Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (of order \(2\), degree \(1\), 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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.16 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.25 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.31914i | − | 0.579785i | −0.957059 | − | 0.289892i | \(-0.906380\pi\) | ||
0.957059 | − | 0.289892i | \(-0.0936195\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.6216 | 0.663850 | ||||||||
\(5\) | 38.6371 | 1.54548 | 0.772742 | − | 0.634720i | \(-0.218885\pi\) | ||||
0.772742 | + | 0.634720i | \(0.218885\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.48964 | 0.193666 | 0.0968331 | − | 0.995301i | \(-0.469129\pi\) | ||||
0.0968331 | + | 0.995301i | \(0.469129\pi\) | |||||||
\(8\) | − | 61.7392i | − | 0.964675i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 89.6048i | − | 0.896048i | ||||||
\(11\) | 58.4880i | 0.483372i | 0.970355 | + | 0.241686i | \(0.0777004\pi\) | ||||
−0.970355 | + | 0.241686i | \(0.922300\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 290.914i | 1.72138i | 0.509125 | + | 0.860692i | \(0.329969\pi\) | ||||
−0.509125 | + | 0.860692i | \(0.670031\pi\) | |||||||
\(14\) | − | 22.0078i | − | 0.112285i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 26.7637 | 0.104546 | ||||||||
\(17\) | 467.291 | 1.61692 | 0.808462 | − | 0.588548i | \(-0.200300\pi\) | ||||
0.808462 | + | 0.588548i | \(0.200300\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −261.109 | −0.723294 | −0.361647 | − | 0.932315i | \(-0.617785\pi\) | ||||
−0.361647 | + | 0.932315i | \(0.617785\pi\) | |||||||
\(20\) | 410.387 | 1.02597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 135.642 | 0.280252 | ||||||||
\(23\) | − | 190.226i | − | 0.359595i | −0.983704 | − | 0.179798i | \(-0.942456\pi\) | ||
0.983704 | − | 0.179798i | \(-0.0575443\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 867.825 | 1.38852 | ||||||||
\(26\) | 674.670 | 0.998033 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 100.795 | 0.128565 | ||||||||
\(29\) | 407.645 | 0.484714 | 0.242357 | − | 0.970187i | \(-0.422079\pi\) | ||||
0.242357 | + | 0.970187i | \(0.422079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1893.18i | 1.97001i | 0.172518 | + | 0.985006i | \(0.444810\pi\) | ||||
−0.172518 | + | 0.985006i | \(0.555190\pi\) | |||||||
\(32\) | − | 1049.90i | − | 1.02529i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1083.71i | − | 0.937468i | ||||||
\(35\) | 366.652 | 0.299308 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 306.386i | − | 0.223803i | −0.993719 | − | 0.111902i | \(-0.964306\pi\) | ||
0.993719 | − | 0.111902i | \(-0.0356941\pi\) | |||||||
\(38\) | 605.549i | 0.419355i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2385.42i | − | 1.49089i | ||||||
\(41\) | 486.816 | 0.289599 | 0.144799 | − | 0.989461i | \(-0.453746\pi\) | ||||
0.144799 | + | 0.989461i | \(0.453746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1830.69i | − | 0.990098i | −0.868865 | − | 0.495049i | \(-0.835150\pi\) | ||
0.868865 | − | 0.495049i | \(-0.164850\pi\) | |||||||
\(44\) | 621.236i | 0.320886i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −441.160 | −0.208488 | ||||||||
\(47\) | 1576.43i | 0.713637i | 0.934174 | + | 0.356819i | \(0.116139\pi\) | ||||
−0.934174 | + | 0.356819i | \(0.883861\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2310.95 | −0.962493 | ||||||||
\(50\) | − | 2012.61i | − | 0.805043i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3089.97i | 1.14274i | ||||||||
\(53\) | 2715.01 | 0.966541 | 0.483271 | − | 0.875471i | \(-0.339449\pi\) | ||||
0.483271 | + | 0.875471i | \(0.339449\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2259.81i | 0.747043i | ||||||||
\(56\) | − | 585.883i | − | 0.186825i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 945.384i | − | 0.281030i | ||||||
\(59\) | −3310.90 | − | 1074.84i | −0.951135 | − | 0.308774i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3956.15i | 1.06320i | 0.846997 | + | 0.531598i | \(0.178408\pi\) | ||||
−0.846997 | + | 0.531598i | \(0.821592\pi\) | |||||||
\(62\) | 4390.55 | 1.14218 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2006.63 | −0.489901 | ||||||||
\(65\) | 11240.1i | 2.66037i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5269.11i | 1.17378i | 0.809666 | + | 0.586891i | \(0.199648\pi\) | ||||
−0.809666 | + | 0.586891i | \(0.800352\pi\) | |||||||
\(68\) | 4963.37 | 1.07339 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 850.317i | − | 0.173534i | ||||||
\(71\) | −7353.03 | −1.45865 | −0.729323 | − | 0.684169i | \(-0.760165\pi\) | ||||
−0.729323 | + | 0.684169i | \(0.760165\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8254.16i | − | 1.54891i | −0.632627 | − | 0.774457i | \(-0.718023\pi\) | ||
0.632627 | − | 0.774457i | \(-0.281977\pi\) | |||||||
\(74\) | −710.553 | −0.129758 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2773.40 | −0.480158 | ||||||||
\(77\) | 555.030i | 0.0936128i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8388.54 | 1.34410 | 0.672051 | − | 0.740505i | \(-0.265414\pi\) | ||||
0.672051 | + | 0.740505i | \(0.265414\pi\) | |||||||
\(80\) | 1034.07 | 0.161574 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1128.99i | − | 0.167905i | ||||||
\(83\) | 8211.40i | 1.19196i | 0.803000 | + | 0.595979i | \(0.203236\pi\) | ||||
−0.803000 | + | 0.595979i | \(0.796764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18054.8 | 2.49893 | ||||||||
\(86\) | −4245.63 | −0.574044 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3611.00 | 0.466297 | ||||||||
\(89\) | − | 13635.4i | − | 1.72142i | −0.509092 | − | 0.860712i | \(-0.670019\pi\) | ||
0.509092 | − | 0.860712i | \(-0.329981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2760.67i | 0.333374i | ||||||||
\(92\) | − | 2020.50i | − | 0.238717i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3655.95 | 0.413756 | ||||||||
\(95\) | −10088.5 | −1.11784 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5348.42i | 0.568436i | 0.958760 | + | 0.284218i | \(0.0917340\pi\) | ||||
−0.958760 | + | 0.284218i | \(0.908266\pi\) | |||||||
\(98\) | 5359.41i | 0.558039i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9217.68 | 0.921768 | ||||||||
\(101\) | − | 11578.9i | − | 1.13508i | −0.823347 | − | 0.567538i | \(-0.807896\pi\) | ||
0.823347 | − | 0.567538i | \(-0.192104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18902.9i | − | 1.78178i | −0.454222 | − | 0.890888i | \(-0.650083\pi\) | ||
0.454222 | − | 0.890888i | \(-0.349917\pi\) | |||||||
\(104\) | 17960.8 | 1.66058 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 6296.50i | − | 0.560386i | ||||||
\(107\) | −15473.8 | −1.35155 | −0.675773 | − | 0.737110i | \(-0.736190\pi\) | ||||
−0.675773 | + | 0.737110i | \(0.736190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10396.5i | − | 0.875049i | −0.899206 | − | 0.437525i | \(-0.855855\pi\) | ||
