Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.36142572544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 53x^{4} + 632x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.5 | ||
Root | \(5.97123i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.k.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.97123i | 1.75759i | 0.477195 | + | 0.878797i | \(0.341653\pi\) | ||||
−0.477195 | + | 0.878797i | \(0.658347\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −16.7131 | −2.08914 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.9137 | 1.01475 | ||||||||
\(7\) | 5.48376i | 0.296095i | 0.988980 | + | 0.148048i | \(0.0472989\pi\) | ||||
−0.988980 | + | 0.148048i | \(0.952701\pi\) | |||||||
\(8\) | − 43.3148i | − 1.91426i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 50.1393i | 1.20616i | ||||||||
\(13\) | − 24.5738i | − 0.524272i | −0.965031 | − | 0.262136i | \(-0.915573\pi\) | ||||
0.965031 | − | 0.262136i | \(-0.0844270\pi\) | |||||||
\(14\) | −27.2610 | −0.520415 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 81.6231 | 1.27536 | ||||||||
\(17\) | − 59.3687i | − 0.847001i | −0.905896 | − | 0.423501i | \(-0.860801\pi\) | ||||
0.905896 | − | 0.423501i | \(-0.139199\pi\) | |||||||
\(18\) | − 44.7411i | − 0.585865i | ||||||||
\(19\) | −5.89234 | −0.0711471 | −0.0355736 | − | 0.999367i | \(-0.511326\pi\) | ||||
−0.0355736 | + | 0.999367i | \(0.511326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.4513 | 0.170951 | ||||||||
\(22\) | 54.6835i | 0.529935i | ||||||||
\(23\) | 68.4570i | 0.620621i | 0.950635 | + | 0.310310i | \(0.100433\pi\) | ||||
−0.950635 | + | 0.310310i | \(0.899567\pi\) | |||||||
\(24\) | −129.945 | −1.10520 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 122.162 | 0.921458 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − 91.6506i | − 0.618584i | ||||||||
\(29\) | 265.022 | 1.69701 | 0.848505 | − | 0.529187i | \(-0.177503\pi\) | ||||
0.848505 | + | 0.529187i | \(0.177503\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −196.554 | −1.13878 | −0.569389 | − | 0.822068i | \(-0.692820\pi\) | ||||
−0.569389 | + | 0.822068i | \(0.692820\pi\) | |||||||
\(32\) | 59.2482i | 0.327303i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | 295.135 | 1.48868 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 150.418 | 0.696379 | ||||||||
\(37\) | 166.575i | 0.740131i | 0.929006 | + | 0.370065i | \(0.120665\pi\) | ||||
−0.929006 | + | 0.370065i | \(0.879335\pi\) | |||||||
\(38\) | − 29.2922i | − 0.125048i | ||||||||
\(39\) | −73.7214 | −0.302689 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 424.101 | 1.61545 | 0.807725 | − | 0.589559i | \(-0.200699\pi\) | ||||
0.807725 | + | 0.589559i | \(0.200699\pi\) | |||||||
\(42\) | 81.7830i | 0.300462i | ||||||||
\(43\) | 177.351i | 0.628970i | 0.949262 | + | 0.314485i | \(0.101832\pi\) | ||||
−0.949262 | + | 0.314485i | \(0.898168\pi\) | |||||||
\(44\) | −183.844 | −0.629899 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −340.316 | −1.09080 | ||||||||
\(47\) | 141.148i | 0.438053i | 0.975719 | + | 0.219026i | \(0.0702881\pi\) | ||||
−0.975719 | + | 0.219026i | \(0.929712\pi\) | |||||||
\(48\) | − 244.869i | − 0.736330i | ||||||||
\(49\) | 312.928 | 0.912328 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −178.106 | −0.489016 | ||||||||
\(52\) | 410.704i | 1.09528i | ||||||||
\(53\) | 339.828i | 0.880736i | 0.897817 | + | 0.440368i | \(0.145152\pi\) | ||||
−0.897817 | + | 0.440368i | \(0.854848\pi\) | |||||||
\(54\) | −134.223 | −0.338249 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 237.528 | 0.566804 | ||||||||
\(57\) | 17.6770i | 0.0410768i | ||||||||
\(58\) | 1317.48i | 2.98266i | ||||||||
\(59\) | −416.784 | −0.919672 | −0.459836 | − | 0.888004i | \(-0.652092\pi\) | ||||
−0.459836 | + | 0.888004i | \(0.652092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 662.146 | 1.38982 | 0.694911 | − | 0.719096i | \(-0.255444\pi\) | ||||
0.694911 | + | 0.719096i | \(0.255444\pi\) | |||||||
\(62\) | − 977.115i | − 2.00151i | ||||||||
\(63\) | − 49.3538i | − 0.0986984i | ||||||||
\(64\) | 358.448 | 0.700094 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 164.051 | 0.305958 | ||||||||
\(67\) | 313.713i | 0.572032i | 0.958225 | + | 0.286016i | \(0.0923311\pi\) | ||||
−0.958225 | + | 0.286016i | \(0.907669\pi\) | |||||||
\(68\) | 992.235i | 1.76950i | ||||||||
\(69\) | 205.371 | 0.358316 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −153.693 | −0.256902 | −0.128451 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128451 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(72\) | 389.834i | 0.638088i | ||||||||
\(73\) | − 153.866i | − 0.246694i | −0.992364 | − | 0.123347i | \(-0.960637\pi\) | ||||
0.992364 | − | 0.123347i | \(-0.0393628\pi\) | |||||||
\(74\) | −828.084 | −1.30085 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 98.4793 | 0.148636 | ||||||||
\(77\) | 60.3213i | 0.0892760i | ||||||||
\(78\) | − 366.486i | − 0.532004i | ||||||||
\(79\) | −403.000 | −0.573938 | −0.286969 | − | 0.957940i | \(-0.592648\pi\) | ||||
−0.286969 | + | 0.957940i | \(0.592648\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 2108.30i | 2.83931i | ||||||||
\(83\) | 652.313i | 0.862659i | 0.902195 | + | 0.431329i | \(0.141955\pi\) | ||||
−0.902195 | + | 0.431329i | \(0.858045\pi\) | |||||||
\(84\) | −274.952 | −0.357139 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −881.650 | −1.10547 | ||||||||
\(87\) | − 795.065i | − 0.979769i | ||||||||
\(88\) | − 476.463i | − 0.577172i | ||||||||
\(89\) | −1226.77 | −1.46109 | −0.730545 | − | 0.682864i | \(-0.760734\pi\) | ||||
−0.730545 | + | 0.682864i | \(0.760734\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 134.757 | 0.155234 | ||||||||
\(92\) | − 1144.13i | − 1.29656i | ||||||||
\(93\) | 589.662i | 0.657474i | ||||||||
\(94\) | −701.677 | −0.769919 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 177.745 | 0.188969 | ||||||||
\(97\) | 959.746i | 1.00461i | 0.864690 | + | 0.502306i | \(0.167515\pi\) | ||||
−0.864690 | + | 0.502306i | \(0.832485\pi\) | |||||||
\(98\) | 1555.64i | 1.60350i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1258.52 | −1.23988 | −0.619939 | − | 0.784650i | \(-0.712843\pi\) | ||||
−0.619939 | + | 0.784650i | \(0.712843\pi\) | |||||||
\(102\) | − 885.406i | − 0.859492i | ||||||||
\(103\) | 493.175i | 0.471786i | 0.971779 | + | 0.235893i | \(0.0758015\pi\) | ||||
−0.971779 | + | 0.235893i | \(0.924198\pi\) | |||||||
\(104\) | −1064.41 | −1.00360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1689.36 | −1.54798 | ||||||||
\(107\) | − 1099.05i | − 0.992983i | −0.868042 | − | 0.496492i | \(-0.834621\pi\) | ||||
0.868042 | − | 0.496492i | \(-0.165379\pi\) | |||||||
\(108\) | − 451.254i | − 0.402055i | ||||||||
\(109\) | −1275.04 | −1.12043 | −0.560216 | − | 0.828347i | \(-0.689282\pi\) | ||||
−0.560216 | + | 0.828347i | \(0.689282\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 499.726 | 0.427315 | ||||||||
\(112\) | 447.601i | 0.377628i | ||||||||
