.26220e6 | −0.308753 | ||||||||
\(646\) | 3.59243e6 | 0.338693 | ||||||||
\(647\) | −34099.0 | −0.00320244 | −0.00160122 | − | 0.999999i | \(-0.500510\pi\) | ||||
−0.00160122 | + | 0.999999i | \(0.500510\pi\) | |||||||
\(648\) | −2.73351e6 | −0.255731 | ||||||||
\(649\) | −1.13440e7 | −1.05720 | ||||||||
\(650\) | −382469. | −0.0355069 | ||||||||
\(651\) | −2.93577e7 | −2.71500 | ||||||||
\(652\) | 9.86788e6 | 0.909086 | ||||||||
\(653\) | 5.21815e6 | 0.478888 | 0.239444 | − | 0.970910i | \(-0.423035\pi\) | ||||
0.239444 | + | 0.970910i | \(0.423035\pi\) | |||||||
\(654\) | 1.10587e6 | 0.101102 | ||||||||
\(655\) | −2.95962e6 | −0.269546 | ||||||||
\(656\) | −4.29050e6 | −0.389268 | ||||||||
\(657\) | −2.29429e7 | −2.07365 | ||||||||
\(658\) | 2.20164e7 | 1.98236 | ||||||||
\(659\) | −3.56361e6 | −0.319651 | −0.159826 | − | 0.987145i | \(-0.551093\pi\) | ||||
−0.159826 | + | 0.987145i | \(0.551093\pi\) | |||||||
\(660\) | 4.06325e6 | 0.363090 | ||||||||
\(661\) | 7.48892e6 | 0.666677 | 0.333339 | − | 0.942807i | \(-0.391825\pi\) | ||||
0.333339 | + | 0.942807i | \(0.391825\pi\) | |||||||
\(662\) | −2.93463e6 | −0.260261 | ||||||||
\(663\) | 1.77882e6 | 0.157162 | ||||||||
\(664\) | −3.49436e6 | −0.307572 | ||||||||
\(665\) | −1.32336e7 | −1.16044 | ||||||||
\(666\) | 2.26101e7 | 1.97523 | ||||||||
\(667\) | −1.24864e6 | −0.108673 | ||||||||
\(668\) | −4.18981e6 | −0.363290 | ||||||||
\(669\) | 1.50506e7 | 1.30013 | ||||||||
\(670\) | −2.57954e6 | −0.222001 | ||||||||
\(671\) | 1.13179e7 | 0.970419 | ||||||||
\(672\) | −7.01752e6 | −0.599460 | ||||||||
\(673\) | −4.25849e6 | −0.362424 | −0.181212 | − | 0.983444i | \(-0.558002\pi\) | ||||
−0.181212 | + | 0.983444i | \(0.558002\pi\) | |||||||
\(674\) | −6.51655e6 | −0.552545 | ||||||||
\(675\) | 3.65066e6 | 0.308398 | ||||||||
\(676\) | −5.56620e6 | −0.468481 | ||||||||
\(677\) | −9.44304e6 | −0.791845 | −0.395923 | − | 0.918284i | \(-0.629575\pi\) | ||||
−0.395923 | + | 0.918284i | \(0.629575\pi\) | |||||||
\(678\) | −411260. | −0.0343591 | ||||||||
\(679\) | 2.66619e7 | 2.21930 | ||||||||
\(680\) | −700225. | −0.0580718 | ||||||||
\(681\) | 2.67147e7 | 2.20741 | ||||||||
\(682\) | 6.55171e6 | 0.539378 | ||||||||
\(683\) | 881961. | 0.0723431 | 0.0361716 | − | 0.999346i | \(-0.488484\pi\) | ||||
0.0361716 | + | 0.999346i | \(0.488484\pi\) | |||||||
\(684\) | −1.51976e7 | −1.24204 | ||||||||
\(685\) | −312880. | −0.0254772 | ||||||||
\(686\) | −3.39676e7 | −2.75584 | ||||||||
\(687\) | 2.65828e7 | 2.14886 | ||||||||
\(688\) | −1.25734e6 | −0.101270 | ||||||||