0.899206 | − | 0.437525i | \(-0.144145\pi\) | |||||||
\(110\) | 5240.80 | 0.433124 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 253.978 | 0.0202470 | ||||||||
\(113\) | − | 3655.52i | − | 0.286281i | −0.989702 | − | 0.143141i | \(-0.954280\pi\) | ||
0.989702 | − | 0.143141i | \(-0.0457201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 7349.77i | − | 0.555748i | ||||||
\(116\) | 4329.83 | 0.321777 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2492.71 | + | 7678.44i | −0.179022 | + | 0.551454i | ||||
\(119\) | 4434.42 | 0.313143 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11220.2 | 0.766352 | ||||||||
\(122\) | 9174.87 | 0.616425 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20108.6i | 1.30779i | ||||||||
\(125\) | 9382.04 | 0.600451 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8960.25 | 0.555536 | 0.277768 | − | 0.960648i | \(-0.410405\pi\) | ||||
0.277768 | + | 0.960648i | \(0.410405\pi\) | |||||||
\(128\) | − | 12144.7i | − | 0.741252i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 26067.3 | 1.54244 | ||||||||
\(131\) | − | 12620.5i | − | 0.735417i | −0.929941 | − | 0.367708i | \(-0.880142\pi\) | ||
0.929941 | − | 0.367708i | \(-0.119858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2477.83 | −0.140078 | ||||||||
\(134\) | 12219.8 | 0.680541 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 28850.2i | − | 1.55981i | ||||||
\(137\) | 21067.5 | 1.12246 | 0.561232 | − | 0.827659i | \(-0.310328\pi\) | ||||
0.561232 | + | 0.827659i | \(0.310328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23705.1 | 1.22691 | 0.613455 | − | 0.789729i | \(-0.289779\pi\) | ||||
0.613455 | + | 0.789729i | \(0.289779\pi\) | |||||||
\(140\) | 3894.43 | 0.198695 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17052.7i | 0.845701i | ||||||||
\(143\) | −17015.0 | −0.832069 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15750.2 | 0.749118 | ||||||||
\(146\) | −19142.5 | −0.898037 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 3254.31i | − | 0.148572i | ||||||
\(149\) | − | 5346.43i | − | 0.240819i | −0.992724 | − | 0.120410i | \(-0.961579\pi\) | ||
0.992724 | − | 0.120410i | \(-0.0384208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 27531.3i | 1.20746i | 0.797188 | + | 0.603731i | \(0.206320\pi\) | ||||
−0.797188 | + | 0.603731i | \(0.793680\pi\) | |||||||
\(152\) | 16120.7i | 0.697744i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1287.19 | 0.0542753 | ||||||||
\(155\) | 73147.1i | 3.04462i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 29614.0i | − | 1.20143i | −0.799465 | − | 0.600713i | \(-0.794883\pi\) | ||
0.799465 | − | 0.600713i | \(-0.205117\pi\) | |||||||
\(158\) | − | 19454.2i | − | 0.779289i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 40564.9i | − | 1.58457i | ||||||
\(161\) | − | 1805.17i | − | 0.0696414i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 523.410 | 0.0197000 | 0.00985001 | − | 0.999951i | \(-0.496865\pi\) | ||||
0.00985001 | + | 0.999951i | \(0.496865\pi\) | |||||||
\(164\) | 5170.76 | 0.192250 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19043.4 | 0.691079 | ||||||||
\(167\) | −8380.72 | −0.300503 | −0.150251 | − | 0.988648i | \(-0.548008\pi\) | ||||
−0.150251 | + | 0.988648i | \(0.548008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −56070.0 | −1.96317 | ||||||||
\(170\) | − | 41871.5i | − | 1.44884i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 19444.9i | − | 0.657276i | ||||||
\(173\) | − | 31624.9i | − | 1.05666i | −0.849038 | − | 0.528331i | \(-0.822818\pi\) | ||
0.849038 | − | 0.528331i | \(-0.177182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8235.35 | 0.268909 | ||||||||
\(176\) | 1565.36i | 0.0505345i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −31622.4 | −0.998055 | ||||||||
\(179\) | 14600.1i | 0.455668i | 0.973700 | + | 0.227834i | \(0.0731644\pi\) | ||||
−0.973700 | + | 0.227834i | \(0.926836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −48410.5 | −1.47769 | −0.738843 | − | 0.673877i | \(-0.764628\pi\) | ||||
−0.738843 | + | 0.673877i | \(0.764628\pi\) | |||||||
\(182\) | 6402.38 | 0.193285 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11744.4 | −0.346892 | ||||||||
\(185\) | − | 11837.9i | − | 0.345884i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27330.9i | 0.781575i | ||||||||
\(188\) | 16744.1i | 0.473748i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 23396.6i | 0.648106i | ||||||||
\(191\) | − | 11986.4i | − | 0.328566i | −0.986413 | − | 0.164283i | \(-0.947469\pi\) | ||
0.986413 | − | 0.164283i | \(-0.0525310\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19496.9 | 0.523420 | 0.261710 | − | 0.965147i | \(-0.415714\pi\) | ||||
0.261710 | + | 0.965147i | \(0.415714\pi\) | |||||||
\(194\) | 12403.7 | 0.329571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24545.9 | −0.638951 | ||||||||
\(197\) | 42645.4 | 1.09885 | 0.549426 | − | 0.835542i | \(-0.314846\pi\) | ||||
0.549426 | + | 0.835542i | \(0.314846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10669.4 | 0.269421 | 0.134711 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134711 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(200\) | − | 53578.8i | − | 1.33947i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −26853.1 | −0.658100 | ||||||||
\(203\) | 3868.40 | 0.0938727 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18809.1 | 0.447570 | ||||||||
\(206\) | −43838.4 | −1.03305 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7785.94i | 0.179963i | ||||||||
\(209\) | − | 15271.8i | − | 0.349620i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15256.3i | − | 0.342677i | −0.985212 | − | 0.171339i | \(-0.945191\pi\) | ||
0.985212 | − | 0.171339i | \(-0.0548092\pi\) | |||||||
\(212\) | 28837.8 | 0.641638 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 35886.0i | 0.783605i | ||||||||
\(215\) | − | 70732.6i | − | 1.53018i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17965.6i | 0.381525i | ||||||||
\(218\) | −24110.8 | −0.507340 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 24002.7i | 0.495924i | ||||||||
\(221\) | 135941.i | 2.78335i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17062.9 | 0.343117 | 0.171558 | − | 0.985174i | \(-0.445120\pi\) | ||||
0.171558 | + | 0.985174i | \(0.445120\pi\) | |||||||
\(224\) | − | 9963.13i | − | 0.198564i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8477.67 | −0.165981 | ||||||||
\(227\) | − | 15718.2i | − | 0.305037i | −0.988301 | − | 0.152518i | \(-0.951262\pi\) | ||
0.988301 | − | 0.152518i | \(-0.0487383\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10725.1i | 0.204518i | 0.994758 | + | 0.102259i | \(0.0326071\pi\) | ||||
−0.994758 | + | 0.102259i | \(0.967393\pi\) | |||||||
\(230\) | −17045.1 | −0.322214 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 25167.6i | − | 0.467591i | ||||||
\(233\) | 34953.2i | 0.643836i | 0.946768 | + | 0.321918i | \(0.104327\pi\) | ||||