\(113\) | 946.433i | 0.787902i | 0.919131 | + | 0.393951i | \(0.128892\pi\) | ||||
−0.919131 | + | 0.393951i | \(0.871108\pi\) | |||||||
\(114\) | −87.8765 | −0.0721964 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4429.34 | −3.54529 | ||||||||
\(117\) | 221.164i | 0.174757i | ||||||||
\(118\) | − 2071.93i | − 1.61641i | ||||||||
\(119\) | 325.563 | 0.250793 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 3291.68i | 2.44274i | ||||||||
\(123\) | − 1272.30i | − 0.932681i | ||||||||
\(124\) | 3285.03 | 2.37907 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 245.349 | 0.173472 | ||||||||
\(127\) | 2260.77i | 1.57962i | 0.613354 | + | 0.789808i | \(0.289820\pi\) | ||||
−0.613354 | + | 0.789808i | \(0.710180\pi\) | |||||||
\(128\) | 2255.91i | 1.55778i | ||||||||
\(129\) | 532.052 | 0.363136 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −57.1277 | −0.0381013 | −0.0190507 | − | 0.999819i | \(-0.506064\pi\) | ||||
−0.0190507 | + | 0.999819i | \(0.506064\pi\) | |||||||
\(132\) | 551.533i | 0.363672i | ||||||||
\(133\) | − 32.3122i | − 0.0210663i | ||||||||
\(134\) | −1559.54 | −1.00540 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2571.54 | −1.62138 | ||||||||
\(137\) | 1919.27i | 1.19689i | 0.801162 | + | 0.598447i | \(0.204215\pi\) | ||||
−0.801162 | + | 0.598447i | \(0.795785\pi\) | |||||||
\(138\) | 1020.95i | 0.629774i | ||||||||
\(139\) | 1690.46 | 1.03153 | 0.515766 | − | 0.856729i | \(-0.327507\pi\) | ||||
0.515766 | + | 0.856729i | \(0.327507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 423.443 | 0.252910 | ||||||||
\(142\) | − 764.044i | − 0.451529i | ||||||||
\(143\) | − 270.312i | − 0.158074i | ||||||||
\(144\) | −734.608 | −0.425120 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 764.904 | 0.433588 | ||||||||
\(147\) | − 938.785i | − 0.526733i | ||||||||
\(148\) | − 2783.99i | − 1.54624i | ||||||||
\(149\) | 2077.88 | 1.14246 | 0.571231 | − | 0.820789i | \(-0.306466\pi\) | ||||
0.571231 | + | 0.820789i | \(0.306466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2711.16 | 1.46113 | 0.730566 | − | 0.682842i | \(-0.239256\pi\) | ||||
0.730566 | + | 0.682842i | \(0.239256\pi\) | |||||||
\(152\) | 255.226i | 0.136194i | ||||||||
\(153\) | 534.318i | 0.282334i | ||||||||
\(154\) | −299.871 | −0.156911 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1232.11 | 0.632359 | ||||||||
\(157\) | 2341.23i | 1.19013i | 0.803677 | + | 0.595066i | \(0.202874\pi\) | ||||
−0.803677 | + | 0.595066i | \(0.797126\pi\) | |||||||
\(158\) | − 2003.41i | − 1.00875i | ||||||||
\(159\) | 1019.48 | 0.508493 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −375.402 | −0.183763 | ||||||||
\(162\) | 402.669i | 0.195288i | ||||||||
\(163\) | − 3523.01i | − 1.69291i | −0.532464 | − | 0.846453i | \(-0.678734\pi\) | ||||
0.532464 | − | 0.846453i | \(-0.321266\pi\) | |||||||
\(164\) | −7088.05 | −3.37490 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3242.80 | −1.51620 | ||||||||
\(167\) | 4011.90i | 1.85898i | 0.368842 | + | 0.929492i | \(0.379754\pi\) | ||||
−0.368842 | + | 0.929492i | \(0.620246\pi\) | |||||||
\(168\) | − 712.584i | − 0.327244i | ||||||||
\(169\) | 1593.13 | 0.725138 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 53.0310 | 0.0237157 | ||||||||
\(172\) | − 2964.08i | − 1.31400i | ||||||||
\(173\) | − 3325.30i | − 1.46137i | −0.682713 | − | 0.730687i | \(-0.739200\pi\) | ||||
0.682713 | − | 0.730687i | \(-0.260800\pi\) | |||||||
\(174\) | 3952.45 | 1.72204 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 897.854 | 0.384536 | ||||||||
\(177\) | 1250.35i | 0.530973i | ||||||||
\(178\) | − 6098.54i | − 2.56800i | ||||||||
\(179\) | 26.6350 | 0.0111217 | 0.00556087 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556087 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1934.25 | 0.794320 | 0.397160 | − | 0.917749i | \(-0.369996\pi\) | ||||
0.397160 | + | 0.917749i | \(0.369996\pi\) | |||||||
\(182\) | 669.906i | 0.272839i | ||||||||
\(183\) | − 1986.44i | − 0.802414i | ||||||||
\(184\) | 2965.21 | 1.18803 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2931.34 | −1.15557 | ||||||||
\(187\) | − 653.055i | − 0.255380i | ||||||||
\(188\) | − 2359.01i | − 0.915153i | ||||||||
\(189\) | −148.061 | −0.0569835 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3341.59 | −1.26591 | −0.632956 | − | 0.774188i | \(-0.718158\pi\) | ||||
−0.632956 | + | 0.774188i | \(0.718158\pi\) | |||||||
\(192\) | − 1075.34i | − 0.404200i | ||||||||
\(193\) | 1293.97i | 0.482600i | 0.970451 | + | 0.241300i | \(0.0775737\pi\) | ||||
−0.970451 | + | 0.241300i | \(0.922426\pi\) | |||||||
\(194\) | −4771.12 | −1.76570 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5230.01 | −1.90598 | ||||||||
\(197\) | − 2301.17i | − 0.832240i | −0.909310 | − | 0.416120i | \(-0.863390\pi\) | ||||
0.909310 | − | 0.416120i | \(-0.136610\pi\) | |||||||
\(198\) | − 492.152i | − 0.176645i | ||||||||
\(199\) | 3039.64 | 1.08279 | 0.541393 | − | 0.840770i | \(-0.317897\pi\) | ||||
0.541393 | + | 0.840770i | \(0.317897\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 941.139 | 0.330263 | ||||||||
\(202\) | − 6256.40i | − 2.17920i | ||||||||
\(203\) | 1453.31i | 0.502476i | ||||||||
\(204\) | 2976.70 | 1.02162 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2451.69 | −0.829209 | ||||||||
\(207\) | − 616.113i | − 0.206874i | ||||||||
\(208\) | − 2005.79i | − 0.668636i | ||||||||
\(209\) | −64.8157 | −0.0214517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2807.86 | 0.916119 | 0.458060 | − | 0.888921i | \(-0.348545\pi\) | ||||
0.458060 | + | 0.888921i | \(0.348545\pi\) | |||||||
\(212\) | − 5679.58i | − 1.83998i | ||||||||
\(213\) | 461.080i | 0.148322i | ||||||||
\(214\) | 5463.63 | 1.74526 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1169.50 | 0.368400 | ||||||||
\(217\) | − 1077.85i | − 0.337187i | ||||||||
\(218\) | − 6338.53i | − 1.96926i | ||||||||
\(219\) | −461.598 | −0.142429 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1458.91 | −0.444059 | ||||||||
\(222\) | 2484.25i | 0.751046i | ||||||||
\(223\) | − 1443.09i | − 0.433348i | −0.976244 | − | 0.216674i | \(-0.930479\pi\) | ||||
0.976244 | − | 0.216674i | \(-0.0695209\pi\) | |||||||
\(224\) | −324.903 | −0.0969129 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4704.94 | −1.38481 | ||||||||
\(227\) | 3658.71i | 1.06977i | 0.844926 | + | 0.534884i | \(0.179645\pi\) | ||||
−0.844926 | + | 0.534884i | \(0.820355\pi\) | |||||||
\(228\) | − 295.438i | − 0.0858151i | ||||||||
\(229\) | 1695.50 | 0.489265 | 0.244632 | − | 0.969616i | \(-0.421333\pi\) | ||||
0.244632 | + | 0.969616i | \(0.421333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 180.964 | 0.0515435 | ||||||||
\(232\) | − 11479.4i | − 3.24853i | ||||||||
\(233\) | 5782.24i | 1.62578i | 0.582417 | + | 0.812890i | \(0.302107\pi\) | ||||
−0.582417 | + | 0.812890i | \(0.697893\pi\) | |||||||
\(234\) | −1099.46 | −0.307153 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6965.76 | 1.92132 | ||||||||
\(237\) | 1209.00i | 0.331363i | ||||||||
\(238\) | 1618.45i | 0.440792i | ||||||||