\(689\) | −5.66037e6 | −0.454252 | ||||||||
\(690\) | 1.40544e6 | 0.112380 | ||||||||
\(691\) | 5.02713e6 | 0.400521 | 0.200260 | − | 0.979743i | \(-0.435821\pi\) | ||||
0.200260 | + | 0.979743i | \(0.435821\pi\) | |||||||
\(692\) | −7.24059e6 | −0.574790 | ||||||||
\(693\) | 4.56485e7 | 3.61072 | ||||||||
\(694\) | −1.34991e7 | −1.06391 | ||||||||
\(695\) | 8.77264e6 | 0.688919 | ||||||||
\(696\) | −4.01345e6 | −0.314047 | ||||||||
\(697\) | −7.33476e6 | −0.571878 | ||||||||
\(698\) | −2.14829e6 | −0.166899 | ||||||||
\(699\) | −2.73238e7 | −2.11518 | ||||||||
\(700\) | 2.57945e6 | 0.198967 | ||||||||
\(701\) | −2.19117e7 | −1.68415 | −0.842076 | − | 0.539359i | \(-0.818667\pi\) | ||||
−0.842076 | + | 0.539359i | \(0.818667\pi\) | |||||||
\(702\) | −3.57444e6 | −0.273757 | ||||||||
\(703\) | 2.50617e7 | 1.91259 | ||||||||
\(704\) | 1.56609e6 | 0.119093 | ||||||||
\(705\) | −1.41729e7 | −1.07395 | ||||||||
\(706\) | −4.66070e6 | −0.351916 | ||||||||
\(707\) | 1.16322e7 | 0.875211 | ||||||||
\(708\) | −1.26121e7 | −0.945596 | ||||||||
\(709\) | 1.18099e7 | 0.882330 | 0.441165 | − | 0.897426i | \(-0.354565\pi\) | ||||
0.441165 | + | 0.897426i | \(0.354565\pi\) | |||||||
\(710\) | −2.71289e6 | −0.201970 | ||||||||
\(711\) | 3.40714e7 | 2.52765 | ||||||||
\(712\) | −1.54371e6 | −0.114121 | ||||||||
\(713\) | 2.26618e6 | 0.166944 | ||||||||
\(714\) | −1.19967e7 | −0.880675 | ||||||||
\(715\) | 1.46236e6 | 0.106976 | ||||||||
\(716\) | 6.26899e6 | 0.456999 | ||||||||
\(717\) | 1.86267e7 | 1.35313 | ||||||||
\(718\) | −8.75846e6 | −0.634040 | ||||||||
\(719\) | 1.49758e7 | 1.08036 | 0.540180 | − | 0.841550i | \(-0.318356\pi\) | ||||
0.540180 | + | 0.841550i | \(0.318356\pi\) | |||||||
\(720\) | 2.96226e6 | 0.212957 | ||||||||
\(721\) | 2.31843e7 | 1.66095 | ||||||||
\(722\) | −6.94100e6 | −0.495540 | ||||||||
\(723\) | −1.33958e7 | −0.953069 | ||||||||
\(724\) | −1.13570e7 | −0.805228 | ||||||||
\(725\) | 1.47523e6 | 0.104235 | ||||||||
\(726\) | 1.57949e6 | 0.111218 | ||||||||
\(727\) | 1.01581e7 | 0.712812 | 0.356406 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356406 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(728\) | −2.52559e6 | −0.176618 | ||||||||
\(729\) | −1.79409e7 | −1.25033 | ||||||||
\(730\) | 4.95683e6 | 0.344268 | ||||||||
\(731\) | −2.14947e6 | −0.148778 | ||||||||
\(732\) | 1.25831e7 | 0.867978 | ||||||||
\(733\) | −1.96629e7 | −1.35172 | −0.675861 | − | 0.737029i | \(-0.736228\pi\) | ||||
−0.675861 | + | 0.737029i | \(0.736228\pi\) | |||||||