−0.946768 | + | 0.321918i | \(0.895673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 60908.5i | 1.10291i | ||||||||
\(236\) | −35167.1 | − | 11416.5i | −0.631411 | − | 0.204979i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 10284.0i | − | 0.181556i | ||||||
\(239\) | −43682.3 | −0.764732 | −0.382366 | − | 0.924011i | \(-0.624891\pi\) | ||||
−0.382366 | + | 0.924011i | \(0.624891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −37284.2 | −0.641935 | −0.320968 | − | 0.947090i | \(-0.604008\pi\) | ||||
−0.320968 | + | 0.947090i | \(0.604008\pi\) | |||||||
\(242\) | − | 26021.1i | − | 0.444319i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 42020.7i | 0.705802i | ||||||||
\(245\) | −89288.3 | −1.48752 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 75960.3i | − | 1.24507i | ||||||
\(248\) | 116884. | 1.90042 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 21758.3i | − | 0.348132i | ||||||
\(251\) | 42855.1 | 0.680229 | 0.340114 | − | 0.940384i | \(-0.389534\pi\) | ||||
0.340114 | + | 0.940384i | \(0.389534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11125.9 | 0.173818 | ||||||||
\(254\) | − | 20780.1i | − | 0.322092i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −60271.3 | −0.919668 | ||||||||
\(257\) | 67944.9 | 1.02870 | 0.514352 | − | 0.857579i | \(-0.328033\pi\) | ||||
0.514352 | + | 0.857579i | \(0.328033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2907.50i | − | 0.0433431i | ||||||
\(260\) | 119387.i | 1.76609i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −29268.7 | −0.426383 | ||||||||
\(263\) | −6967.85 | −0.100737 | −0.0503683 | − | 0.998731i | \(-0.516040\pi\) | ||||
−0.0503683 | + | 0.998731i | \(0.516040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 104900. | 1.49377 | ||||||||
\(266\) | 5746.44i | 0.0812149i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 55966.3i | 0.779215i | ||||||||
\(269\) | 19627.0i | 0.271238i | 0.990761 | + | 0.135619i | \(0.0433023\pi\) | ||||
−0.990761 | + | 0.135619i | \(0.956698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25914.9 | −0.352866 | −0.176433 | − | 0.984313i | \(-0.556456\pi\) | ||||
−0.176433 | + | 0.984313i | \(0.556456\pi\) | |||||||
\(272\) | 12506.4 | 0.169043 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 48858.5i | − | 0.650787i | ||||||
\(275\) | 50757.3i | 0.671171i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −104861. | −1.36664 | −0.683318 | − | 0.730121i | \(-0.739464\pi\) | ||||
−0.683318 | + | 0.730121i | \(0.739464\pi\) | |||||||
\(278\) | − | 54975.5i | − | 0.711344i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 22636.8i | − | 0.288735i | ||||||
\(281\) | 14867.0 | 0.188283 | 0.0941417 | − | 0.995559i | \(-0.469989\pi\) | ||||
0.0941417 | + | 0.995559i | \(0.469989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 72926.7i | 0.910570i | 0.890346 | + | 0.455285i | \(0.150463\pi\) | ||||
−0.890346 | + | 0.455285i | \(0.849537\pi\) | |||||||
\(284\) | −78100.9 | −0.968322 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 39460.1i | 0.482421i | ||||||||
\(287\) | 4619.71 | 0.0560855 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 134840. | 1.61444 | ||||||||
\(290\) | − | 36526.9i | − | 0.434327i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 87672.3i | − | 1.02825i | ||||||
\(293\) | −69720.2 | −0.812125 | −0.406063 | − | 0.913845i | \(-0.633099\pi\) | ||||
−0.406063 | + | 0.913845i | \(0.633099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −127924. | − | 41528.8i | −1.46996 | − | 0.477205i | ||||
\(296\) | −18916.1 | −0.215897 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12399.1 | −0.139623 | ||||||||
\(299\) | 55339.4 | 0.619002 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 17372.6i | − | 0.191748i | ||||||
\(302\) | 63849.0 | 0.700068 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6988.25 | −0.0756173 | ||||||||
\(305\) | 152854.i | 1.64315i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −140429. | −1.48997 | −0.744987 | − | 0.667079i | \(-0.767544\pi\) | ||||
−0.744987 | + | 0.667079i | \(0.767544\pi\) | |||||||
\(308\) | 5895.30i | 0.0621448i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 169638. | 1.76523 | ||||||||
\(311\) | 106994. | 1.10621 | 0.553105 | − | 0.833112i | \(-0.313443\pi\) | ||||
0.553105 | + | 0.833112i | \(0.313443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 111408.i | − | 1.13717i | −0.822623 | − | 0.568587i | \(-0.807490\pi\) | ||
0.822623 | − | 0.568587i | \(-0.192510\pi\) | |||||||
\(314\) | −68678.9 | −0.696569 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 89099.6 | 0.892281 | ||||||||
\(317\) | −139639. | −1.38960 | −0.694799 | − | 0.719204i | \(-0.744507\pi\) | ||||
−0.694799 | + | 0.719204i | \(0.744507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23842.3i | 0.234297i | ||||||||
\(320\) | −77530.5 | −0.757134 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4186.45 | −0.0403770 | ||||||||
\(323\) | −122014. | −1.16951 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 252462.i | 2.39018i | ||||||||
\(326\) | − | 1213.86i | − | 0.0114218i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 30055.6i | − | 0.279369i | ||||||
\(329\) | 14959.7i | 0.138207i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 54555.5 | 0.497947 | 0.248973 | − | 0.968510i | \(-0.419907\pi\) | ||||
0.248973 | + | 0.968510i | \(0.419907\pi\) | |||||||
\(332\) | 87218.1i | 0.791281i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19436.1i | 0.174227i | ||||||||
\(335\) | 203583.i | 1.81406i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 48646.0i | 0.428339i | 0.976797 | + | 0.214169i | \(0.0687045\pi\) | ||||
−0.976797 | + | 0.214169i | \(0.931296\pi\) | |||||||
\(338\) | 130034.i | 1.13821i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 191770. | 1.65891 | ||||||||
\(341\) | −110728. | −0.952249 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −44714.7 | −0.380069 | ||||||||
\(344\) | −113025. | −0.955123 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −73342.5 | −0.612637 | ||||||||
\(347\) | − | 115161.i | − | 0.956413i | −0.878248 | − | 0.478206i | \(-0.841287\pi\) | ||
0.878248 | − | 0.478206i | \(-0.158713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 45753.9i | − | 0.375645i | −0.982203 | − | 0.187822i | \(-0.939857\pi\) | ||
0.982203 | − | 0.187822i | \(-0.0601429\pi\) | |||||||
\(350\) | − | 19098.9i | − | 0.155909i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 61406.3 | 0.495596 | ||||||||
\(353\) | − | 118207.i | − | 0.948622i | −0.880357 | − | 0.474311i | \(-0.842697\pi\) | ||
0.880357 | − | 0.474311i | \(-0.157303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −284100. | −2.25431 | ||||||||
\(356\) | − | 144830.i | − | 1.14277i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 33859.6 | 0.264189 | ||||||||
\(359\) | −210839. | −1.63592 | −0.817961 | − | 0.575274i | \(-0.804896\pi\) | ||||