\(239\) | 5836.16 | 1.57954 | 0.789770 | − | 0.613404i | \(-0.210200\pi\) | ||||
0.789770 | + | 0.613404i | \(0.210200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −982.308 | −0.262556 | −0.131278 | − | 0.991346i | \(-0.541908\pi\) | ||||
−0.131278 | + | 0.991346i | \(0.541908\pi\) | |||||||
\(242\) | 601.519i | 0.159781i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | −11066.5 | −2.90353 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6324.91 | 1.63927 | ||||||||
\(247\) | 144.797i | 0.0373005i | ||||||||
\(248\) | 8513.70i | 2.17992i | ||||||||
\(249\) | 1956.94 | 0.498056 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4320.23 | 1.08642 | 0.543209 | − | 0.839598i | \(-0.317209\pi\) | ||||
0.543209 | + | 0.839598i | \(0.317209\pi\) | |||||||
\(252\) | 824.856i | 0.206195i | ||||||||
\(253\) | 753.027i | 0.187124i | ||||||||
\(254\) | −11238.8 | −2.77633 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8347.07 | −2.03786 | ||||||||
\(257\) | − 6224.29i | − 1.51074i | −0.655298 | − | 0.755371i | \(-0.727457\pi\) | ||||
0.655298 | − | 0.755371i | \(-0.272543\pi\) | |||||||
\(258\) | 2644.95i | 0.638246i | ||||||||
\(259\) | −913.459 | −0.219149 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2385.20 | −0.565670 | ||||||||
\(262\) | − 283.995i | − 0.0669666i | ||||||||
\(263\) | 2588.95i | 0.607002i | 0.952831 | + | 0.303501i | \(0.0981555\pi\) | ||||
−0.952831 | + | 0.303501i | \(0.901844\pi\) | |||||||
\(264\) | −1429.39 | −0.333230 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 160.631 | 0.0370260 | ||||||||
\(267\) | 3680.30i | 0.843561i | ||||||||
\(268\) | − 5243.12i | − 1.19505i | ||||||||
\(269\) | 5871.53 | 1.33083 | 0.665415 | − | 0.746473i | \(-0.268254\pi\) | ||||
0.665415 | + | 0.746473i | \(0.268254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3306.93 | −0.741261 | −0.370630 | − | 0.928780i | \(-0.620858\pi\) | ||||
−0.370630 | + | 0.928780i | \(0.620858\pi\) | |||||||
\(272\) | − 4845.85i | − 1.08023i | ||||||||
\(273\) | − 404.270i | − 0.0896247i | ||||||||
\(274\) | −9541.14 | −2.10366 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3432.39 | −0.748571 | ||||||||
\(277\) | − 2861.37i | − 0.620660i | −0.950629 | − | 0.310330i | \(-0.899560\pi\) | ||||
0.950629 | − | 0.310330i | \(-0.100440\pi\) | |||||||
\(278\) | 8403.66i | 1.81302i | ||||||||
\(279\) | 1768.99 | 0.379593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2988.05 | −0.634349 | −0.317174 | − | 0.948367i | \(-0.602734\pi\) | ||||
−0.317174 | + | 0.948367i | \(0.602734\pi\) | |||||||
\(282\) | 2105.03i | 0.444513i | ||||||||
\(283\) | − 1454.60i | − 0.305536i | −0.988262 | − | 0.152768i | \(-0.951181\pi\) | ||||
0.988262 | − | 0.152768i | \(-0.0488188\pi\) | |||||||
\(284\) | 2568.69 | 0.536704 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1343.78 | 0.277830 | ||||||||
\(287\) | 2325.67i | 0.478327i | ||||||||
\(288\) | − 533.234i | − 0.109101i | ||||||||
\(289\) | 1388.36 | 0.282589 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2879.24 | 0.580014 | ||||||||
\(292\) | 2571.58i | 0.515378i | ||||||||
\(293\) | 8586.52i | 1.71205i | 0.516937 | + | 0.856023i | \(0.327072\pi\) | ||||
−0.516937 | + | 0.856023i | \(0.672928\pi\) | |||||||
\(294\) | 4666.92 | 0.925782 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7215.19 | 1.41681 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | 10329.6i | 2.00798i | ||||||||
\(299\) | 1682.25 | 0.325374 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −972.547 | −0.186235 | ||||||||
\(302\) | 13477.8i | 2.56808i | ||||||||
\(303\) | 3775.57i | 0.715844i | ||||||||
\(304\) | −480.951 | −0.0907382 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2656.22 | −0.496228 | ||||||||
\(307\) | 529.029i | 0.0983495i | 0.998790 | + | 0.0491748i | \(0.0156591\pi\) | ||||
−0.998790 | + | 0.0491748i | \(0.984341\pi\) | |||||||
\(308\) | − 1008.16i | − 0.186510i | ||||||||
\(309\) | 1479.53 | 0.272386 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5008.00 | −0.913111 | −0.456555 | − | 0.889695i | \(-0.650917\pi\) | ||||
−0.456555 | + | 0.889695i | \(0.650917\pi\) | |||||||
\(312\) | 3193.23i | 0.579426i | ||||||||
\(313\) | − 7858.53i | − 1.41914i | −0.704635 | − | 0.709570i | \(-0.748889\pi\) | ||||
0.704635 | − | 0.709570i | \(-0.251111\pi\) | |||||||
\(314\) | −11638.8 | −2.09177 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6735.39 | 1.19904 | ||||||||
\(317\) | 7747.04i | 1.37261i | 0.727315 | + | 0.686304i | \(0.240768\pi\) | ||||
−0.727315 | + | 0.686304i | \(0.759232\pi\) | |||||||
\(318\) | 5068.09i | 0.893724i | ||||||||
\(319\) | 2915.24 | 0.511668 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3297.15 | −0.573299 | ||||||||
\(322\) | − 1866.21i | − 0.322980i | ||||||||
\(323\) | 349.820i | 0.0602617i | ||||||||
\(324\) | −1353.76 | −0.232126 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17513.7 | 2.97544 | ||||||||
\(327\) | 3825.13i | 0.646882i | ||||||||
\(328\) | − 18369.9i | − 3.09240i | ||||||||
\(329\) | −774.019 | −0.129705 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1355.08 | 0.225022 | 0.112511 | − | 0.993650i | \(-0.464111\pi\) | ||||
0.112511 | + | 0.993650i | \(0.464111\pi\) | |||||||
\(332\) | − 10902.2i | − 1.80221i | ||||||||
\(333\) | − 1499.18i | − 0.246710i | ||||||||
\(334\) | −19944.1 | −3.26734 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1342.80 | 0.218024 | ||||||||
\(337\) | 2596.97i | 0.419780i | 0.977725 | + | 0.209890i | \(0.0673106\pi\) | ||||
−0.977725 | + | 0.209890i | \(0.932689\pi\) | |||||||
\(338\) | 7919.81i | 1.27450i | ||||||||
\(339\) | 2839.30 | 0.454896 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2162.09 | −0.343355 | ||||||||
\(342\) | 263.629i | 0.0416826i | ||||||||
\(343\) | 3596.95i | 0.566231i | ||||||||
\(344\) | 7681.91 | 1.20401 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16530.8 | 2.56850 | ||||||||
\(347\) | 266.820i | 0.0412785i | 0.999787 | + | 0.0206392i | \(0.00657014\pi\) | ||||
−0.999787 | + | 0.0206392i | \(0.993430\pi\) | |||||||
\(348\) | 13288.0i | 2.04687i | ||||||||
\(349\) | 10549.4 | 1.61804 | 0.809021 | − | 0.587780i | \(-0.199998\pi\) | ||||
0.809021 | + | 0.587780i | \(0.199998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 663.492 | 0.100896 | ||||||||
\(352\) | 651.730i | 0.0986856i | ||||||||
\(353\) | − 7152.63i | − 1.07846i | −0.842159 | − | 0.539229i | \(-0.818716\pi\) | ||||
0.842159 | − | 0.539229i | \(-0.181284\pi\) | |||||||
\(354\) | −6215.79 | −0.933235 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20503.1 | 3.05242 | ||||||||
\(357\) | − 976.690i | − 0.144795i | ||||||||
\(358\) | 132.409i | 0.0195475i | ||||||||
\(359\) | −359.182 | −0.0528047 | −0.0264024 | − | 0.999651i | \(-0.508405\pi\) | ||||
−0.0264024 | + | 0.999651i | \(0.508405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6824.28 | −0.994938 | ||||||||
\(362\) | 9615.62i | 1.39609i | ||||||||
\(363\) | − 363.000i | − 0.0524864i | ||||||||