\(734\) | −1.84989e7 | −1.26738 | ||||||||
\(735\) | 3.30295e7 | 2.25519 | ||||||||
\(736\) | 541696. | 0.0368605 | ||||||||
\(737\) | 9.86277e6 | 0.668852 | ||||||||
\(738\) | 3.10293e7 | 2.09716 | ||||||||
\(739\) | −8.71300e6 | −0.586890 | −0.293445 | − | 0.955976i | \(-0.594802\pi\) | ||||
−0.293445 | + | 0.955976i | \(0.594802\pi\) | |||||||
\(740\) | −4.88494e6 | −0.327929 | ||||||||
\(741\) | −8.34112e6 | −0.558058 | ||||||||
\(742\) | 3.81746e7 | 2.54545 | ||||||||
\(743\) | 1.28335e7 | 0.852854 | 0.426427 | − | 0.904522i | \(-0.359772\pi\) | ||||
0.426427 | + | 0.904522i | \(0.359772\pi\) | |||||||
\(744\) | 7.28409e6 | 0.482440 | ||||||||
\(745\) | 159488. | 0.0105278 | ||||||||
\(746\) | −1.72592e7 | −1.13546 | ||||||||
\(747\) | 2.52715e7 | 1.65703 | ||||||||
\(748\) | 2.67728e6 | 0.174960 | ||||||||
\(749\) | −3.27666e7 | −2.13416 | ||||||||
\(750\) | −1.66049e6 | −0.107791 | ||||||||
\(751\) | 5.80666e6 | 0.375687 | 0.187844 | − | 0.982199i | \(-0.439850\pi\) | ||||
0.187844 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(752\) | −5.46262e6 | −0.352254 | ||||||||
\(753\) | −3.28643e7 | −2.11221 | ||||||||
\(754\) | −1.44443e6 | −0.0925270 | ||||||||
\(755\) | −1.29223e7 | −0.825034 | ||||||||
\(756\) | 2.41067e7 | 1.53403 | ||||||||
\(757\) | −2.36785e7 | −1.50181 | −0.750905 | − | 0.660410i | \(-0.770383\pi\) | ||||
−0.750905 | + | 0.660410i | \(0.770383\pi\) | |||||||
\(758\) | 9.98146e6 | 0.630988 | ||||||||
\(759\) | −5.37365e6 | −0.338583 | ||||||||
\(760\) | 3.28345e6 | 0.206204 | ||||||||
\(761\) | −1.08104e7 | −0.676672 | −0.338336 | − | 0.941025i | \(-0.609864\pi\) | ||||
−0.338336 | + | 0.941025i | \(0.609864\pi\) | |||||||
\(762\) | −1.04166e7 | −0.649890 | ||||||||
\(763\) | −2.68419e6 | −0.166917 | ||||||||
\(764\) | 2.52978e6 | 0.156801 | ||||||||
\(765\) | 5.06409e6 | 0.312858 | ||||||||
\(766\) | 5.97157e6 | 0.367720 | ||||||||
\(767\) | −4.53908e6 | −0.278599 | ||||||||
\(768\) | 1.74115e6 | 0.106521 | ||||||||
\(769\) | 2.04035e7 | 1.24420 | 0.622098 | − | 0.782939i | \(-0.286280\pi\) | ||||
0.622098 | + | 0.782939i | \(0.286280\pi\) | |||||||
\(770\) | −9.86240e6 | −0.599454 | ||||||||
\(771\) | 5.10011e6 | 0.308989 | ||||||||
\(772\) | 5.22789e6 | 0.315707 | ||||||||
\(773\) | 1.26279e7 | 0.760119 | 0.380059 | − | 0.924962i | \(-0.375904\pi\) | ||||
0.380059 | + | 0.924962i | \(0.375904\pi\) | |||||||
\(774\) | 9.09322e6 | 0.545588 | ||||||||
\(775\) | −2.67743e6 | −0.160127 | ||||||||
\(776\) | −6.61522e6 | −0.394357 | ||||||||