−0.817961 | + | 0.575274i | \(0.804896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −62143.0 | −0.476846 | ||||||||
\(362\) | 112271.i | 0.856741i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 29322.7i | 0.221310i | ||||||||
\(365\) | − | 318917.i | − | 2.39382i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29773.6i | 0.221054i | 0.993873 | + | 0.110527i | \(0.0352539\pi\) | ||||
−0.993873 | + | 0.110527i | \(0.964746\pi\) | |||||||
\(368\) | − | 5091.15i | − | 0.0375942i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27453.7 | −0.200538 | ||||||||
\(371\) | 25764.5 | 0.187186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25947.3 | −0.186498 | −0.0932492 | − | 0.995643i | \(-0.529725\pi\) | ||||
−0.0932492 | + | 0.995643i | \(0.529725\pi\) | |||||||
\(374\) | 63384.2 | 0.453146 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 97327.2 | 0.688428 | ||||||||
\(377\) | 118590.i | 0.834379i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −268474. | −1.86906 | −0.934530 | − | 0.355884i | \(-0.884180\pi\) | ||||
−0.934530 | + | 0.355884i | \(0.884180\pi\) | |||||||
\(380\) | −107156. | −0.742077 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27798.2 | −0.190498 | ||||||||
\(383\) | −164228. | −1.11956 | −0.559782 | − | 0.828640i | \(-0.689115\pi\) | ||||
−0.559782 | + | 0.828640i | \(0.689115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21444.7i | 0.144677i | ||||||||
\(386\) | − | 45216.0i | − | 0.303471i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 56808.7i | 0.377356i | ||||||||
\(389\) | 231786. | 1.53175 | 0.765876 | − | 0.642988i | \(-0.222305\pi\) | ||||
0.765876 | + | 0.642988i | \(0.222305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 88890.8i | − | 0.581438i | ||||||
\(392\) | 142676.i | 0.928493i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 98900.6i | − | 0.637098i | ||||||
\(395\) | 324109. | 2.07729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 66558.9i | 0.422304i | 0.977453 | + | 0.211152i | \(0.0677215\pi\) | ||||
−0.977453 | + | 0.211152i | \(0.932278\pi\) | |||||||
\(398\) | − | 24743.7i | − | 0.156206i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23226.2 | 0.145164 | ||||||||
\(401\) | − | 22759.8i | − | 0.141540i | −0.997493 | − | 0.0707702i | \(-0.977454\pi\) | ||
0.997493 | − | 0.0707702i | \(-0.0225457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −550753. | −3.39115 | ||||||||
\(404\) | − | 122986.i | − | 0.753520i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 8971.36i | − | 0.0544260i | ||||||
\(407\) | 17919.9 | 0.108180 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 312184.i | 1.86623i | 0.359583 | + | 0.933113i | \(0.382919\pi\) | ||||
−0.359583 | + | 0.933113i | \(0.617081\pi\) | |||||||
\(410\) | − | 43621.0i | − | 0.259494i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 200779.i | − | 1.18283i | ||||||
\(413\) | −31419.3 | − | 10199.9i | −0.184203 | − | 0.0597991i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 317264.i | 1.84215i | ||||||||
\(416\) | 305429. | 1.76492 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −35417.3 | −0.202704 | ||||||||
\(419\) | − | 314728.i | − | 1.79270i | −0.443346 | − | 0.896351i | \(-0.646209\pi\) | ||
0.443346 | − | 0.896351i | \(-0.353791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25224.4i | − | 0.142317i | −0.997465 | − | 0.0711585i | \(-0.977330\pi\) | ||
0.997465 | − | 0.0711585i | \(-0.0226696\pi\) | |||||||
\(422\) | −35381.6 | −0.198679 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 167623.i | − | 0.932398i | ||||||
\(425\) | 405527. | 2.24513 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37542.5i | 0.205905i | ||||||||
\(428\) | −164357. | −0.897223 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −164039. | −0.887175 | ||||||||
\(431\) | − | 58420.2i | − | 0.314491i | −0.987560 | − | 0.157246i | \(-0.949739\pi\) | ||
0.987560 | − | 0.157246i | \(-0.0502614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 59683.1 | 0.318328 | 0.159164 | − | 0.987252i | \(-0.449120\pi\) | ||||
0.159164 | + | 0.987252i | \(0.449120\pi\) | |||||||
\(434\) | 41664.8 | 0.221202 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 110427.i | − | 0.580901i | ||||||
\(437\) | 49669.7i | 0.260093i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 200004. | 1.03779 | 0.518895 | − | 0.854838i | \(-0.326344\pi\) | ||||
0.518895 | + | 0.854838i | \(0.326344\pi\) | |||||||
\(440\) | 139519. | 0.720654 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 315267. | 1.61374 | ||||||||
\(443\) | 299059.i | 1.52388i | 0.647649 | + | 0.761939i | \(0.275752\pi\) | ||||
−0.647649 | + | 0.761939i | \(0.724248\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 526832.i | − | 2.66043i | ||||||
\(446\) | − | 39571.1i | − | 0.198934i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19042.2 | −0.0948773 | ||||||||
\(449\) | −308677. | −1.53113 | −0.765565 | − | 0.643359i | \(-0.777540\pi\) | ||||
−0.765565 | + | 0.643359i | \(0.777540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28472.9i | 0.139984i | ||||||||
\(452\) | − | 38827.5i | − | 0.190048i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −36452.8 | −0.176856 | ||||||||
\(455\) | 106664.i | 0.515224i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 224815.i | 1.07645i | 0.842803 | + | 0.538223i | \(0.180904\pi\) | ||||
−0.842803 | + | 0.538223i | \(0.819096\pi\) | |||||||
\(458\) | 24873.1 | 0.118577 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 78066.3i | − | 0.368933i | ||||||
\(461\) | −186398. | −0.877079 | −0.438539 | − | 0.898712i | \(-0.644504\pi\) | ||||
−0.438539 | + | 0.898712i | \(0.644504\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 45013.2i | − | 0.209980i | −0.994473 | − | 0.104990i | \(-0.966519\pi\) | ||
0.994473 | − | 0.104990i | \(-0.0334810\pi\) | |||||||
\(464\) | 10910.1 | 0.0506748 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 81061.3 | 0.373286 | ||||||||
\(467\) | − | 243089.i | − | 1.11463i | −0.830300 | − | 0.557316i | \(-0.811831\pi\) | ||
0.830300 | − | 0.557316i | \(-0.188169\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50001.9i | 0.227322i | ||||||||
\(470\) | 141255. | 0.639453 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −66359.9 | + | 204412.i | −0.297866 | + | 0.917536i | ||||
\(473\) | 107073. | 0.478586 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −226597. | −1.00431 | ||||||||
\(476\) | 47100.6 | 0.207880 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 101305.i | 0.443380i | ||||||||
\(479\) | −115564. | −0.503677 | −0.251839 | − | 0.967769i | \(-0.581035\pi\) | ||||
−0.251839 | + | 0.967769i | \(0.581035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 89132.1 | 0.385251 | ||||||||
\(482\) | 86467.3i | 0.372184i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 119176. | 0.508742 | ||||||||
\(485\) | 206647.i | 0.878509i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 151048. | 0.636880 | 0.318440 | − | 0.947943i | \(-0.396841\pi\) | ||||