\(364\) | −2252.20 | −0.324306 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9875.04 | 1.41032 | ||||||||
\(367\) | 9042.47i | 1.28614i | 0.765808 | + | 0.643070i | \(0.222339\pi\) | ||||
−0.765808 | + | 0.643070i | \(0.777661\pi\) | |||||||
\(368\) | 5587.67i | 0.791515i | ||||||||
\(369\) | −3816.91 | −0.538483 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1863.54 | −0.260781 | ||||||||
\(372\) | − 9855.08i | − 1.37355i | ||||||||
\(373\) | 11929.0i | 1.65592i | 0.560787 | + | 0.827960i | \(0.310499\pi\) | ||||
−0.560787 | + | 0.827960i | \(0.689501\pi\) | |||||||
\(374\) | 3246.49 | 0.448855 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6113.78 | 0.838549 | ||||||||
\(377\) | − 6512.59i | − 0.889696i | ||||||||
\(378\) | − 736.047i | − 0.100154i | ||||||||
\(379\) | −6556.08 | −0.888557 | −0.444279 | − | 0.895889i | \(-0.646540\pi\) | ||||
−0.444279 | + | 0.895889i | \(0.646540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6782.32 | 0.911992 | ||||||||
\(382\) | − 16611.8i | − 2.22496i | ||||||||
\(383\) | − 10703.1i | − 1.42795i | −0.700172 | − | 0.713975i | \(-0.746893\pi\) | ||||
0.700172 | − | 0.713975i | \(-0.253107\pi\) | |||||||
\(384\) | 6767.74 | 0.899388 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6432.60 | −0.848214 | ||||||||
\(387\) | − 1596.15i | − 0.209657i | ||||||||
\(388\) | − 16040.3i | − 2.09878i | ||||||||
\(389\) | 6450.30 | 0.840728 | 0.420364 | − | 0.907355i | \(-0.361902\pi\) | ||||
0.420364 | + | 0.907355i | \(0.361902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4064.20 | 0.525667 | ||||||||
\(392\) | − 13554.4i | − 1.74644i | ||||||||
\(393\) | 171.383i | 0.0219978i | ||||||||
\(394\) | 11439.6 | 1.46274 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1654.60 | 0.209966 | ||||||||
\(397\) | − 12526.0i | − 1.58353i | −0.610828 | − | 0.791764i | \(-0.709163\pi\) | ||||
0.610828 | − | 0.791764i | \(-0.290837\pi\) | |||||||
\(398\) | 15110.7i | 1.90310i | ||||||||
\(399\) | −96.9365 | −0.0121626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9119.52 | 1.13568 | 0.567839 | − | 0.823139i | \(-0.307779\pi\) | ||||
0.567839 | + | 0.823139i | \(0.307779\pi\) | |||||||
\(402\) | 4678.62i | 0.580468i | ||||||||
\(403\) | 4830.08i | 0.597030i | ||||||||
\(404\) | 21033.8 | 2.59028 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7224.76 | −0.883150 | ||||||||
\(407\) | 1832.33i | 0.223158i | ||||||||
\(408\) | 7714.63i | 0.936106i | ||||||||
\(409\) | 596.921 | 0.0721658 | 0.0360829 | − | 0.999349i | \(-0.488512\pi\) | ||||
0.0360829 | + | 0.999349i | \(0.488512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5757.82 | 0.691027 | ||||||||
\(412\) | − 8242.49i | − 0.985627i | ||||||||
\(413\) | − 2285.54i | − 0.272310i | ||||||||
\(414\) | 3062.84 | 0.363600 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1455.95 | 0.171596 | ||||||||
\(417\) | − 5071.38i | − 0.595555i | ||||||||
\(418\) | − 322.214i | − 0.0377033i | ||||||||
\(419\) | −11560.5 | −1.34789 | −0.673944 | − | 0.738782i | \(-0.735401\pi\) | ||||
−0.673944 | + | 0.738782i | \(0.735401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15182.6 | 1.75761 | 0.878805 | − | 0.477182i | \(-0.158342\pi\) | ||||
0.878805 | + | 0.477182i | \(0.158342\pi\) | |||||||
\(422\) | 13958.5i | 1.61017i | ||||||||
\(423\) | − 1270.33i | − 0.146018i | ||||||||
\(424\) | 14719.6 | 1.68596 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2292.13 | −0.260691 | ||||||||
\(427\) | 3631.05i | 0.411519i | ||||||||
\(428\) | 18368.5i | 2.07448i | ||||||||
\(429\) | −810.935 | −0.0912641 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14902.7 | −1.66551 | −0.832757 | − | 0.553639i | \(-0.813239\pi\) | ||||
−0.832757 | + | 0.553639i | \(0.813239\pi\) | |||||||
\(432\) | 2203.82i | 0.245443i | ||||||||
\(433\) | 2269.85i | 0.251922i | 0.992035 | + | 0.125961i | \(0.0402014\pi\) | ||||
−0.992035 | + | 0.125961i | \(0.959799\pi\) | |||||||
\(434\) | 5358.26 | 0.592637 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21309.9 | 2.34074 | ||||||||
\(437\) | − 403.372i | − 0.0441554i | ||||||||
\(438\) | − 2294.71i | − 0.250332i | ||||||||
\(439\) | 13418.7 | 1.45886 | 0.729431 | − | 0.684054i | \(-0.239785\pi\) | ||||
0.729431 | + | 0.684054i | \(0.239785\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2816.36 | −0.304109 | ||||||||
\(442\) | − 7252.59i | − 0.780476i | ||||||||
\(443\) | − 11507.5i | − 1.23417i | −0.786896 | − | 0.617086i | \(-0.788313\pi\) | ||||
0.786896 | − | 0.617086i | \(-0.211687\pi\) | |||||||
\(444\) | −8351.98 | −0.892719 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7173.94 | 0.761650 | ||||||||
\(447\) | − 6233.65i | − 0.659601i | ||||||||
\(448\) | 1965.64i | 0.207294i | ||||||||
\(449\) | 16203.8 | 1.70313 | 0.851564 | − | 0.524250i | \(-0.175654\pi\) | ||||
0.851564 | + | 0.524250i | \(0.175654\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4665.11 | 0.487077 | ||||||||
\(452\) | − 15817.8i | − 1.64604i | ||||||||
\(453\) | − 8133.48i | − 0.843585i | ||||||||
\(454\) | −18188.3 | −1.88022 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 765.677 | 0.0786318 | ||||||||
\(457\) | 4912.79i | 0.502868i | 0.967874 | + | 0.251434i | \(0.0809022\pi\) | ||||
−0.967874 | + | 0.251434i | \(0.919098\pi\) | |||||||
\(458\) | 8428.70i | 0.859929i | ||||||||
\(459\) | 1602.95 | 0.163005 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14270.8 | −1.44178 | −0.720888 | − | 0.693051i | \(-0.756266\pi\) | ||||
−0.720888 | + | 0.693051i | \(0.756266\pi\) | |||||||
\(462\) | 899.613i | 0.0905926i | ||||||||
\(463\) | − 6656.46i | − 0.668146i | −0.942547 | − | 0.334073i | \(-0.891577\pi\) | ||||
0.942547 | − | 0.334073i | \(-0.108423\pi\) | |||||||
\(464\) | 21631.9 | 2.16430 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28744.8 | −2.85746 | ||||||||
\(467\) | 19347.7i | 1.91714i | 0.284853 | + | 0.958571i | \(0.408055\pi\) | ||||
−0.284853 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(468\) | − 3696.34i | − 0.365093i | ||||||||
\(469\) | −1720.33 | −0.169376 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7023.70 | 0.687123 | ||||||||
\(472\) | 18052.9i | 1.76050i | ||||||||
\(473\) | 1950.86i | 0.189642i | ||||||||
\(474\) | −6010.22 | −0.582402 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5441.18 | −0.523941 | ||||||||
\(477\) | − 3058.45i | − 0.293579i | ||||||||
\(478\) | 29012.9i | 2.77619i | ||||||||
\(479\) | −9826.69 | −0.937355 | −0.468678 | − | 0.883369i | \(-0.655269\pi\) | ||||
−0.468678 | + | 0.883369i | \(0.655269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4093.39 | 0.388030 | ||||||||
\(482\) | − 4883.28i | − 0.461467i | ||||||||
\(483\) | 1126.21i | 0.106095i | ||||||||
\(484\) | −2022.29 | −0.189922 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1208.01 | 0.112750 | ||||||||
\(487\) | 10278.1i | 0.956353i | 0.878264 | + | 0.478176i | \(0.158702\pi\) | ||||
−0.878264 | + | 0.478176i | \(0.841298\pi\) | |||||||
\(488\) | − 28680.7i | − 2.66048i | ||||||||
\(489\) | −10569.0 | −0.977400 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11397.1 | 1.04755 | 0.523773 | − | 0.851858i | \(-0.324524\pi\) | ||||
0.523773 | + | 0.851858i | \(0.324524\pi\) | |||||||
\(492\) | 21264.1i | 1.94850i | ||||||||
\(493\) | − 15734.0i | − 1.43737i | ||||||||
\(494\) | −719.819 | −0.0655591 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16043.3 | −1.45235 | ||||||||
\(497\) | − 842.817i | − 0.0760674i | ||||||||
\(498\) | 9728.39i | 0.875381i | ||||||||
\(499\) | 9179.17 | 0.823479 | 0.411740 | − | 0.911302i | \(-0.364921\pi\) | ||||
0.411740 | + | 0.911302i | \(0.364921\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12035.7 | 1.07329 | ||||||||
\(502\) | 21476.9i | 1.90948i | ||||||||
\(503\) | − 6782.80i | − 0.601253i | −0.953742 | − | 0.300626i | \(-0.902804\pi\) | ||||
0.953742 | − | 0.300626i | \(-0.0971957\pi\) | |||||||
\(504\) | −2137.75 | −0.188935 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3743.47 | −0.328889 | ||||||||
\(507\) | − 4779.39i | − 0.418659i | ||||||||
\(508\) | − 37784.6i | − 3.30004i | ||||||||
\(509\) | −6814.24 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 843.765 | 0.0730449 | ||||||||
\(512\) | − 23447.9i | − 2.02395i | ||||||||
\(513\) | − 159.093i | − 0.0136923i | ||||||||
\(514\) | 30942.4 | 2.65527 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8892.23 | −0.758641 | ||||||||
\(517\) | 1552.62i | 0.132078i | ||||||||
\(518\) | − 4541.01i | − 0.385175i | ||||||||
\(519\) | −9975.89 | −0.843724 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 206.712 | 0.0173824 | 0.00869118 | − | 0.999962i | \(-0.497233\pi\) | ||||
0.00869118 | + | 0.999962i | \(0.497233\pi\) | |||||||
\(522\) | − 11857.4i | − 0.994219i | ||||||||
\(523\) | 11375.9i | 0.951118i | 0.879684 | + | 0.475559i | \(0.157754\pi\) | ||||
−0.879684 | + | 0.475559i | \(0.842246\pi\) | |||||||
\(524\) | 954.781 | 0.0795989 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12870.3 | −1.06686 | ||||||||
\(527\) | 11669.1i | 0.964547i | ||||||||
\(528\) | − 2693.56i | − 0.222012i | ||||||||
\(529\) | 7480.63 | 0.614830 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3751.06 | 0.306557 | ||||||||
\(532\) | 540.036i | 0.0440104i | ||||||||
\(533\) | − 10421.8i | − 0.846936i | ||||||||
\(534\) | −18295.6 | −1.48264 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13588.4 | 1.09502 | ||||||||
\(537\) | − 79.9049i | − 0.00642114i | ||||||||
\(538\) | 29188.7i | 2.33906i | ||||||||
\(539\) | 3442.21 | 0.275077 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10228.1 | −0.812831 | −0.406415 | − | 0.913688i | \(-0.633221\pi\) | ||||
−0.406415 | + | 0.913688i | \(0.633221\pi\) | |||||||
\(542\) | − 16439.5i | − 1.30284i | ||||||||
\(543\) | − 5802.76i | − 0.458601i | ||||||||
\(544\) | 3517.49 | 0.277226 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2009.72 | 0.157524 | ||||||||
\(547\) | − 15538.9i | − 1.21461i | −0.794467 | − | 0.607307i | \(-0.792250\pi\) | ||||
0.794467 | − | 0.607307i | \(-0.207750\pi\) | |||||||
\(548\) | − 32077.0i | − 2.50048i | ||||||||
\(549\) | −5959.31 | −0.463274 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1561.60 | −0.120737 | ||||||||
\(552\) | − 8895.62i | − 0.685911i | ||||||||
\(553\) | − 2209.96i | − 0.169940i | ||||||||
\(554\) | 14224.5 | 1.09087 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28252.8 | −2.15501 | ||||||||
\(557\) | − 5191.17i | − 0.394896i | −0.980313 | − | 0.197448i | \(-0.936735\pi\) | ||||
0.980313 | − | 0.197448i | \(-0.0632653\pi\) | |||||||
\(558\) | 8794.03i | 0.667170i | ||||||||
\(559\) | 4358.17 | 0.329752 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1959.17 | −0.147444 | ||||||||
\(562\) | − 14854.3i | − 1.11493i | ||||||||
\(563\) | − 13722.9i | − 1.02727i | −0.858009 | − | 0.513635i | \(-0.828299\pi\) | ||||
0.858009 | − | 0.513635i | \(-0.171701\pi\) | |||||||
\(564\) | −7077.04 | −0.528364 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7231.13 | 0.537009 | ||||||||
\(567\) | 444.184i | 0.0328995i | ||||||||
\(568\) | 6657.20i | 0.491778i | ||||||||
\(569\) | −23209.0 | −1.70997 | −0.854986 | − | 0.518652i | \(-0.826434\pi\) | ||||
−0.854986 | + | 0.518652i | \(0.826434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13130.5 | −0.962337 | −0.481168 | − | 0.876628i | \(-0.659787\pi\) | ||||
−0.481168 | + | 0.876628i | \(0.659787\pi\) | |||||||
\(572\) | 4517.75i | 0.330239i | ||||||||
\(573\) | 10024.8i | 0.730874i | ||||||||
\(574\) | −11561.4 | −0.840705 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3226.03 | −0.233365 | ||||||||
\(577\) | − 12261.0i | − 0.884633i | −0.896859 | − | 0.442317i | \(-0.854157\pi\) | ||||
0.896859 | − | 0.442317i | \(-0.145843\pi\) | |||||||
\(578\) | 6901.86i | 0.496677i | ||||||||
\(579\) | 3881.90 | 0.278629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3577.13 | −0.255429 | ||||||||
\(582\) | 14313.3i | 1.01943i | ||||||||
\(583\) | 3738.11i | 0.265552i | ||||||||
\(584\) | −6664.69 | −0.472238 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −42685.5 | −3.00908 | ||||||||
\(587\) | − 3553.42i | − 0.249856i | −0.992166 | − | 0.124928i | \(-0.960130\pi\) | ||||
0.992166 | − | 0.124928i | \(-0.0398700\pi\) | |||||||
\(588\) | 15690.0i | 1.10042i | ||||||||
\(589\) | 1158.16 | 0.0810208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6903.50 | −0.480494 | ||||||||
\(592\) | 13596.4i | 0.943933i | ||||||||
\(593\) | − 1942.83i | − 0.134540i | −0.997735 | − | 0.0672701i | \(-0.978571\pi\) | ||||
0.997735 | − | 0.0672701i | \(-0.0214289\pi\) | |||||||
\(594\) | −1476.45 | −0.101986 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34727.9 | −2.38676 | ||||||||
\(597\) | − 9118.92i | − 0.625147i | ||||||||
\(598\) | 8362.84i | 0.571876i | ||||||||
\(599\) | −18585.4 | −1.26774 | −0.633871 | − | 0.773439i | \(-0.718535\pi\) | ||||
−0.633871 | + | 0.773439i | \(0.718535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8010.10 | 0.543658 | 0.271829 | − | 0.962346i | \(-0.412371\pi\) | ||||
0.271829 | + | 0.962346i | \(0.412371\pi\) | |||||||
\(602\) | − 4834.75i | − 0.327325i | ||||||||
\(603\) | − 2823.42i | − 0.190677i | ||||||||
\(604\) | −45311.9 | −3.05251 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18769.2 | −1.25816 | ||||||||
\(607\) | − 1537.69i | − 0.102822i | −0.998678 | − | 0.0514111i | \(-0.983628\pi\) | ||||
0.998678 | − | 0.0514111i | \(-0.0163719\pi\) | |||||||
\(608\) | − 349.110i | − 0.0232867i | ||||||||
\(609\) | 4359.94 | 0.290105 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3468.53 | 0.229659 | ||||||||
\(612\) | − 8930.11i | − 0.589834i | ||||||||
\(613\) | − 2298.75i | − 0.151461i | −0.997128 | − | 0.0757304i | \(-0.975871\pi\) | ||||
0.997128 | − | 0.0757304i | \(-0.0241289\pi\) | |||||||
\(614\) | −2629.93 | −0.172859 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2612.81 | 0.170898 | ||||||||
\(617\) | 6089.51i | 0.397333i | 0.980067 | + | 0.198666i | \(0.0636610\pi\) | ||||
−0.980067 | + | 0.198666i | \(0.936339\pi\) | |||||||
\(618\) | 7355.06i | 0.478744i | ||||||||
\(619\) | −12255.4 | −0.795775 | −0.397887 | − | 0.917434i | \(-0.630257\pi\) | ||||
−0.397887 | + | 0.917434i | \(0.630257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1848.34 | −0.119439 | ||||||||
\(622\) | − 24895.9i | − 1.60488i | ||||||||
\(623\) | − 6727.29i | − 0.432622i | ||||||||
\(624\) | −6017.36 | −0.386037 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39066.6 | 2.49427 | ||||||||
\(627\) | 194.447i | 0.0123851i | ||||||||
\(628\) | − 39129.3i | − 2.48635i | ||||||||
\(629\) | 9889.36 | 0.626891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25746.5 | −1.62433 | −0.812165 | − | 0.583428i | \(-0.801711\pi\) | ||||
−0.812165 | + | 0.583428i | \(0.801711\pi\) | |||||||
\(632\) | 17455.9i | 1.09867i | ||||||||
\(633\) | − 8423.58i | − 0.528922i | ||||||||
\(634\) | −38512.3 | −2.41249 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17038.8 | −1.06231 | ||||||||
\(637\) | − 7689.84i | − 0.478308i | ||||||||
\(638\) | 14492.3i | 0.899305i | ||||||||
\(639\) | 1383.24 | 0.0856340 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −598.022 | −0.0368494 | −0.0184247 | − | 0.999830i | \(-0.505865\pi\) | ||||
−0.0184247 | + | 0.999830i | \(0.505865\pi\) | |||||||
\(642\) | − 16390.9i | − 1.00763i | ||||||||
\(643\) | − 14610.9i | − 0.896109i | −0.894006 | − | 0.448054i | \(-0.852117\pi\) | ||||
0.894006 | − | 0.448054i | \(-0.147883\pi\) | |||||||
\(644\) | 6274.13 | 0.383906 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1739.04 | −0.105916 | ||||||||
\(647\) | − 17252.3i | − 1.04831i | −0.851622 | − | 0.524156i | \(-0.824381\pi\) | ||||
0.851622 | − | 0.524156i | \(-0.175619\pi\) | |||||||
\(648\) | − 3508.50i | − 0.212696i | ||||||||
\(649\) | −4584.63 | −0.277292 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3233.56 | −0.194675 | ||||||||
\(652\) | 58880.5i | 3.53671i | ||||||||
\(653\) | 17768.6i | 1.06484i | 0.846481 | + | 0.532418i | \(0.178717\pi\) | ||||
−0.846481 | + | 0.532418i | \(0.821283\pi\) | |||||||
\(654\) | −19015.6 | −1.13696 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34616.4 | 2.06028 | ||||||||
\(657\) | 1384.80i | 0.0822314i | ||||||||
\(658\) | − 3847.82i | − 0.227969i | ||||||||
\(659\) | 17594.9 | 1.04006 | 0.520031 | − | 0.854147i | \(-0.325920\pi\) | ||||
0.520031 | + | 0.854147i | \(0.325920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23355.9 | 1.37434 | 0.687170 | − | 0.726497i | \(-0.258853\pi\) | ||||
0.687170 | + | 0.726497i | \(0.258853\pi\) | |||||||
\(662\) | 6736.44i | 0.395497i | ||||||||
\(663\) | 4376.74i | 0.256378i | ||||||||
\(664\) | 28254.8 | 1.65136 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7452.76 | 0.433617 | ||||||||
\(667\) | 18142.6i | 1.05320i | ||||||||
\(668\) | − 67051.4i | − 3.88368i | ||||||||
\(669\) | −4329.28 | −0.250194 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7283.61 | 0.419047 | ||||||||
\(672\) | 974.708i | 0.0559527i | ||||||||
\(673\) | 2340.47i | 0.134054i | 0.997751 | + | 0.0670271i | \(0.0213514\pi\) | ||||
−0.997751 | + | 0.0670271i | \(0.978649\pi\) | |||||||
\(674\) | −12910.1 | −0.737803 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26626.1 | −1.51491 | ||||||||
\(677\) | − 16562.2i | − 0.940234i | −0.882604 | − | 0.470117i | \(-0.844212\pi\) | ||||
0.882604 | − | 0.470117i | \(-0.155788\pi\) | |||||||
\(678\) | 14114.8i | 0.799522i | ||||||||
\(679\) | −5263.01 | −0.297461 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10976.1 | 0.617630 | ||||||||
\(682\) | − 10748.3i | − 0.603478i | ||||||||
\(683\) | − 22303.4i | − 1.24951i | −0.780821 | − | 0.624755i | \(-0.785199\pi\) | ||||
0.780821 | − | 0.624755i | \(-0.214801\pi\) | |||||||
\(684\) | −886.313 | −0.0495454 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17881.3 | −0.995204 | ||||||||
\(687\) | − 5086.49i | − 0.282477i | ||||||||
\(688\) | 14475.9i | 0.802163i | ||||||||
\(689\) | 8350.87 | 0.461745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6244.91 | 0.343802 | 0.171901 | − | 0.985114i | \(-0.445009\pi\) | ||||
0.171901 | + | 0.985114i | \(0.445009\pi\) | |||||||
\(692\) | 55576.0i | 3.05301i | ||||||||
\(693\) | − 542.892i | − 0.0297587i | ||||||||
\(694\) | −1326.42 | −0.0725508 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34438.1 | −1.87554 | ||||||||
\(697\) | − 25178.3i | − 1.36829i | ||||||||
\(698\) | 52443.5i | 2.84386i | ||||||||
\(699\) | 17346.7 | 0.938645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15277.7 | −0.823154 | −0.411577 | − | 0.911375i | \(-0.635022\pi\) | ||||
−0.411577 | + | 0.911375i | \(0.635022\pi\) | |||||||
\(702\) | 3298.37i | 0.177335i | ||||||||
\(703\) | − 981.519i | − 0.0526582i | ||||||||
\(704\) | 3942.93 | 0.211086 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35557.3 | 1.89549 | ||||||||
\(707\) | − 6901.43i | − 0.367122i | ||||||||
\(708\) | − 20897.3i | − 1.10928i | ||||||||
\(709\) | 11732.1 | 0.621449 | 0.310725 | − | 0.950500i | \(-0.399428\pi\) | ||||
0.310725 | + | 0.950500i | \(0.399428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3627.00 | 0.191313 | ||||||||
\(712\) | 53137.2i | 2.79691i | ||||||||
\(713\) | − 13455.5i | − 0.706750i | ||||||||
\(714\) | 4855.35 | 0.254491 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −445.153 | −0.0232349 | ||||||||
\(717\) | − 17508.5i | − 0.911947i | ||||||||
\(718\) | − 1785.57i | − 0.0928093i | ||||||||
\(719\) | 19006.2 | 0.985828 | 0.492914 | − | 0.870078i | \(-0.335932\pi\) | ||||
0.492914 | + | 0.870078i | \(0.335932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2704.45 | −0.139694 | ||||||||
\(722\) | − 33925.1i | − 1.74870i | ||||||||
\(723\) | 2946.92i | 0.151587i | ||||||||
\(724\) | −32327.4 | −1.65945 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1804.56 | 0.0922498 | ||||||||
\(727\) | 2650.77i | 0.135229i | 0.997712 | + | 0.0676146i | \(0.0215388\pi\) | ||||
−0.997712 | + | 0.0676146i | \(0.978461\pi\) | |||||||
\(728\) | − 5836.96i | − 0.297160i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10529.1 | 0.532738 | ||||||||
\(732\) | 33199.5i | 1.67635i | ||||||||
\(733\) | 8854.22i | 0.446164i | 0.974800 | + | 0.223082i | \(0.0716117\pi\) | ||||
−0.974800 | + | 0.223082i | \(0.928388\pi\) | |||||||
\(734\) | −44952.2 | −2.26051 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4055.96 | −0.203131 | ||||||||
\(737\) | 3450.84i | 0.172474i | ||||||||
\(738\) | − 18974.7i | − 0.946435i | ||||||||
\(739\) | −17174.8 | −0.854921 | −0.427460 | − | 0.904034i | \(-0.640592\pi\) | ||||
−0.427460 | + | 0.904034i | \(0.640592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 434.391 | 0.0215354 | ||||||||
\(742\) | − 9264.06i | − 0.458348i | ||||||||
\(743\) | 9800.30i | 0.483901i | 0.970289 | + | 0.241950i | \(0.0777871\pi\) | ||||
−0.970289 | + | 0.241950i | \(0.922213\pi\) | |||||||
\(744\) | 25541.1 | 1.25858 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −59301.6 | −2.91044 | ||||||||
\(747\) | − 5870.82i | − 0.287553i | ||||||||
\(748\) | 10914.6i | 0.533525i | ||||||||
\(749\) | 6026.92 | 0.294017 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2781.25 | 0.135139 | 0.0675695 | − | 0.997715i | \(-0.478476\pi\) | ||||
0.0675695 | + | 0.997715i | \(0.478476\pi\) | |||||||
\(752\) | 11520.9i | 0.558675i | ||||||||
\(753\) | − 12960.7i | − 0.627243i | ||||||||
\(754\) | 32375.6 | 1.56372 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2474.57 | 0.119046 | ||||||||
\(757\) | 3010.87i | 0.144560i | 0.997384 | + | 0.0722800i | \(0.0230275\pi\) | ||||
−0.997384 | + | 0.0722800i | \(0.976972\pi\) | |||||||
\(758\) | − 32591.8i | − 1.56172i | ||||||||
\(759\) | 2259.08 | 0.108036 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2709.54 | −0.129068 | −0.0645340 | − | 0.997916i | \(-0.520556\pi\) | ||||
−0.0645340 | + | 0.997916i | \(0.520556\pi\) | |||||||
\(762\) | 33716.5i | 1.60291i | ||||||||
\(763\) | − 6992.03i | − 0.331754i | ||||||||
\(764\) | 55848.4 | 2.64466 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 53207.7 | 2.50976 | ||||||||
\(767\) | 10242.0i | 0.482159i | ||||||||
\(768\) | 25041.2i | 1.17656i | ||||||||
\(769\) | 28121.1 | 1.31869 | 0.659345 | − | 0.751841i | \(-0.270834\pi\) | ||||
0.659345 | + | 0.751841i | \(0.270834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18672.9 | −0.872227 | ||||||||
\(772\) | − 21626.2i | − 1.00822i | ||||||||
\(773\) | − 4274.61i | − 0.198897i | −0.995043 | − | 0.0994483i | \(-0.968292\pi\) | ||||
0.995043 | − | 0.0994483i | \(-0.0317078\pi\) | |||||||
\(774\) | 7934.85 | 0.368491 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 41571.2 | 1.92309 | ||||||||
\(777\) | 2740.38i | 0.126526i | ||||||||
\(778\) | 32065.9i | 1.47766i | ||||||||
\(779\) | −2498.95 | −0.114935 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1690.63 | −0.0774589 | ||||||||
\(782\) | 20204.1i | 0.923909i | ||||||||
\(783\) | 7155.59i | 0.326590i | ||||||||
\(784\) | 25542.2 | 1.16355 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −851.985 | −0.0386632 | ||||||||
\(787\) | 19107.9i | 0.865469i | 0.901522 | + | 0.432734i | \(0.142451\pi\) | ||||
−0.901522 | + | 0.432734i | \(0.857549\pi\) | |||||||
\(788\) | 38459.6i | 1.73866i | ||||||||
\(789\) | 7766.85 | 0.350453 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5190.01 | −0.233294 | ||||||||
\(792\) | 4288.17i | 0.192391i | ||||||||
\(793\) | − 16271.4i | − 0.728645i | ||||||||
\(794\) | 62269.4 | 2.78320 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −50801.9 | −2.26209 | ||||||||
\(797\) | 27518.4i | 1.22303i | 0.791234 | + | 0.611513i | \(0.209439\pi\) | ||||
−0.791234 | + | 0.611513i | \(0.790561\pi\) | |||||||
\(798\) | − 481.893i | − 0.0213770i | ||||||||
\(799\) | 8379.74 | 0.371031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11040.9 | 0.487030 | ||||||||
\(802\) | 45335.2i | 1.99606i | ||||||||
\(803\) | − 1692.53i | − 0.0743811i | ||||||||
\(804\) | −15729.4 | −0.689965 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24011.4 | −1.04934 | ||||||||
\(807\) | − 17614.6i | − 0.768356i | ||||||||
\(808\) | 54512.7i | 2.37345i | ||||||||
\(809\) | −21986.6 | −0.955511 | −0.477755 | − | 0.878493i | \(-0.658550\pi\) | ||||
−0.477755 | + | 0.878493i | \(0.658550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11835.1 | 0.512437 | 0.256218 | − | 0.966619i | \(-0.417523\pi\) | ||||
0.256218 | + | 0.966619i | \(0.417523\pi\) | |||||||
\(812\) | − 24289.4i | − 1.04974i | ||||||||
\(813\) | 9920.79i | 0.427967i | ||||||||
\(814\) | −9108.93 | −0.392221 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14537.6 | −0.623672 | ||||||||
\(817\) | − 1045.01i | − 0.0447494i | ||||||||
\(818\) | 2967.43i | 0.126838i | ||||||||
\(819\) | −1212.81 | −0.0517448 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7890.58 | −0.335424 | −0.167712 | − | 0.985836i | \(-0.553638\pi\) | ||||
−0.167712 | + | 0.985836i | \(0.553638\pi\) | |||||||
\(822\) | 28623.4i | 1.21455i | ||||||||
\(823\) | − 1000.74i | − 0.0423861i | −0.999775 | − | 0.0211930i | \(-0.993254\pi\) | ||||
0.999775 | − | 0.0211930i | \(-0.00674646\pi\) | |||||||
\(824\) | 21361.8 | 0.903123 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11362.0 | 0.478611 | ||||||||
\(827\) | 22764.2i | 0.957181i | 0.878038 | + | 0.478590i | \(0.158852\pi\) | ||||
−0.878038 | + | 0.478590i | \(0.841148\pi\) | |||||||
\(828\) | 10297.2i | 0.432188i | ||||||||
\(829\) | −39835.8 | −1.66894 | −0.834471 | − | 0.551051i | \(-0.814227\pi\) | ||||
−0.834471 | + | 0.551051i | \(0.814227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8584.10 | −0.358338 | ||||||||
\(832\) | − 8808.43i | − 0.367040i | ||||||||
\(833\) | − 18578.1i | − 0.772742i | ||||||||
\(834\) | 25211.0 | 1.04674 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1083.27 | 0.0448155 | ||||||||
\(837\) | − 5306.96i | − 0.219158i | ||||||||
\(838\) | − 57469.7i | − 2.36904i | ||||||||
\(839\) | −23330.9 | −0.960037 | −0.480019 | − | 0.877258i | \(-0.659370\pi\) | ||||
−0.480019 | + | 0.877258i | \(0.659370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45847.5 | 1.87984 | ||||||||
\(842\) | 75476.0i | 3.08916i | ||||||||
\(843\) | 8964.14i | 0.366241i | ||||||||
\(844\) | −46928.1 | −1.91390 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6315.09 | 0.256640 | ||||||||
\(847\) | 663.535i | 0.0269177i | ||||||||
\(848\) | 27737.8i | 1.12326i | ||||||||
\(849\) | −4363.79 | −0.176402 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11403.3 | −0.459341 | ||||||||
\(852\) | − 7706.08i | − 0.309866i | ||||||||
\(853\) | − 22937.3i | − 0.920701i | −0.887737 | − | 0.460351i | \(-0.847724\pi\) | ||||
0.887737 | − | 0.460351i | \(-0.152276\pi\) | |||||||
\(854\) | −18050.8 | −0.723284 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −47605.2 | −1.90083 | ||||||||
\(857\) | − 38472.3i | − 1.53348i | −0.641961 | − | 0.766738i | \(-0.721879\pi\) | ||||
0.641961 | − | 0.766738i | \(-0.278121\pi\) | |||||||
\(858\) | − 4031.34i | − 0.160405i | ||||||||
\(859\) | 22970.3 | 0.912384 | 0.456192 | − | 0.889881i | \(-0.349213\pi\) | ||||
0.456192 | + | 0.889881i | \(0.349213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6977.00 | 0.276162 | ||||||||
\(862\) | − 74084.5i | − 2.92730i | ||||||||
\(863\) | 33587.6i | 1.32484i | 0.749133 | + | 0.662420i | \(0.230470\pi\) | ||||
−0.749133 | + | 0.662420i | \(0.769530\pi\) | |||||||
\(864\) | −1599.70 | −0.0629895 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11284.0 | −0.442777 | ||||||||
\(867\) | − 4165.08i | − 0.163153i | ||||||||
\(868\) | 18014.3i | 0.704430i | ||||||||
\(869\) | −4433.00 | −0.173049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7709.12 | 0.299901 | ||||||||
\(872\) | 55228.3i | 2.14480i | ||||||||
\(873\) | − 8637.71i | − 0.334871i | ||||||||
\(874\) | 2005.25 | 0.0776073 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7714.74 | 0.297554 | ||||||||
\(877\) | − 704.130i | − 0.0271115i | −0.999908 | − | 0.0135558i | \(-0.995685\pi\) | ||||
0.999908 | − | 0.0135558i | \(-0.00431506\pi\) | |||||||
\(878\) | 66707.5i | 2.56409i | ||||||||
\(879\) | 25759.5 | 0.988450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9746.33 | 0.372715 | 0.186358 | − | 0.982482i | \(-0.440332\pi\) | ||||
0.186358 | + | 0.982482i | \(0.440332\pi\) | |||||||
\(882\) | − 14000.7i | − 0.534501i | ||||||||
\(883\) | 8774.24i | 0.334402i | 0.985923 | + | 0.167201i | \(0.0534728\pi\) | ||||
−0.985923 | + | 0.167201i | \(0.946527\pi\) | |||||||
\(884\) | 24383.0 | 0.927701 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 57206.4 | 2.16917 | ||||||||
\(887\) | − 13505.1i | − 0.511224i | −0.966779 | − | 0.255612i | \(-0.917723\pi\) | ||||
0.966779 | − | 0.255612i | \(-0.0822770\pi\) | |||||||
\(888\) | − 21645.6i | − 0.817993i | ||||||||
\(889\) | −12397.5 | −0.467717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 24118.6i | 0.905324i | ||||||||
\(893\) | − 831.689i | − 0.0311662i | ||||||||
\(894\) | 30988.9 | 1.15931 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12370.9 | −0.461252 | ||||||||
\(897\) | − 5046.75i | − 0.187855i | ||||||||
\(898\) | 80552.8i | 2.99341i | ||||||||
\(899\) | −52091.1 | −1.93252 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20175.1 | 0.745984 | ||||||||
\(902\) | 23191.3i | 0.856083i | ||||||||
\(903\) | 2917.64i | 0.107523i | ||||||||
\(904\) | 40994.6 | 1.50825 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 40433.4 | 1.48268 | ||||||||
\(907\) | − 2523.23i | − 0.0923732i | −0.998933 | − | 0.0461866i | \(-0.985293\pi\) | ||||
0.998933 | − | 0.0461866i | \(-0.0147069\pi\) | |||||||
\(908\) | − 61148.4i | − 2.23489i | ||||||||
\(909\) | 11326.7 | 0.413293 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32285.3 | −1.17416 | −0.587080 | − | 0.809529i | \(-0.699723\pi\) | ||||
−0.587080 | + | 0.809529i | \(0.699723\pi\) | |||||||
\(912\) | 1442.85i | 0.0523877i | ||||||||
\(913\) | 7175.45i | 0.260101i | ||||||||
\(914\) | −24422.6 | −0.883838 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28337.0 | −1.02214 | ||||||||
\(917\) | − 313.274i | − 0.0112816i | ||||||||
\(918\) | 7968.65i | 0.286497i | ||||||||
\(919\) | 40956.5 | 1.47011 | 0.735055 | − | 0.678008i | \(-0.237156\pi\) | ||||
0.735055 | + | 0.678008i | \(0.237156\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1587.09 | 0.0567821 | ||||||||
\(922\) | − 70943.6i | − 2.53406i | ||||||||
\(923\) | 3776.83i | 0.134687i | ||||||||
\(924\) | −3024.47 | −0.107682 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33090.8 | 1.17433 | ||||||||
\(927\) | − 4438.58i | − 0.157262i | ||||||||
\(928\) | 15702.1i | 0.555437i | ||||||||
\(929\) | 6728.41 | 0.237623 | 0.118812 | − | 0.992917i | \(-0.462092\pi\) | ||||
0.118812 | + | 0.992917i | \(0.462092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1843.88 | −0.0649095 | ||||||||
\(932\) | − 96639.1i | − 3.39648i | ||||||||
\(933\) | 15024.0i | 0.527185i | ||||||||
\(934\) | −96181.9 | −3.36956 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9579.69 | 0.334532 | ||||||||
\(937\) | − 36377.8i | − 1.26831i | −0.773205 | − | 0.634157i | \(-0.781347\pi\) | ||||
0.773205 | − | 0.634157i | \(-0.218653\pi\) | |||||||
\(938\) | − 8552.13i | − 0.297694i | ||||||||
\(939\) | −23575.6 | −0.819340 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25907.0 | 0.897496 | 0.448748 | − | 0.893658i | \(-0.351870\pi\) | ||||
0.448748 | + | 0.893658i | \(0.351870\pi\) | |||||||
\(942\) | 34916.4i | 1.20768i | ||||||||
\(943\) | 29032.7i | 1.00258i | ||||||||
\(944\) | −34019.2 | −1.17291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9698.15 | −0.333313 | ||||||||
\(947\) | 37096.3i | 1.27293i | 0.771304 | + | 0.636466i | \(0.219605\pi\) | ||||
−0.771304 | + | 0.636466i | \(0.780395\pi\) | |||||||
\(948\) | − 20206.2i | − 0.692263i | ||||||||
\(949\) | −3781.07 | −0.129335 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23241.1 | 0.792476 | ||||||||
\(952\) | − 14101.7i | − 0.480084i | ||||||||
\(953\) | 15323.7i | 0.520865i | 0.965492 | + | 0.260432i | \(0.0838651\pi\) | ||||
−0.965492 | + | 0.260432i | \(0.916135\pi\) | |||||||
\(954\) | 15204.3 | 0.515992 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −97540.4 | −3.29988 | ||||||||
\(957\) | − 8745.72i | − 0.295412i | ||||||||
\(958\) | − 48850.7i | − 1.64749i | ||||||||
\(959\) | −10524.8 | −0.354395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8842.46 | 0.296817 | ||||||||
\(962\) | 20349.2i | 0.682000i | ||||||||
\(963\) | 9891.45i | 0.330994i | ||||||||
\(964\) | 16417.4 | 0.548516 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5598.62 | −0.186473 | ||||||||
\(967\) | − 53388.0i | − 1.77543i | −0.460391 | − | 0.887716i | \(-0.652291\pi\) | ||||
0.460391 | − | 0.887716i | \(-0.347709\pi\) | |||||||
\(968\) | − 5241.10i | − 0.174024i | ||||||||
\(969\) | 1049.46 | 0.0347921 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36325.7 | −1.20056 | −0.600281 | − | 0.799789i | \(-0.704945\pi\) | ||||
−0.600281 | + | 0.799789i | \(0.704945\pi\) | |||||||
\(972\) | 4061.28i | 0.134018i | ||||||||
\(973\) | 9270.07i | 0.305432i | ||||||||
\(974\) | −51094.6 | −1.68088 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 54046.4 | 1.77252 | ||||||||
\(977\) | 48608.7i | 1.59174i | 0.605468 | + | 0.795870i | \(0.292986\pi\) | ||||
−0.605468 | + | 0.795870i | \(0.707014\pi\) | |||||||
\(978\) | − 52541.1i | − 1.71787i | ||||||||
\(979\) | −13494.4 | −0.440535 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11475.4 | 0.373477 | ||||||||
\(982\) | 56657.7i | 1.84116i | ||||||||
\(983\) | − 31762.6i | − 1.03059i | −0.857013 | − | 0.515295i | \(-0.827682\pi\) | ||||
0.857013 | − | 0.515295i | \(-0.172318\pi\) | |||||||
\(984\) | −55109.6 | −1.78540 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 78217.2 | 2.52631 | ||||||||
\(987\) | 2322.06i | 0.0748854i | ||||||||
\(988\) | − 2420.01i | − 0.0779258i | ||||||||
\(989\) | −12140.9 | −0.390352 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5073.82 | −0.162639 | −0.0813195 | − | 0.996688i | \(-0.525913\pi\) | ||||
−0.0813195 | + | 0.996688i | \(0.525913\pi\) | |||||||
\(992\) | − 11645.5i | − 0.372726i | ||||||||
\(993\) | − 4065.25i | − 0.129916i | ||||||||
\(994\) | 4189.83 | 0.133696 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −32706.5 | −1.04051 | ||||||||
\(997\) | 24607.0i | 0.781657i | 0.920464 | + | 0.390828i | \(0.127811\pi\) | ||||
−0.920464 | + | 0.390828i | \(0.872189\pi\) | |||||||
\(998\) | 45631.8i | 1.44734i | ||||||||
\(999\) | −4497.54 | −0.142438 |
(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 | 825.4.c.k.199.5 | 6 | ||
5.2 | odd | 4 | 825.4.a.r.1.1 | 3 | |||
5.3 | odd | 4 | 165.4.a.e.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 825.4.c.k.199.2 | 6 | ||
15.2 | even | 4 | 2475.4.a.t.1.3 | 3 | |||
15.8 | even | 4 | 495.4.a.k.1.1 | 3 | |||
55.43 | even | 4 | 1815.4.a.r.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.e.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
495.4.a.k.1.1 | 3 | 15.8 | even | 4 | |||
825.4.a.r.1.1 | 3 | 5.2 | odd | 4 | |||
825.4.c.k.199.2 | 6 | 5.4 | even | 2 | inner | ||
825.4.c.k.199.5 | 6 | 1.1 | even | 1 | trivial | ||
1815.4.a.r.1.1 | 3 | 55.43 | even | 4 | |||
2475.4.a.t.1.3 | 3 | 15.2 | even | 4 |