\(777\) | −8.36918e7 | −4.97314 | ||||||||
\(778\) | −2.14494e7 | −1.27047 | ||||||||
\(779\) | 3.43937e7 | 2.03065 | ||||||||
\(780\) | 1.62583e6 | 0.0956836 | ||||||||
\(781\) | 1.03726e7 | 0.608500 | ||||||||
\(782\) | 926047. | 0.0541522 | ||||||||
\(783\) | 1.37870e7 | 0.803650 | ||||||||
\(784\) | 1.27305e7 | 0.739698 | ||||||||
\(785\) | 4.68158e6 | 0.271155 | ||||||||
\(786\) | 1.25809e7 | 0.726368 | ||||||||
\(787\) | −1.15243e7 | −0.663252 | −0.331626 | − | 0.943411i | \(-0.607597\pi\) | ||||
−0.331626 | + | 0.943411i | \(0.607597\pi\) | |||||||
\(788\) | 1.51939e6 | 0.0871673 | ||||||||
\(789\) | −2.27795e7 | −1.30272 | ||||||||
\(790\) | −7.36116e6 | −0.419642 | ||||||||
\(791\) | 998219. | 0.0567263 | ||||||||
\(792\) | −1.13261e7 | −0.641604 | ||||||||
\(793\) | 4.52862e6 | 0.255731 | ||||||||
\(794\) | 7.33968e6 | 0.413167 | ||||||||
\(795\) | −2.45746e7 | −1.37901 | ||||||||
\(796\) | −2.55569e6 | −0.142964 | ||||||||
\(797\) | 2.38509e7 | 1.33002 | 0.665010 | − | 0.746834i | \(-0.268427\pi\) | ||||
0.665010 | + | 0.746834i | \(0.268427\pi\) | |||||||
\(798\) | 5.62541e7 | 3.12714 | ||||||||
\(799\) | −9.33852e6 | −0.517501 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 1.11643e7 | 0.614821 | ||||||||
\(802\) | −3.50884e6 | −0.192631 | ||||||||
\(803\) | −1.89522e7 | −1.03722 | ||||||||
\(804\) | 1.09653e7 | 0.598246 | ||||||||
\(805\) | −3.41132e6 | −0.185538 | ||||||||
\(806\) | 2.62153e6 | 0.142140 | ||||||||
\(807\) | 1.12443e7 | 0.607783 | ||||||||
\(808\) | −2.88612e6 | −0.155520 | ||||||||
\(809\) | −1.75973e7 | −0.945311 | −0.472656 | − | 0.881247i | \(-0.656705\pi\) | ||||
−0.472656 | + | 0.881247i | \(0.656705\pi\) | |||||||
\(810\) | −4.27111e6 | −0.228732 | ||||||||
\(811\) | −2.13966e7 | −1.14233 | −0.571167 | − | 0.820834i | \(-0.693509\pi\) | ||||
−0.571167 | + | 0.820834i | \(0.693509\pi\) | |||||||
\(812\) | 9.74152e6 | 0.518485 | ||||||||
\(813\) | −5.89164e7 | −3.12615 | ||||||||
\(814\) | 1.86774e7 | 0.987994 | ||||||||
\(815\) | 1.54186e7 | 0.813111 | ||||||||
\(816\) | 2.97656e6 | 0.156491 | ||||||||
\(817\) | 1.00792e7 | 0.528286 | ||||||||
\(818\) | −9.83546e6 | −0.513939 | ||||||||
\(819\) | 1.82653e7 | 0.951518 | ||||||||
\(820\) | −6.70391e6 | −0.348172 | ||||||||
\(821\) | 5.53624e6 | 0.286653 | 0.143327 | − | 0.989675i | \(-0.454220\pi\) | ||||
0.143327 | + | 0.989675i | \(0.454220\pi\) | |||||||
\(822\) | 1.33001e6 | 0.0686556 | ||||||||
\(823\) | 2.12780e7 | 1.09504 | 0.547522 | − | 0.836792i | \(-0.315571\pi\) | ||||
0.547522 | + | 0.836792i | \(0.315571\pi\) | |||||||