0.318440 | + | 0.947943i | \(0.396841\pi\) | |||||||
\(488\) | 244250. | 1.02564 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 207072.i | 0.862440i | ||||||||
\(491\) | 20445.7 | 0.0848086 | 0.0424043 | − | 0.999101i | \(-0.486498\pi\) | ||||
0.0424043 | + | 0.999101i | \(0.486498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 190489. | 0.783746 | ||||||||
\(494\) | −176163. | −0.721871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 50668.6i | 0.205957i | ||||||||
\(497\) | −69777.7 | −0.282490 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −59385.2 | −0.238494 | −0.119247 | − | 0.992865i | \(-0.538048\pi\) | ||||
−0.119247 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(500\) | 99652.2 | 0.398609 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 99386.9i | − | 0.394386i | ||||||
\(503\) | 156531.i | 0.618677i | 0.950952 | + | 0.309339i | \(0.100108\pi\) | ||||
−0.950952 | + | 0.309339i | \(0.899892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 447375.i | − | 1.75424i | ||||||
\(506\) | − | 25802.6i | − | 0.100777i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 95172.1 | 0.368793 | ||||||||
\(509\) | − | 250897.i | − | 0.968410i | −0.874954 | − | 0.484205i | \(-0.839109\pi\) | ||
0.874954 | − | 0.484205i | \(-0.160891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 78329.0i | − | 0.299972i | ||||||
\(512\) | − | 54537.0i | − | 0.208042i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 157574.i | − | 0.596427i | ||||||
\(515\) | − | 730352.i | − | 2.75371i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −92201.9 | −0.344952 | ||||||||
\(518\) | −6742.89 | −0.0251297 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 693953. | 2.56639 | ||||||||
\(521\) | 149931. | 0.552351 | 0.276175 | − | 0.961107i | \(-0.410933\pi\) | ||||
0.276175 | + | 0.961107i | \(0.410933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −90744.5 | −0.331754 | −0.165877 | − | 0.986146i | \(-0.553046\pi\) | ||||
−0.165877 | + | 0.986146i | \(0.553046\pi\) | |||||||
\(524\) | − | 134050.i | − | 0.488206i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16159.4i | 0.0584055i | ||||||||
\(527\) | 884667.i | 3.18536i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 243655. | 0.870691 | ||||||||
\(530\) | − | 243278.i | − | 0.866067i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26318.5 | −0.0929904 | ||||||||
\(533\) | 141621.i | 0.498511i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −597864. | −2.08879 | ||||||||
\(536\) | 325310. | 1.13232 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45517.8 | 0.157259 | ||||||||
\(539\) | − | 135163.i | − | 0.465242i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 293061.i | − | 1.00130i | −0.865650 | − | 0.500650i | \(-0.833094\pi\) | ||
0.865650 | − | 0.500650i | \(-0.166906\pi\) | |||||||
\(542\) | 60100.2i | 0.204587i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 490607.i | − | 1.65781i | ||||||
\(545\) | − | 401689.i | − | 1.35237i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −264316. | −0.883384 | −0.441692 | − | 0.897167i | \(-0.645622\pi\) | ||||
−0.441692 | + | 0.897167i | \(0.645622\pi\) | |||||||
\(548\) | 223771. | 0.745147 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 117713. | 0.389135 | ||||||||
\(551\) | −106440. | −0.350591 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 79604.2 | 0.260307 | ||||||||
\(554\) | 243187.i | 0.792355i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 251786. | 0.814484 | ||||||||
\(557\) | −349573. | −1.12675 | −0.563375 | − | 0.826202i | \(-0.690497\pi\) | ||||
−0.563375 | + | 0.826202i | \(0.690497\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 532574. | 1.70434 | ||||||||
\(560\) | 9812.97 | 0.0312914 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 34478.7i | − | 0.109164i | ||||||
\(563\) | − | 87644.3i | − | 0.276508i | −0.990397 | − | 0.138254i | \(-0.955851\pi\) | ||
0.990397 | − | 0.138254i | \(-0.0441490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 141239.i | − | 0.442443i | ||||||
\(566\) | 169127. | 0.527935 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 453970.i | 1.40712i | ||||||||
\(569\) | 81258.9i | 0.250984i | 0.992095 | + | 0.125492i | \(0.0400510\pi\) | ||||
−0.992095 | + | 0.125492i | \(0.959949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 490531.i | 1.50451i | 0.658875 | + | 0.752253i | \(0.271033\pi\) | ||||
−0.658875 | + | 0.752253i | \(0.728967\pi\) | |||||||
\(572\) | −180726. | −0.552369 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 10713.7i | − | 0.0325175i | ||||||
\(575\) | − | 165083.i | − | 0.499305i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 458744. | 1.37790 | 0.688951 | − | 0.724807i | \(-0.258071\pi\) | ||||
0.688951 | + | 0.724807i | \(0.258071\pi\) | |||||||
\(578\) | − | 312712.i | − | 0.936029i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 167292. | 0.497301 | ||||||||
\(581\) | 77923.2i | 0.230842i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 158796.i | 0.467199i | ||||||||
\(584\) | −509605. | −1.49420 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 161691.i | 0.470858i | ||||||||
\(587\) | 346247.i | 1.00487i | 0.864615 | + | 0.502435i | \(0.167562\pi\) | ||||
−0.864615 | + | 0.502435i | \(0.832438\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 494327.i | − | 1.42490i | ||||||
\(590\) | −96311.0 | + | 296673.i | −0.276676 | + | 0.852263i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 8200.04i | − | 0.0233977i | ||||||
\(593\) | −507006. | −1.44180 | −0.720898 | − | 0.693041i | \(-0.756271\pi\) | ||||
−0.720898 | + | 0.693041i | \(0.756271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 171333. | 0.483958 | ||||||||
\(596\) | − | 56787.6i | − | 0.159868i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 128340.i | − | 0.358888i | ||||||
\(599\) | −571461. | −1.59270 | −0.796348 | − | 0.604838i | \(-0.793238\pi\) | ||||
−0.796348 | + | 0.604838i | \(0.793238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 393314.i | 1.08891i | 0.838792 | + | 0.544453i | \(0.183263\pi\) | ||||
−0.838792 | + | 0.544453i | \(0.816737\pi\) | |||||||
\(602\) | −40289.5 | −0.111173 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 292427.i | 0.801573i | ||||||||
\(605\) | 433514. | 1.18438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −130471. | −0.354108 | −0.177054 | − | 0.984201i | \(-0.556657\pi\) | ||||
−0.177054 | + | 0.984201i | \(0.556657\pi\) | |||||||
\(608\) | 274137.i | 0.741585i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 354490. | 0.952675 | ||||||||
\(611\) | −458604. | −1.22844 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 512655.i | 1.36428i | 0.731220 | + | 0.682142i | \(0.238951\pi\) | ||||
−0.731220 | + | 0.682142i | \(0.761049\pi\) | |||||||
\(614\) | 325673.i | 0.863864i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 34267.1 | 0.0903059 | ||||||||