\(824\) | −5.75237e6 | −0.295141 | ||||||||
\(825\) | 6.34883e6 | 0.324757 | ||||||||
\(826\) | 3.06124e7 | 1.56116 | ||||||||
\(827\) | −1.64976e7 | −0.838795 | −0.419397 | − | 0.907803i | \(-0.637759\pi\) | ||||
−0.419397 | + | 0.907803i | \(0.637759\pi\) | |||||||
\(828\) | −3.91759e6 | −0.198584 | ||||||||
\(829\) | 6.72349e6 | 0.339788 | 0.169894 | − | 0.985462i | \(-0.445657\pi\) | ||||
0.169894 | + | 0.985462i | \(0.445657\pi\) | |||||||
\(830\) | −5.45994e6 | −0.275101 | ||||||||
\(831\) | 2.04821e7 | 1.02890 | ||||||||
\(832\) | 626638. | 0.0313840 | ||||||||
\(833\) | 2.17632e7 | 1.08670 | ||||||||
\(834\) | −3.72913e7 | −1.85649 | ||||||||
\(835\) | −6.54658e6 | −0.324936 | ||||||||
\(836\) | −1.25541e7 | −0.621257 | ||||||||
\(837\) | −2.50224e7 | −1.23457 | ||||||||
\(838\) | 2.03344e7 | 1.00028 | ||||||||
\(839\) | 6.09269e6 | 0.298816 | 0.149408 | − | 0.988776i | \(-0.452263\pi\) | ||||
0.149408 | + | 0.988776i | \(0.452263\pi\) | |||||||
\(840\) | −1.09649e7 | −0.536174 | ||||||||
\(841\) | −1.49398e7 | −0.728375 | ||||||||
\(842\) | −7.65707e6 | −0.372205 | ||||||||
\(843\) | −6.77014e7 | −3.28117 | ||||||||
\(844\) | 1.65322e7 | 0.798868 | ||||||||
\(845\) | −8.69719e6 | −0.419023 | ||||||||
\(846\) | 3.95061e7 | 1.89775 | ||||||||
\(847\) | −3.83376e6 | −0.183618 | ||||||||
\(848\) | −9.47171e6 | −0.452313 | ||||||||
\(849\) | 1.00520e7 | 0.478614 | ||||||||
\(850\) | −1.09410e6 | −0.0519410 | ||||||||
\(851\) | 6.46033e6 | 0.305795 | ||||||||
\(852\) | 1.15321e7 | 0.544265 | ||||||||
\(853\) | 1.92555e7 | 0.906111 | 0.453055 | − | 0.891482i | \(-0.350334\pi\) | ||||
0.453055 | + | 0.891482i | \(0.350334\pi\) | |||||||
\(854\) | −3.05419e7 | −1.43302 | ||||||||
\(855\) | −2.37462e7 | −1.11091 | ||||||||
\(856\) | 8.12989e6 | 0.379228 | ||||||||
\(857\) | −1.64010e7 | −0.762815 | −0.381408 | − | 0.924407i | \(-0.624561\pi\) | ||||
−0.381408 | + | 0.924407i | \(0.624561\pi\) | |||||||
\(858\) | −6.21628e6 | −0.288278 | ||||||||
\(859\) | −2.54001e6 | −0.117450 | −0.0587250 | − | 0.998274i | \(-0.518704\pi\) | ||||
−0.0587250 | + | 0.998274i | \(0.518704\pi\) | |||||||
\(860\) | −1.96460e6 | −0.0905790 | ||||||||
\(861\) | −1.14856e8 | −5.28012 | ||||||||
\(862\) | 4.04590e6 | 0.185458 | ||||||||
\(863\) | 1.59304e7 | 0.728114 | 0.364057 | − | 0.931377i | \(-0.381391\pi\) | ||||
0.364057 | + | 0.931377i | \(0.381391\pi\) | |||||||
\(864\) | −5.98124e6 | −0.272588 | ||||||||
\(865\) | −1.13134e7 | −0.514107 | ||||||||
\(866\) | −4.52108e6 | −0.204855 | ||||||||
\(867\) | −3.26341e7 | −1.47443 | ||||||||
\(868\) | −1.76801e7 | −0.796499 | ||||||||
\(869\) | 2.81451e7 | 1.26431 | ||||||||
\(870\) | −6.27101e6 | −0.280892 | ||||||||
\(871\) | 3.94638e6 | 0.176260 | ||||||||
\(872\) | 665988. | 0.0296603 | ||||||||
\(873\) | 4.78418e7 | 2.12458 | ||||||||
\(874\) | −4.34236e6 | −0.192286 | ||||||||
\(875\) | 4.03038e6 | 0.177962 | ||||||||
\(876\) | −2.10708e7 | −0.927730 | ||||||||
\(877\) | −1.21324e7 | −0.532656 | −0.266328 | − | 0.963882i | \(-0.585810\pi\) | ||||
−0.266328 | + | 0.963882i | \(0.585810\pi\) | |||||||
\(878\) | 1.45089e7 | 0.635181 | ||||||||
\(879\) | −3.48725e7 | −1.52234 | ||||||||
\(880\) | 2.44701e6 | 0.106520 | ||||||||
\(881\) | 1.34649e7 | 0.584473 | 0.292236 | − | 0.956346i | \(-0.405601\pi\) | ||||
0.292236 | + | 0.956346i | \(0.405601\pi\) | |||||||
\(882\) | −9.20679e7 | −3.98508 | ||||||||
\(883\) | 780486. | 0.0336871 | 0.0168435 | − | 0.999858i | \(-0.494638\pi\) | ||||
0.0168435 | + | 0.999858i | \(0.494638\pi\) | |||||||
\(884\) | 1.07126e6 | 0.0461066 | ||||||||
\(885\) | −1.97065e7 | −0.845767 | ||||||||
\(886\) | −1.04224e7 | −0.446052 | ||||||||
\(887\) | −1.29634e7 | −0.553235 | −0.276617 | − | 0.960980i | \(-0.589213\pi\) | ||||
−0.276617 | + | 0.960980i | \(0.589213\pi\) | |||||||
\(888\) | 2.07652e7 | 0.883698 | ||||||||
\(889\) | 2.52835e7 | 1.07296 | ||||||||
\(890\) | −2.41205e6 | −0.102073 | ||||||||
\(891\) | 1.63304e7 | 0.689132 | ||||||||
\(892\) | 9.06390e6 | 0.381420 | ||||||||
\(893\) | 4.37896e7 | 1.83756 | ||||||||
\(894\) | −677963. | −0.0283702 | ||||||||
\(895\) | 9.79530e6 | 0.408752 | ||||||||
\(896\) | −4.22616e6 | −0.175864 | ||||||||
\(897\) | −2.15015e6 | −0.0892254 | ||||||||
\(898\) | 2.54670e6 | 0.105387 | ||||||||
\(899\) | −1.01116e7 | −0.417272 | ||||||||
\(900\) | 4.62854e6 | 0.190475 | ||||||||
\(901\) | −1.61922e7 | −0.664498 | ||||||||
\(902\) | 2.56321e7 | 1.04898 | ||||||||
\(903\) | −3.36587e7 | −1.37366 | ||||||||
\(904\) | −247673. | −0.0100799 | ||||||||
\(905\) | −1.77454e7 | −0.720218 | ||||||||
\(906\) | 5.49309e7 | 2.22329 | ||||||||
\(907\) | −3.31097e7 | −1.33640 | −0.668201 | − | 0.743981i | \(-0.732935\pi\) | ||||
−0.668201 | + | 0.743981i | \(0.732935\pi\) | |||||||
\(908\) | 1.60884e7 | 0.647587 | ||||||||
\(909\) | 2.08727e7 | 0.837855 | ||||||||
\(910\) | −3.94624e6 | −0.157972 | ||||||||
\(911\) | −4.57024e7 | −1.82450 | −0.912248 | − | 0.409637i | \(-0.865655\pi\) | ||||
−0.912248 | + | 0.409637i | \(0.865655\pi\) | |||||||