\(617\) | −120180. | −0.315692 | −0.157846 | − | 0.987464i | \(-0.550455\pi\) | ||||
−0.157846 | + | 0.987464i | \(0.550455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 460899. | 1.20289 | 0.601443 | − | 0.798916i | \(-0.294593\pi\) | ||||
0.601443 | + | 0.798916i | \(0.294593\pi\) | |||||||
\(620\) | 776938.i | 2.02117i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 248133.i | − | 0.641364i | ||||||
\(623\) | − | 129395.i | − | 0.333382i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −179896. | −0.460533 | ||||||||
\(626\) | −258370. | −0.659316 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 314547.i | − | 0.797566i | ||||||
\(629\) | − | 143172.i | − | 0.361873i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 218188. | 0.547989 | 0.273995 | − | 0.961731i | \(-0.411655\pi\) | ||||
0.273995 | + | 0.961731i | \(0.411655\pi\) | |||||||
\(632\) | − | 517901.i | − | 1.29662i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 323843.i | 0.805668i | ||||||||
\(635\) | 346198. | 0.858572 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 672287.i | − | 1.65682i | ||||||
\(638\) | 55293.6 | 0.135842 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 469235.i | − | 1.14559i | ||||||
\(641\) | 761314. | 1.85288 | 0.926441 | − | 0.376440i | \(-0.122852\pi\) | ||||
0.926441 | + | 0.376440i | \(0.122852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −131827. | −0.318848 | −0.159424 | − | 0.987210i | \(-0.550964\pi\) | ||||
−0.159424 | + | 0.987210i | \(0.550964\pi\) | |||||||
\(644\) | − | 19173.8i | − | 0.0462314i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 282967.i | 0.678065i | ||||||||
\(647\) | 673769. | 1.60954 | 0.804771 | − | 0.593585i | \(-0.202288\pi\) | ||||
0.804771 | + | 0.593585i | \(0.202288\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 62865.4 | − | 193648.i | 0.149253 | − | 0.459752i | ||||
\(650\) | 585495. | 1.38579 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5559.45 | 0.0130779 | ||||||||
\(653\) | 310717. | 0.728684 | 0.364342 | − | 0.931265i | \(-0.381294\pi\) | ||||
0.364342 | + | 0.931265i | \(0.381294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 487619.i | − | 1.13657i | ||||||
\(656\) | 13029.0 | 0.0302763 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 34693.6 | 0.0801306 | ||||||||
\(659\) | 459674.i | 1.05847i | 0.848475 | + | 0.529235i | \(0.177521\pi\) | ||||
−0.848475 | + | 0.529235i | \(0.822479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −70113.4 | −0.160472 | −0.0802358 | − | 0.996776i | \(-0.525567\pi\) | ||||
−0.0802358 | + | 0.996776i | \(0.525567\pi\) | |||||||
\(662\) | − | 126522.i | − | 0.288702i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 506965. | 1.14985 | ||||||||
\(665\) | −95736.2 | −0.216488 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 77544.5i | − | 0.174301i | ||||||
\(668\) | −89016.6 | −0.199489 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 472137. | 1.05177 | ||||||||
\(671\) | −231388. | −0.513919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 832203.i | 1.83738i | 0.394979 | + | 0.918690i | \(0.370752\pi\) | ||||
−0.394979 | + | 0.918690i | \(0.629248\pi\) | |||||||
\(674\) | 112817. | 0.248344 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −595552. | −1.30325 | ||||||||
\(677\) | −372770. | −0.813323 | −0.406661 | − | 0.913579i | \(-0.633307\pi\) | ||||
−0.406661 | + | 0.913579i | \(0.633307\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50754.6i | 0.110087i | ||||||||
\(680\) | − | 1.11469e6i | − | 2.41065i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 256795.i | 0.552099i | ||||||||
\(683\) | 231892.i | 0.497102i | 0.968619 | + | 0.248551i | \(0.0799543\pi\) | ||||
−0.968619 | + | 0.248551i | \(0.920046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 813988. | 1.73475 | ||||||||
\(686\) | 103700.i | 0.220358i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 48996.1i | − | 0.103511i | ||||||
\(689\) | 789836.i | 1.66379i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 177978.i | − | 0.372744i | −0.982479 | − | 0.186372i | \(-0.940327\pi\) | ||
0.982479 | − | 0.186372i | \(-0.0596730\pi\) | |||||||
\(692\) | − | 335906.i | − | 0.701465i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −267074. | −0.554514 | ||||||||
\(695\) | 915898. | 1.89617 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 227485. | 0.468259 | ||||||||
\(698\) | −106110. | −0.217793 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 87472.5 | 0.178515 | ||||||||
\(701\) | 316317.i | 0.643705i | 0.946790 | + | 0.321852i | \(0.104305\pi\) | ||||
−0.946790 | + | 0.321852i | \(0.895695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80000.3i | 0.161875i | ||||||||
\(704\) | − | 117364.i | − | 0.236804i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −274138. | −0.549997 | ||||||||
\(707\) | − | 109880.i | − | 0.219826i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 288012. | 0.572952 | 0.286476 | − | 0.958087i | \(-0.407516\pi\) | ||||
0.286476 | + | 0.958087i | \(0.407516\pi\) | |||||||
\(710\) | 658867.i | 1.30702i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −841838. | −1.66061 | ||||||||
\(713\) | 360132. | 0.708407 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −657409. | −1.28595 | ||||||||
\(716\) | 155076.i | 0.302495i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 488966.i | 0.948483i | ||||||||
\(719\) | − | 622044.i | − | 1.20327i | −0.798771 | − | 0.601636i | \(-0.794516\pi\) | ||
0.798771 | − | 0.601636i | \(-0.205484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 179381.i | − | 0.345070i | ||||||
\(722\) | 144118.i | 0.276468i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −514197. | −0.980962 | ||||||||
\(725\) | 353764. | 0.673035 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −323221. | −0.611548 | −0.305774 | − | 0.952104i | \(-0.598915\pi\) | ||||
−0.305774 | + | 0.952104i | \(0.598915\pi\) | |||||||
\(728\) | 170441. | 0.321597 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −739612. | −1.38790 | ||||||||
\(731\) | − | 855466.i | − | 1.60091i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −314696. | −0.585711 | −0.292856 | − | 0.956157i | \(-0.594606\pi\) | ||||
−0.292856 | + | 0.956157i | \(0.594606\pi\) | |||||||
\(734\) | 69049.0 | 0.128164 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −199717. | −0.368689 | ||||||||
\(737\) | −308180. | −0.567373 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 703004.i | − | 1.28727i | −0.765334 | − | 0.643634i | \(-0.777426\pi\) | ||
0.765334 | − | 0.643634i | \(-0.222574\pi\) | |||||||
\(740\) | − | 125737.i | − | 0.229615i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 59751.5i | − | 0.108528i | ||||||
\(743\) | 128013. | 0.231886 | 0.115943 | − | 0.993256i | \(-0.463011\pi\) | ||||
0.115943 | + | 0.993256i | \(0.463011\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 206571.i | − | 0.372182i | ||||||
\(746\) | 60175.5i | 0.108129i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 290298.i | 0.518849i | ||||||||
\(749\) | −146841. | −0.261749 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 905740.i | − | 1.60592i | −0.596034 | − | 0.802959i | \(-0.703258\pi\) | ||
0.596034 | − | 0.802959i | \(-0.296742\pi\) | |||||||
\(752\) | 42191.0i | 0.0746078i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 275026. | 0.483760 | ||||||||
\(755\) | 1.06373e6i | 1.86611i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 302200. | 0.527355 | 0.263678 | − | 0.964611i | \(-0.415065\pi\) | ||||
0.263678 | + | 0.964611i | \(0.415065\pi\) | |||||||
\(758\) | 622628.i | 1.08365i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 622856.i | 1.07835i | ||||||||
\(761\) | −844330. | −1.45795 | −0.728976 | − | 0.684539i | \(-0.760003\pi\) | ||||
−0.728976 | + | 0.684539i | \(0.760003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 98658.6i | − | 0.169467i | ||||||
\(764\) | − | 127315.i | − | 0.218118i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 380867.i | 0.649107i | ||||||||
\(767\) | 312687. | − | 963188.i | 0.531519 | − | 1.63727i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 232294.i | 0.392813i | 0.980523 | + | 0.196406i | \(0.0629272\pi\) | ||||
−0.980523 | + | 0.196406i | \(0.937073\pi\) | |||||||
\(770\) | 49733.4 | 0.0838815 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 207088. | 0.347472 | ||||||||
\(773\) | − | 340313.i | − | 0.569534i | −0.958597 | − | 0.284767i | \(-0.908084\pi\) | ||
0.958597 | − | 0.284767i | \(-0.0919162\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.64295e6i | 2.73540i | ||||||||
\(776\) | 330207. | 0.548356 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 537545.i | − | 0.888087i | ||||||
\(779\) | −127112. | −0.209465 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 430064.i | − | 0.705068i | ||||||
\(782\) | −206150. | −0.337109 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −61849.5 | −0.100625 | ||||||||
\(785\) | − | 1.14420e6i | − | 1.85679i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18969.9 | −0.0306278 | −0.0153139 | − | 0.999883i | \(-0.504875\pi\) | ||||
−0.0153139 | + | 0.999883i | \(0.504875\pi\) | |||||||
\(788\) | 452962. | 0.729473 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 751653.i | − | 1.20438i | ||||||
\(791\) | − | 34689.6i | − | 0.0554429i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.15090e6 | −1.83017 | ||||||||
\(794\) | 154359. | 0.244846 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 113326. | 0.178855 | ||||||||
\(797\) | 845431.i | 1.33095i | 0.746421 | + | 0.665474i | \(0.231771\pi\) | ||||
−0.746421 | + | 0.665474i | \(0.768229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 736649.i | 1.15390i | ||||||||
\(800\) | − | 911125.i | − | 1.42363i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −52783.2 | −0.0820629 | ||||||||
\(803\) | 482769. | 0.748701 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 69746.7i | − | 0.107630i | ||||||
\(806\) | 1.27727e6i | 1.96614i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −714872. | −1.09498 | ||||||||
\(809\) | − | 146619.i | − | 0.224023i | −0.993707 | − | 0.112012i | \(-0.964271\pi\) | ||
0.993707 | − | 0.112012i | \(-0.0357294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 807106.i | 1.22712i | 0.789646 | + | 0.613562i | \(0.210264\pi\) | ||||
−0.789646 | + | 0.613562i | \(0.789736\pi\) | |||||||
\(812\) | 41088.6 | 0.0623173 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 41558.8i | − | 0.0627212i | ||||||
\(815\) | 20223.0 | 0.0304461 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 478010.i | 0.716132i | ||||||||
\(818\) | 723999. | 1.08201 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 199783. | 0.297119 | ||||||||
\(821\) | − | 1.32897e6i | − | 1.97164i | −0.167797 | − | 0.985822i | \(-0.553665\pi\) | ||
0.167797 | − | 0.985822i | \(-0.446335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 49834.3i | − | 0.0735748i | −0.999323 | − | 0.0367874i | \(-0.988288\pi\) | ||
0.999323 | − | 0.0367874i | \(-0.0117124\pi\) | |||||||
\(824\) | −1.16705e6 | −1.71884 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23654.9 | + | 72865.7i | −0.0346706 | + | 0.106798i | ||||
\(827\) | −40785.1 | −0.0596335 | −0.0298167 | − | 0.999555i | \(-0.509492\pi\) | ||||
−0.0298167 | + | 0.999555i | \(0.509492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 333941. | 0.485916 | 0.242958 | − | 0.970037i | \(-0.421882\pi\) | ||||
0.242958 | + | 0.970037i | \(0.421882\pi\) | |||||||
\(830\) | 735780. | 1.06805 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 583758.i | − | 0.843308i | ||||||
\(833\) | −1.07988e6 | −1.55628 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −323807. | −0.464422 | ||||||||
\(836\) | − | 162210.i | − | 0.232095i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −729899. | −1.03938 | ||||||||
\(839\) | − | 183481.i | − | 0.260656i | −0.991471 | − | 0.130328i | \(-0.958397\pi\) | ||
0.991471 | − | 0.130328i | \(-0.0416030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −541107. | −0.765052 | ||||||||
\(842\) | −58498.9 | −0.0825133 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 162047.i | − | 0.227486i | ||||||
\(845\) | −2.16638e6 | −3.03404 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 106475. | 0.148416 | ||||||||
\(848\) | 72663.9 | 0.101048 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 940473.i | − | 1.30169i | ||||||
\(851\) | −58282.6 | −0.0804785 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −179610. | −0.246850 | −0.123425 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123425 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(854\) | 87066.2 | 0.119381 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 955342.i | 1.30380i | ||||||||
\(857\) | 787527.i | 1.07227i | 0.844133 | + | 0.536134i | \(0.180116\pi\) | ||||
−0.844133 | + | 0.536134i | \(0.819884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 345592.i | 0.468357i | 0.972194 | + | 0.234179i | \(0.0752401\pi\) | ||||
−0.972194 | + | 0.234179i | \(0.924760\pi\) | |||||||
\(860\) | − | 751293.i | − | 1.01581i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −135485. | −0.182337 | ||||||||
\(863\) | 1.32129e6i | 1.77410i | 0.461677 | + | 0.887048i | \(0.347248\pi\) | ||||
−0.461677 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.22189e6i | − | 1.63306i | ||||||
\(866\) | − | 138413.i | − | 0.184562i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 190824.i | 0.253275i | ||||||||
\(869\) | 490629.i | 0.649701i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.53286e6 | −2.02053 | ||||||||
\(872\) | −641869. | −0.844138 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 115191. | 0.150798 | ||||||||
\(875\) | 89032.2 | 0.116287 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.10906e6 | 1.44197 | 0.720984 | − | 0.692951i | \(-0.243690\pi\) | ||||
0.720984 | + | 0.692951i | \(0.243690\pi\) | |||||||
\(878\) | − | 463837.i | − | 0.601695i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 60480.8i | 0.0781002i | ||||||||
\(881\) | 17042.2i | 0.0219571i | 0.999940 | + | 0.0109786i | \(0.00349465\pi\) | ||||
−0.999940 | + | 0.0109786i | \(0.996505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −554450. | −0.711117 | −0.355559 | − | 0.934654i | \(-0.615709\pi\) | ||||
−0.355559 | + | 0.934654i | \(0.615709\pi\) | |||||||
\(884\) | 1.44392e6i | 1.84772i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 693561. | 0.883521 | ||||||||
\(887\) | − | 563820.i | − | 0.716627i | −0.933601 | − | 0.358313i | \(-0.883352\pi\) | ||
0.933601 | − | 0.358313i | \(-0.116648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 85029.5 | 0.107589 | ||||||||
\(890\) | −1.22180e6 | −1.54248 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 181235. | 0.227778 | ||||||||
\(893\) | − | 411619.i | − | 0.516170i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 564104.i | 0.704227i | ||||||||
\(896\) | − | 115249.i | − | 0.143555i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 715865.i | 0.887726i | ||||||||
\(899\) | 771745.i | 0.954893i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26870e6 | 1.56282 | ||||||||
\(902\) | 66032.6 | 0.0811606 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −225689. | −0.276168 | ||||||||
\(905\) | −1.87044e6 | −2.28374 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −220065. | −0.267508 | −0.133754 | − | 0.991015i | \(-0.542703\pi\) | ||||
−0.133754 | + | 0.991015i | \(0.542703\pi\) | |||||||
\(908\) | − | 166953.i | − | 0.202499i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 247369. | 0.298719 | ||||||||
\(911\) | −631121. | −0.760459 | −0.380230 | − | 0.924892i | \(-0.624155\pi\) | ||||
−0.380230 | + | 0.924892i | \(0.624155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −480268. | −0.576159 | ||||||||
\(914\) | 521376. | 0.624107 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 113918.i | 0.135769i | ||||||||
\(917\) | − | 119764.i | − | 0.142425i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 655325.i | − | 0.775936i | −0.921673 | − | 0.387968i | \(-0.873177\pi\) | ||
0.921673 | − | 0.387968i | \(-0.126823\pi\) | |||||||
\(920\) | −453769. | −0.536116 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 432282.i | 0.508517i | ||||||||
\(923\) | − | 2.13910e6i | − | 2.51089i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 265890.i | − | 0.310755i | ||||||
\(926\) | −104392. | −0.121743 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 427984.i | − | 0.496972i | ||||||
\(929\) | 1.56736e6i | 1.81609i | 0.418874 | + | 0.908044i | \(0.362425\pi\) | ||||
−0.418874 | + | 0.908044i | \(0.637575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 603409. | 0.696166 | ||||||||
\(932\) | 371259.i | 0.427410i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −563757. | −0.646247 | ||||||||
\(935\) | 1.05599e6i | 1.20791i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 287024.i | − | 0.326918i | −0.986550 | − | 0.163459i | \(-0.947735\pi\) | ||
0.986550 | − | 0.163459i | \(-0.0522651\pi\) | |||||||
\(938\) | 115961. | 0.131798 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 646945.i | 0.732170i | ||||||||
\(941\) | − | 865888.i | − | 0.977873i | −0.872319 | − | 0.488937i | \(-0.837385\pi\) | ||
0.872319 | − | 0.488937i | \(-0.162615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 92604.9i | − | 0.104138i | ||||||
\(944\) | −88612.1 | − | 28766.8i | −0.0994372 | − | 0.0322810i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 248318.i | − | 0.277477i | ||||||
\(947\) | 1.35112e6 | 1.50659 | 0.753294 | − | 0.657684i | \(-0.228464\pi\) | ||||
0.753294 | + | 0.657684i | \(0.228464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.40125e6 | 2.66628 | ||||||||
\(950\) | 525510.i | 0.582283i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 273778.i | − | 0.302082i | ||||||
\(953\) | 851986. | 0.938095 | 0.469047 | − | 0.883173i | \(-0.344597\pi\) | ||||
0.469047 | + | 0.883173i | \(0.344597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 463120.i | − | 0.507793i | ||||||
\(956\) | −463975. | −0.507667 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 268009.i | 0.292024i | ||||||||
\(959\) | 199923. | 0.217383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.66062e6 | −2.88095 | ||||||||
\(962\) | − | 206710.i | − | 0.223363i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −396018. | −0.426148 | ||||||||
\(965\) | 753302. | 0.808937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.19167e6i | 1.27439i | 0.770703 | + | 0.637194i | \(0.219905\pi\) | ||||
−0.770703 | + | 0.637194i | \(0.780095\pi\) | |||||||
\(968\) | − | 692723.i | − | 0.739280i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 479244. | 0.509346 | ||||||||
\(971\) | −336441. | −0.356837 | −0.178419 | − | 0.983955i | \(-0.557098\pi\) | ||||
−0.178419 | + | 0.983955i | \(0.557098\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 224953. | 0.237611 | ||||||||
\(974\) | − | 350302.i | − | 0.369254i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 105881.i | 0.111153i | ||||||||
\(977\) | 1.10642e6i | 1.15912i | 0.814929 | + | 0.579561i | \(0.196776\pi\) | ||||
−0.814929 | + | 0.579561i | \(0.803224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 797507. | 0.832088 | ||||||||
\(980\) | −948384. | −0.987488 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 47416.5i | − | 0.0491707i | ||||||
\(983\) | − | 1.26199e6i | − | 1.30602i | −0.757351 | − | 0.653008i | \(-0.773507\pi\) | ||
0.757351 | − | 0.653008i | \(-0.226493\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.64769e6 | 1.69826 | ||||||||
\(986\) | − | 441770.i | − | 0.454404i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 806820.i | − | 0.826537i | ||||||
\(989\) | −348245. | −0.356034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.38128e6i | − | 1.40649i | −0.710950 | − | 0.703243i | \(-0.751735\pi\) | ||
0.710950 | − | 0.703243i | \(-0.248265\pi\) | |||||||
\(992\) | 1.98764e6 | 2.01983 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 161824.i | 0.163784i | ||||||||
\(995\) | 412233. | 0.416386 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.91430e6 | −1.92584 | −0.962918 | − | 0.269795i | \(-0.913044\pi\) | ||||
−0.962918 | + | 0.269795i | \(0.913044\pi\) | |||||||
\(998\) | 137722.i | 0.138275i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.5.c.d.235.16 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.25 | yes | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.25 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.16 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.16 | ✓ | 40 | 177.176 | even | 2 | ||
177.5.c.a.58.25 | yes | 40 | 3.2 | odd | 2 | ||
531.5.c.d.235.16 | 40 | 1.1 | even | 1 | trivial | ||
531.5.c.d.235.25 | 40 | 59.58 | odd | 2 | inner |