\(912\) | −1.39575e7 | −0.555675 | ||||||||
\(913\) | 2.08758e7 | 0.828833 | ||||||||
\(914\) | 9.78633e6 | 0.387485 | ||||||||
\(915\) | 1.96610e7 | 0.776344 | ||||||||
\(916\) | 1.60090e7 | 0.630412 | ||||||||
\(917\) | −3.05367e7 | −1.19922 | ||||||||
\(918\) | −1.02251e7 | −0.400462 | ||||||||
\(919\) | −5.81218e6 | −0.227013 | −0.113506 | − | 0.993537i | \(-0.536208\pi\) | ||||
−0.113506 | + | 0.993537i | \(0.536208\pi\) | |||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | −7.28405e7 | −2.82959 | ||||||||
\(922\) | −3.32669e7 | −1.28880 | ||||||||
\(923\) | 4.15039e6 | 0.160356 | ||||||||
\(924\) | 4.19237e7 | 1.61540 | ||||||||
\(925\) | −7.63272e6 | −0.293309 | ||||||||
\(926\) | −1.31048e7 | −0.502230 | ||||||||
\(927\) | 4.16017e7 | 1.59005 | ||||||||
\(928\) | −2.41702e6 | −0.0921319 | ||||||||
\(929\) | 2.41127e6 | 0.0916657 | 0.0458328 | − | 0.998949i | \(-0.485406\pi\) | ||||
0.0458328 | + | 0.998949i | \(0.485406\pi\) | |||||||
\(930\) | 1.13814e7 | 0.431507 | ||||||||
\(931\) | −1.02051e8 | −3.85870 | ||||||||
\(932\) | −1.64552e7 | −0.620532 | ||||||||
\(933\) | 1.21458e7 | 0.456795 | ||||||||
\(934\) | 3.40663e7 | 1.27779 | ||||||||
\(935\) | 4.18325e6 | 0.156489 | ||||||||
\(936\) | −4.53190e6 | −0.169079 | ||||||||
\(937\) | −4.01649e7 | −1.49451 | −0.747253 | − | 0.664540i | \(-0.768627\pi\) | ||||
−0.747253 | + | 0.664540i | \(0.768627\pi\) | |||||||
\(938\) | −2.66152e7 | −0.987693 | ||||||||
\(939\) | 6.11718e7 | 2.26406 | ||||||||
\(940\) | −8.53534e6 | −0.315066 | ||||||||
\(941\) | −1.31127e7 | −0.482744 | −0.241372 | − | 0.970433i | \(-0.577597\pi\) | ||||
−0.241372 | + | 0.970433i | \(0.577597\pi\) | |||||||
\(942\) | −1.99007e7 | −0.730705 | ||||||||
\(943\) | 8.86592e6 | 0.324672 | ||||||||
\(944\) | −7.59541e6 | −0.277410 | ||||||||
\(945\) | 3.76667e7 | 1.37208 | ||||||||
\(946\) | 7.51156e6 | 0.272899 | ||||||||
\(947\) | 3.67023e7 | 1.32990 | 0.664949 | − | 0.746889i | \(-0.268453\pi\) | ||||
0.664949 | + | 0.746889i | \(0.268453\pi\) | |||||||
\(948\) | 3.12913e7 | 1.13084 | ||||||||
\(949\) | −7.58335e6 | −0.273335 | ||||||||
\(950\) | 5.13039e6 | 0.184434 | ||||||||
\(951\) | 1.60761e7 | 0.576406 | ||||||||
\(952\) | −7.22477e6 | −0.258364 | ||||||||
\(953\) | −1.55702e7 | −0.555346 | −0.277673 | − | 0.960676i | \(-0.589563\pi\) | ||||
−0.277673 | + | 0.960676i | \(0.589563\pi\) | |||||||
\(954\) | 6.85002e7 | 2.43681 | ||||||||
\(955\) | 3.95278e6 | 0.140247 | ||||||||
\(956\) | 1.12176e7 | 0.396967 | ||||||||
\(957\) | 2.39769e7 | 0.846280 | ||||||||
\(958\) | −6.83845e6 | −0.240738 | ||||||||
\(959\) | −3.22823e6 | −0.113349 | ||||||||
\(960\) | 2.72055e6 | 0.0952751 | ||||||||
\(961\) | −1.02774e7 | −0.358985 | ||||||||
\(962\) | 7.47336e6 | 0.260362 | ||||||||
\(963\) | −5.87960e7 | −2.04307 | ||||||||
\(964\) | −8.06739e6 | −0.279602 | ||||||||
\(965\) | 8.16859e6 | 0.282377 | ||||||||
\(966\) | 1.45010e7 | 0.499985 | ||||||||
\(967\) | 3.65611e7 | 1.25734 | 0.628670 | − | 0.777672i | \(-0.283600\pi\) | ||||
0.628670 | + | 0.777672i | \(0.283600\pi\) | |||||||
\(968\) | 951214. | 0.0326280 | ||||||||
\(969\) | −2.38608e7 | −0.816349 | ||||||||
\(970\) | −1.03363e7 | −0.352724 | ||||||||
\(971\) | 3.92822e7 | 1.33705 | 0.668524 | − | 0.743690i | \(-0.266926\pi\) | ||||
0.668524 | + | 0.743690i | \(0.266926\pi\) | |||||||
\(972\) | −4.55411e6 | −0.154610 | ||||||||
\(973\) | 9.05142e7 | 3.06503 | ||||||||
\(974\) | −3.15019e7 | −1.06400 | ||||||||
\(975\) | 2.54035e6 | 0.0855820 | ||||||||
\(976\) | 7.57791e6 | 0.254639 | ||||||||
\(977\) | 2.11757e7 | 0.709743 | 0.354872 | − | 0.934915i | \(-0.384525\pi\) | ||||
0.354872 | + | 0.934915i | \(0.384525\pi\) | |||||||
\(978\) | −6.55422e7 | −2.19116 | ||||||||
\(979\) | 9.22237e6 | 0.307529 | ||||||||
\(980\) | 1.98914e7 | 0.661606 | ||||||||
\(981\) | −4.81648e6 | −0.159793 | ||||||||
\(982\) | −398455. | −0.0131856 | ||||||||
\(983\) | −2.99811e7 | −0.989610 | −0.494805 | − | 0.869004i | \(-0.664761\pi\) | ||||
−0.494805 | + | 0.869004i | \(0.664761\pi\) | |||||||
\(984\) | 2.84974e7 | 0.938248 | ||||||||
\(985\) | 2.37405e6 | 0.0779648 | ||||||||
\(986\) | −4.13197e6 | −0.135352 | ||||||||
\(987\) | −1.46233e8 | −4.77806 | ||||||||
\(988\) | −5.02328e6 | −0.163717 | ||||||||
\(989\) | 2.59818e6 | 0.0844654 | ||||||||
\(990\) | −1.76970e7 | −0.573868 | ||||||||
\(991\) | −1.61393e7 | −0.522036 | −0.261018 | − | 0.965334i | \(-0.584058\pi\) | ||||
−0.261018 | + | 0.965334i | \(0.584058\pi\) | |||||||
\(992\) | 4.38670e6 | 0.141533 | ||||||||
\(993\) | 1.94918e7 | 0.627304 | ||||||||
\(994\) | −2.79910e7 | −0.898571 | ||||||||
\(995\) | −3.99327e6 | −0.127871 | ||||||||
\(996\) | 2.32095e7 | 0.741338 | ||||||||
\(997\) | 4.42811e7 | 1.41085 | 0.705425 | − | 0.708784i | \(-0.250756\pi\) | ||||
0.705425 | + | 0.708784i | \(0.250756\pi\) | |||||||
\(998\) | 1.61468e7 | 0.513168 | ||||||||
\(999\) | −7.13329e7 | −2.26139 |
(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 | 230.6.a.f.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.f.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |