Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(17,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.g (of order \(6\), degree \(2\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(-3.41053 + 2.74723i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.17 |
Dual form | 108.5.g.a.89.4 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 34.8718 | + | 20.1332i | 1.39487 | + | 0.805329i | 0.993849 | − | 0.110740i | \(-0.0353221\pi\) |
0.401021 | + | 0.916069i | \(0.368655\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.38688 | − | 12.7945i | −0.150753 | − | 0.261111i | 0.780752 | − | 0.624841i | \(-0.214836\pi\) |
−0.931504 | + | 0.363730i | \(0.881503\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 70.7125 | − | 40.8259i | 0.584400 | − | 0.337404i | −0.178480 | − | 0.983944i | \(-0.557118\pi\) |
0.762880 | + | 0.646540i | \(0.223785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −139.053 | + | 240.848i | −0.822801 | + | 1.42513i | 0.0807868 | + | 0.996731i | \(0.474257\pi\) |
−0.903588 | + | 0.428402i | \(0.859077\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.8854i | 0.0376658i | 0.999823 | + | 0.0188329i | \(0.00599505\pi\) | ||||
−0.999823 | + | 0.0188329i | \(0.994005\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 532.815 | 1.47594 | 0.737971 | − | 0.674833i | \(-0.235784\pi\) | ||||
0.737971 | + | 0.674833i | \(0.235784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 702.045 | + | 405.326i | 1.32712 | + | 0.766211i | 0.984853 | − | 0.173393i | \(-0.0554730\pi\) |
0.342264 | + | 0.939604i | \(0.388806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 498.193 | + | 862.895i | 0.797109 | + | 1.38063i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 257.640 | − | 148.749i | 0.306350 | − | 0.176871i | −0.338942 | − | 0.940807i | \(-0.610069\pi\) |
0.645292 | + | 0.763936i | \(0.276736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −97.5447 | + | 168.952i | −0.101503 | + | 0.175809i | −0.912304 | − | 0.409513i | \(-0.865699\pi\) |
0.810801 | + | 0.585322i | \(0.199032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 594.887i | − | 0.485622i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2097.18 | −1.53191 | −0.765954 | − | 0.642896i | \(-0.777733\pi\) | ||||
−0.765954 | + | 0.642896i | \(0.777733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1359.41 | + | 784.854i | 0.808689 | + | 0.466897i | 0.846500 | − | 0.532388i | \(-0.178705\pi\) |
−0.0378113 | + | 0.999285i | \(0.512039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.0863 | + | 79.8239i | 0.0249250 | + | 0.0431714i | 0.878219 | − | 0.478259i | \(-0.158732\pi\) |
−0.853294 | + | 0.521430i | \(0.825399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1849.15 | + | 1067.61i | −0.837098 | + | 0.483299i | −0.856277 | − | 0.516517i | \(-0.827228\pi\) |
0.0191789 | + | 0.999816i | \(0.493895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1091.37 | − | 1890.30i | 0.454547 | − | 0.787299i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2579.42i | − | 0.918271i | −0.888366 | − | 0.459135i | \(-0.848159\pi\) | ||
0.888366 | − | 0.459135i | \(-0.151841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3287.82 | 1.08688 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1349.04 | − | 778.868i | −0.387544 | − | 0.223748i | 0.293552 | − | 0.955943i | \(-0.405163\pi\) |
−0.681095 | + | 0.732195i | \(0.738496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2685.97 | − | 4652.24i | −0.721842 | − | 1.25027i | −0.960261 | − | 0.279105i | \(-0.909962\pi\) |
0.238419 | − | 0.971162i | \(-0.423371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9698.07 | + | 5599.19i | −2.29540 | + | 1.32525i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −457.641 | + | 792.658i | −0.101947 | + | 0.176578i | −0.912487 | − | 0.409106i | \(-0.865841\pi\) |
0.810540 | + | 0.585684i | \(0.199174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8215.93i | − | 1.62982i | −0.579587 | − | 0.814910i | \(-0.696786\pi\) | ||
0.579587 | − | 0.814910i | \(-0.303214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3438.63 | −0.645267 | −0.322634 | − | 0.946524i | \(-0.604568\pi\) | ||||
−0.322634 | + | 0.946524i | \(0.604568\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1044.69 | − | 603.152i | −0.176200 | − | 0.101729i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2316.17 | − | 4011.73i | −0.371122 | − | 0.642802i | 0.618617 | − | 0.785693i | \(-0.287693\pi\) |
−0.989738 | + | 0.142891i | \(0.954360\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5195.52 | − | 2999.63i | 0.754176 | − | 0.435424i | −0.0730250 | − | 0.997330i | \(-0.523265\pi\) |
0.827201 | + | 0.561907i | \(0.189932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −219.158 | + | 379.593i | −0.0303333 | + | 0.0525389i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8434.43i | 1.06482i | 0.846487 | + | 0.532409i | \(0.178713\pi\) | ||||
−0.846487 | + | 0.532409i | \(0.821287\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4108.69 | 0.496158 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18580.2 | + | 10727.3i | 2.05875 | + | 1.18862i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3015.58 | + | 5223.13i | 0.320499 | + | 0.555121i | 0.980591 | − | 0.196064i | \(-0.0628160\pi\) |
−0.660092 | + | 0.751185i | \(0.729483\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5181.24 | + | 2991.39i | −0.507915 | + | 0.293245i | −0.731976 | − | 0.681330i | \(-0.761402\pi\) |
0.224061 | + | 0.974575i | \(0.428069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 765.718 | − | 1326.26i | 0.0721763 | − | 0.125013i | −0.827679 | − | 0.561202i | \(-0.810339\pi\) |
0.899855 | + | 0.436189i | \(0.143672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 20499.8i | − | 1.79053i | −0.445536 | − | 0.895264i | \(-0.646987\pi\) | ||
0.445536 | − | 0.895264i | \(-0.353013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9404.21 | −0.791534 | −0.395767 | − | 0.918351i | \(-0.629521\pi\) | ||||
−0.395767 | + | 0.918351i | \(0.629521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2598.59 | − | 1500.29i | −0.203507 | − | 0.117495i | 0.394783 | − | 0.918774i | \(-0.370820\pi\) |
−0.598290 | + | 0.801279i | \(0.704153\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16321.0 | + | 28268.8i | 1.23410 | + | 2.13753i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 139.273 | − | 80.4092i | 0.00983496 | − | 0.00567822i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3987.00 | + | 6905.69i | −0.272317 | + | 0.471668i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14954.4i | 0.957081i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9817.40 | 0.608680 | 0.304340 | − | 0.952563i | \(-0.401564\pi\) | ||||
0.304340 | + | 0.952563i | \(0.401564\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 553.194 | + | 319.387i | 0.0322356 | + | 0.0186112i | 0.516031 | − | 0.856570i | \(-0.327409\pi\) |
−0.483796 | + | 0.875181i | \(0.660742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3935.84 | − | 6817.07i | −0.222502 | − | 0.385385i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 27716.3 | − | 16002.0i | 1.47670 | − | 0.852575i | 0.477050 | − | 0.878876i | \(-0.341706\pi\) |
0.999654 | + | 0.0263010i | \(0.00837284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2792.13 | − | 4836.11i | 0.144513 | − | 0.250303i | −0.784678 | − | 0.619903i | \(-0.787172\pi\) |
0.929191 | + | 0.369600i | \(0.120505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22707.9i | 1.11047i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11979.2 | 0.569758 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7118.75 | + | 4110.01i | 0.320650 | + | 0.185127i | 0.651682 | − | 0.758492i | \(-0.274064\pi\) |
−0.331032 | + | 0.943619i | \(0.607397\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10236.0 | − | 17729.2i | −0.448927 | − | 0.777564i | 0.549389 | − | 0.835566i | \(-0.314860\pi\) |
−0.998316 | + | 0.0580020i | \(0.981527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6803.11 | + | 3927.78i | −0.283168 | + | 0.163487i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12896.9 | + | 22338.2i | −0.523224 | + | 0.906250i | 0.476411 | + | 0.879223i | \(0.341937\pi\) |
−0.999635 | + | 0.0270273i | \(0.991396\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11976.4i | − | 0.462034i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16488.3 | −0.620584 | −0.310292 | − | 0.950641i | \(-0.600427\pi\) | ||||
−0.310292 | + | 0.950641i | \(0.600427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −34263.0 | − | 19781.8i | −1.22855 | − | 0.709304i | −0.261824 | − | 0.965116i | \(-0.584324\pi\) |
−0.966727 | + | 0.255812i | \(0.917657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24391.2 | − | 42246.8i | −0.854004 | − | 1.47918i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4204.22 | + | 2427.31i | −0.140473 | + | 0.0811022i | −0.568589 | − | 0.822621i | \(-0.692511\pi\) |
0.428116 | + | 0.903724i | \(0.359177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7360.19 | − | 12748.2i | 0.240333 | − | 0.416268i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4764.02i | 0.148685i | 0.997233 | + | 0.0743425i | \(0.0236858\pi\) | ||||
−0.997233 | + | 0.0743425i | \(0.976314\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3741.40 | 0.114203 | 0.0571014 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571014 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −73132.4 | − | 42223.0i | −2.13681 | − | 1.23369i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 444.406 | + | 769.734i | 0.0127086 | + | 0.0220119i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9003.63 | + | 5198.25i | −0.246803 | + | 0.142492i | −0.618300 | − | 0.785943i | \(-0.712178\pi\) |
0.371496 | + | 0.928434i | \(0.378845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21606.1 | − | 37422.9i | 0.580045 | − | 1.00467i | −0.415428 | − | 0.909626i | \(-0.636368\pi\) |
0.995473 | − | 0.0950419i | \(-0.0302985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 49899.7i | 1.28578i | 0.765960 | + | 0.642889i | \(0.222264\pi\) | ||||
−0.765960 | + | 0.642889i | \(0.777736\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7613.76 | −0.192262 | −0.0961310 | − | 0.995369i | \(-0.530647\pi\) | ||||
−0.0961310 | + | 0.995369i | \(0.530647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3806.32 | − | 2197.58i | −0.0923662 | − | 0.0533276i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31603.3 | + | 54738.5i | 0.752011 | + | 1.30252i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37676.6 | − | 21752.6i | 0.862541 | − | 0.497988i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28097.7 | − | 48666.7i | 0.631112 | − | 1.09312i | −0.356213 | − | 0.934405i | \(-0.615932\pi\) |
0.987325 | − | 0.158713i | \(-0.0507344\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3711.47i | 0.0802913i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2882.21 | 0.0612076 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2621.72 | − | 1513.65i | −0.0536788 | − | 0.0309915i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18961.1 | − | 32841.6i | −0.381289 | − | 0.660412i | 0.609958 | − | 0.792434i | \(-0.291186\pi\) |
−0.991247 | + | 0.132022i | \(0.957853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8461.24 | + | 4885.10i | −0.164203 | + | 0.0948029i | −0.579850 | − | 0.814723i | \(-0.696889\pi\) |
0.415646 | + | 0.909526i | \(0.363555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18965.0 | + | 32848.4i | −0.361645 | + | 0.626387i | −0.988232 | − | 0.152964i | \(-0.951118\pi\) |
0.626587 | + | 0.779352i | \(0.284451\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3372.35i | 0.0621185i | 0.999518 | + | 0.0310592i | \(0.00988805\pi\) | ||||
−0.999518 | + | 0.0310592i | \(0.990112\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −85977.4 | −1.55686 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 64618.9 | + | 37307.7i | 1.13126 | + | 0.653135i | 0.944252 | − | 0.329223i | \(-0.106787\pi\) |
0.187011 | + | 0.982358i | \(0.440120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12127.1 | + | 21004.7i | 0.208796 | + | 0.361645i | 0.951336 | − | 0.308157i | \(-0.0997122\pi\) |
−0.742540 | + | 0.669802i | \(0.766379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 76115.8 | − | 43945.5i | 1.26807 | − | 0.732120i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −74089.7 | + | 128327.i | −1.21441 | + | 2.10341i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 25543.7i | − | 0.405449i | −0.979236 | − | 0.202724i | \(-0.935020\pi\) | ||
0.979236 | − | 0.202724i | \(-0.0649795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 66191.1 | 1.03409 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18961.7 | − | 10947.6i | −0.287086 | − | 0.165749i | 0.349541 | − | 0.936921i | \(-0.386338\pi\) |
−0.636627 | + | 0.771172i | \(0.719671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15491.6 | + | 26832.3i | 0.230939 | + | 0.399998i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6539.22 | + | 3775.42i | −0.0945397 | + | 0.0545825i | −0.546524 | − | 0.837443i | \(-0.684049\pi\) |
0.451985 | + | 0.892026i | \(0.350716\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51932.1 | − | 89949.0i | 0.739510 | − | 1.28087i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 106275.i | 1.46868i | 0.678780 | + | 0.734342i | \(0.262509\pi\) | ||||
−0.678780 | + | 0.734342i | \(0.737491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 82971.5 | 1.12977 | 0.564885 | − | 0.825170i | \(-0.308920\pi\) | ||||
0.564885 | + | 0.825170i | \(0.308920\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 70456.9 | + | 40678.3i | 0.931661 | + | 0.537895i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32616.8 | + | 56494.0i | 0.425091 | + | 0.736280i | 0.996429 | − | 0.0844353i | \(-0.0269086\pi\) |
−0.571338 | + | 0.820715i | \(0.693575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 82142.7 | − | 47425.1i | 1.04029 | − | 0.600614i | 0.120378 | − | 0.992728i | \(-0.461590\pi\) |
0.919917 | + | 0.392114i | \(0.128256\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −52834.0 | + | 91511.3i | −0.659692 | + | 1.14262i | 0.321004 | + | 0.947078i | \(0.395980\pi\) |
−0.980695 | + | 0.195542i | \(0.937354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 23190.5i | − | 0.281544i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 83402.5 | 0.998581 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 61404.7 | + | 35452.0i | 0.715264 | + | 0.412958i | 0.813007 | − | 0.582254i | \(-0.197829\pi\) |
−0.0977432 | + | 0.995212i | \(0.531162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31362.3 | − | 54321.0i | −0.360382 | − | 0.624200i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −195243. | + | 112724.i | −2.18391 | + | 1.26088i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 680.869 | − | 1179.30i | 0.00751503 | − | 0.0130164i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 216309.i | − | 2.32528i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27339.7 | 0.290079 | 0.145040 | − | 0.989426i | \(-0.453669\pi\) | ||||
0.145040 | + | 0.989426i | \(0.453669\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −88117.5 | − | 50874.6i | −0.911048 | − | 0.525994i | −0.0302797 | − | 0.999541i | \(-0.509640\pi\) |
−0.880768 | + | 0.473548i | \(0.842973\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22810.8 | + | 39509.5i | 0.232837 | + | 0.403286i | 0.958642 | − | 0.284615i | \(-0.0918658\pi\) |
−0.725805 | + | 0.687901i | \(0.758532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20556.7 | + | 11868.4i | −0.204567 | + | 0.118107i | −0.598784 | − | 0.800911i | \(-0.704349\pi\) |
0.394217 | + | 0.919017i | \(0.371016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12145.6 | − | 21036.8i | 0.119354 | − | 0.206727i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5799.91i | 0.0555925i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −277102. | −2.62345 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27318.9 | + | 15772.6i | 0.252389 | + | 0.145717i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −63701.2 | − | 110334.i | −0.581422 | − | 1.00705i | −0.995311 | − | 0.0967256i | \(-0.969163\pi\) |
0.413889 | − | 0.910327i | \(-0.364170\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31917.5 | + | 18427.6i | −0.284406 | + | 0.164202i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8353.80 | − | 14469.2i | 0.0735571 | − | 0.127405i | −0.826901 | − | 0.562348i | \(-0.809898\pi\) |
0.900458 | + | 0.434943i | \(0.143232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15929.4i | 0.136990i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −67719.0 | −0.575602 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 153069. | + | 88374.3i | 1.27124 | + | 0.733951i | 0.975221 | − | 0.221231i | \(-0.0710074\pi\) |
0.296019 | + | 0.955182i | \(0.404341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −49219.9 | − | 85251.3i | −0.404101 | − | 0.699923i | 0.590116 | − | 0.807319i | \(-0.299082\pi\) |
−0.994216 | + | 0.107396i | \(0.965749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −108285. | + | 62518.3i | −0.868997 | + | 0.501716i | −0.867015 | − | 0.498282i | \(-0.833964\pi\) |
−0.00198242 | + | 0.999998i | \(0.500631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 165413. | − | 286504.i | 1.31254 | − | 2.27339i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 130777.i | − | 1.01471i | −0.861737 | − | 0.507356i | \(-0.830623\pi\) | ||
0.861737 | − | 0.507356i | \(-0.169377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 153571. | 1.17840 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −119911. | − | 69230.7i | −0.900064 | − | 0.519652i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 64119.3 | + | 111058.i | 0.476054 | + | 0.824550i | 0.999624 | − | 0.0274329i | \(-0.00873325\pi\) |
−0.523569 | + | 0.851983i | \(0.675400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33002.3 | + | 19053.9i | −0.239771 | + | 0.138432i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31604.2 | + | 54740.0i | −0.227157 | + | 0.393448i | −0.956964 | − | 0.290205i | \(-0.906276\pi\) |
0.729807 | + | 0.683653i | \(0.239610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 82736.1i | 0.582120i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −101202. | −0.704547 | −0.352273 | − | 0.935897i | \(-0.614591\pi\) | ||||
−0.352273 | + | 0.935897i | \(0.614591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16878.5 | + | 9744.83i | 0.115063 | + | 0.0664319i | 0.556427 | − | 0.830896i | \(-0.312172\pi\) |
−0.441364 | + | 0.897328i | \(0.645505\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24286.8 | − | 42065.9i | −0.163851 | − | 0.283798i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −49519.1 | + | 28589.9i | −0.327245 | + | 0.188935i | −0.654617 | − | 0.755960i | \(-0.727170\pi\) |
0.327372 | + | 0.944895i | \(0.393837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4412.14 | + | 7642.04i | −0.0288599 | + | 0.0499869i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 186528.i | − | 1.19550i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −75878.7 | −0.481436 | −0.240718 | − | 0.970595i | \(-0.577383\pi\) | ||||
−0.240718 | + | 0.970595i | \(0.577383\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −210130. | − | 121319.i | −1.30677 | − | 0.754464i | −0.325215 | − | 0.945640i | \(-0.605437\pi\) |
−0.981556 | + | 0.191176i | \(0.938770\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27127.9 | − | 46986.8i | −0.167034 | − | 0.289312i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −148297. | + | 85619.2i | −0.895248 | + | 0.516871i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −60915.8 | + | 105509.i | −0.364153 | + | 0.630731i | −0.988640 | − | 0.150304i | \(-0.951975\pi\) |
0.624487 | + | 0.781035i | \(0.285308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23013.6i | 0.134923i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 241569. | 1.40264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 107882. | + | 62285.6i | 0.614498 | + | 0.354780i | 0.774724 | − | 0.632300i | \(-0.217889\pi\) |
−0.160226 | + | 0.987080i | \(0.551222\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12647.9 | − | 21906.8i | −0.0713600 | − | 0.123599i | 0.828138 | − | 0.560525i | \(-0.189401\pi\) |
−0.899498 | + | 0.436926i | \(0.856067\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9392.97 | + | 5423.03i | −0.0520026 | + | 0.0300237i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39682.0 | + | 68731.2i | −0.217639 | + | 0.376962i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 153800.i | − | 0.827944i | −0.910290 | − | 0.413972i | \(-0.864141\pi\) | ||
0.910290 | − | 0.413972i | \(-0.135859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 112975. | 0.602569 | 0.301285 | − | 0.953534i | \(-0.402585\pi\) | ||||
0.301285 | + | 0.953534i | \(0.402585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 374060. | + | 215963.i | 1.95875 | + | 1.13088i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 89083.3 | + | 154297.i | 0.462239 | + | 0.800622i | 0.999072 | − | 0.0430665i | \(-0.0137127\pi\) |
−0.536833 | + | 0.843689i | \(0.680379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 258569. | − | 149285.i | 1.31756 | − | 0.760691i | 0.334221 | − | 0.942495i | \(-0.391527\pi\) |
0.983335 | + | 0.181804i | \(0.0581935\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169812. | + | 294123.i | −0.857529 | + | 1.48528i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 201956.i | 1.00176i | 0.865516 | + | 0.500881i | \(0.166991\pi\) | ||||
−0.865516 | + | 0.500881i | \(0.833009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 128169. | 0.630131 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 143277. | + | 82721.1i | 0.692076 | + | 0.399570i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −147659. | − | 255752.i | −0.707011 | − | 1.22458i | −0.965961 | − | 0.258689i | \(-0.916710\pi\) |
0.258949 | − | 0.965891i | \(-0.416624\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 171120. | − | 98796.4i | 0.805193 | − | 0.464878i | −0.0400909 | − | 0.999196i | \(-0.512765\pi\) |
0.845284 | + | 0.534318i | \(0.179431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −43231.3 | + | 74878.8i | −0.201668 | + | 0.349299i | −0.949066 | − | 0.315078i | \(-0.897969\pi\) |
0.747398 | + | 0.664376i | \(0.231303\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 249159.i | 1.14247i | 0.820788 | + | 0.571233i | \(0.193535\pi\) | ||||
−0.820788 | + | 0.571233i | \(0.806465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13522.2 | 0.0614753 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6517.76 | + | 3763.03i | 0.0291324 | + | 0.0168196i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 265445. | + | 459763.i | 1.17649 | + | 2.03773i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 363916. | − | 210107.i | 1.58610 | − | 0.915734i | 0.592157 | − | 0.805823i | \(-0.298277\pi\) |
0.993941 | − | 0.109911i | \(-0.0350566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 291620. | − | 505101.i | 1.26046 | − | 2.18317i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 242853.i | 1.03243i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −394498. | −1.66336 | −0.831680 | − | 0.555255i | \(-0.812621\pi\) | ||||
−0.831680 | + | 0.555255i | \(0.812621\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −291929. | − | 168545.i | −1.21092 | − | 0.699123i | −0.247958 | − | 0.968771i | \(-0.579760\pi\) |
−0.962959 | + | 0.269647i | \(0.913093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1619.19 | + | 2804.52i | 0.00666199 | + | 0.0115389i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −105118. | + | 60690.1i | −0.425565 | + | 0.245700i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −227950. | + | 394821.i | −0.915458 | + | 1.58562i | −0.109227 | + | 0.994017i | \(0.534838\pi\) |
−0.806230 | + | 0.591602i | \(0.798496\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33893.3i | − | 0.133961i | −0.997754 | − | 0.0669804i | \(-0.978663\pi\) | ||
0.997754 | − | 0.0669804i | \(-0.0213365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −240905. | −0.944635 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −186058. | − | 107421.i | −0.718147 | − | 0.414622i | 0.0959233 | − | 0.995389i | \(-0.469420\pi\) |
−0.814070 | + | 0.580766i | \(0.802753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25400.7 | + | 43995.4i | 0.0972758 | + | 0.168487i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 53403.9 | − | 30832.7i | 0.201353 | − | 0.116251i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −87171.9 | + | 150986.i | −0.326134 | + | 0.564880i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 256109.i | − | 0.943516i | −0.881728 | − | 0.471758i | \(-0.843620\pi\) | ||
0.881728 | − | 0.471758i | \(-0.156380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 372105. | 1.36038 | 0.680192 | − | 0.733034i | \(-0.261896\pi\) | ||||
0.680192 | + | 0.733034i | \(0.261896\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1839.12 | − | 1061.81i | −0.00662198 | − | 0.00382320i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 188657. | + | 326764.i | 0.674159 | + | 1.16768i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −378060. | + | 218273.i | −1.33078 | + | 0.768327i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 412726. | − | 714863.i | 1.44196 | − | 2.49755i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 178224.i | − | 0.613464i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38292.3 | 0.130833 | 0.0654164 | − | 0.997858i | \(-0.479162\pi\) | ||||
0.0654164 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −327941. | − | 189337.i | −1.10409 | − | 0.637445i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −251103. | − | 434923.i | −0.839223 | − | 1.45358i | −0.890545 | − | 0.454894i | \(-0.849677\pi\) |
0.0513228 | − | 0.998682i | \(-0.483656\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 137275. | − | 79255.5i | 0.452155 | − | 0.261052i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34218.6 | + | 59268.3i | −0.111895 | + | 0.193808i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 601940.i | 1.94018i | 0.242737 | + | 0.970092i | \(0.421955\pi\) | ||||
−0.242737 | + | 0.970092i | \(0.578045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25633.9 | −0.0820333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −135970. | − | 78502.5i | −0.428970 | − | 0.247666i | 0.269938 | − | 0.962878i | \(-0.412997\pi\) |
−0.698908 | + | 0.715212i | \(0.746330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −60411.5 | − | 104636.i | −0.189244 | − | 0.327781i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 422713. | − | 244054.i | 1.30563 | − | 0.753808i | 0.324270 | − | 0.945965i | \(-0.394881\pi\) |
0.981364 | + | 0.192156i | \(0.0615481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 85604.0 | − | 148270.i | 0.262556 | − | 0.454760i | −0.704365 | − | 0.709838i | \(-0.748768\pi\) |
0.966920 | + | 0.255078i | \(0.0821013\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 807721.i | 2.44301i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −120517. | −0.361990 | −0.180995 | − | 0.983484i | \(-0.557932\pi\) | ||||
−0.180995 | + | 0.983484i | \(0.557932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −76757.3 | − | 44315.9i | −0.227388 | − | 0.131283i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −105307. | − | 182397.i | −0.309828 | − | 0.536638i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40161.9 | + | 23187.5i | −0.116557 | + | 0.0672942i | −0.557145 | − | 0.830415i | \(-0.688103\pi\) |
0.440588 | + | 0.897709i | \(0.354770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51973.3 | + | 90020.3i | −0.149813 | + | 0.259484i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 511267.i | − | 1.45391i | −0.686683 | − | 0.726957i | \(-0.740934\pi\) | ||
0.686683 | − | 0.726957i | \(-0.259066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6475.59 | 0.0182913 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −558562. | − | 322486.i | −1.55675 | − | 0.898787i | −0.997565 | − | 0.0697410i | \(-0.977783\pi\) |
−0.559180 | − | 0.829046i | \(-0.688884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −296605. | − | 513735.i | −0.821163 | − | 1.42230i | −0.904817 | − | 0.425801i | \(-0.859992\pi\) |
0.0836541 | − | 0.996495i | \(-0.473341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −278067. | + | 160542.i | −0.759695 | + | 0.438610i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −220510. | + | 381935.i | −0.598482 | + | 1.03660i | 0.394563 | + | 0.918869i | \(0.370896\pi\) |
−0.993045 | + | 0.117733i | \(0.962437\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 593817.i | − | 1.59063i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −397447. | −1.05769 | −0.528845 | − | 0.848718i | \(-0.677375\pi\) | ||||
−0.528845 | + | 0.848718i | \(0.677375\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1401.15 | + | 808.953i | 0.00368056 | + | 0.00212497i | 0.501839 | − | 0.864961i | \(-0.332657\pi\) |
−0.498159 | + | 0.867086i | \(0.665990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −274485. | − | 475422.i | −0.716370 | − | 1.24079i | −0.962429 | − | 0.271535i | \(-0.912469\pi\) |
0.246059 | − | 0.969255i | \(-0.420864\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 107914. | − | 62304.1i | 0.278036 | − | 0.160524i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10290.7 | − | 17824.0i | 0.0263442 | − | 0.0456294i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 22828.7i | − | 0.0577005i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 378413. | 0.950403 | 0.475202 | − | 0.879877i | \(-0.342375\pi\) | ||||
0.475202 | + | 0.879877i | \(0.342375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 342350. | + | 197656.i | 0.849030 | + | 0.490188i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 303517. | + | 525707.i | 0.748004 | + | 1.29558i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 62090.7 | − | 35848.1i | 0.151116 | − | 0.0872469i | −0.422535 | − | 0.906346i | \(-0.638860\pi\) |
0.573651 | + | 0.819100i | \(0.305526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −83582.4 | + | 144769.i | −0.202159 | + | 0.350149i | −0.949224 | − | 0.314602i | \(-0.898129\pi\) |
0.747065 | + | 0.664751i | \(0.231462\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 678022.i | 1.61970i | 0.586635 | + | 0.809852i | \(0.300452\pi\) | ||||
−0.586635 | + | 0.809852i | \(0.699548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −127192. | −0.301974 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 256473. | + | 148075.i | 0.601472 | + | 0.347260i | 0.769620 | − | 0.638502i | \(-0.220446\pi\) |
−0.168149 | + | 0.985762i | \(0.553779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12860.6 | + | 22275.2i | 0.0299763 | + | 0.0519204i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −684065. | + | 394945.i | −1.57517 | + | 0.909423i | −0.579648 | + | 0.814867i | \(0.696810\pi\) |
−0.995520 | + | 0.0945561i | \(0.969857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 212744. | − | 368484.i | 0.486917 | − | 0.843365i | −0.512970 | − | 0.858407i | \(-0.671455\pi\) |
0.999887 | + | 0.0150418i | \(0.00478812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 316964.i | − | 0.716749i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 241167. | 0.542083 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −379864. | − | 219314.i | −0.843690 | − | 0.487104i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 181403. | + | 314199.i | 0.400511 | + | 0.693705i | 0.993788 | − | 0.111294i | \(-0.0354994\pi\) |
−0.593277 | + | 0.804998i | \(0.702166\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 747854. | − | 431774.i | 1.63170 | − | 0.942061i | 0.648127 | − | 0.761532i | \(-0.275553\pi\) |
0.983570 | − | 0.180528i | \(-0.0577808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44551.4 | − | 77165.3i | 0.0966322 | − | 0.167372i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 323967.i | 0.694479i | 0.937776 | + | 0.347239i | \(0.112881\pi\) | ||||
−0.937776 | + | 0.347239i | \(0.887119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.28869e6 | 2.74641 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 621248. | + | 358678.i | 1.30866 | + | 0.755554i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 328629. | + | 569202.i | 0.688255 | + | 1.19209i | 0.972402 | + | 0.233312i | \(0.0749563\pi\) |
−0.284147 | + | 0.958781i | \(0.591710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 194733. | − | 112429.i | 0.403153 | − | 0.232760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8543.45 | + | 14797.7i | −0.0175860 | + | 0.0304599i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 695995.i | − | 1.41635i | −0.706038 | − | 0.708174i | \(-0.749519\pi\) | ||
0.706038 | − | 0.708174i | \(-0.250481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.11741e6 | −2.26101 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 76546.5 | + | 44194.1i | 0.153139 | + | 0.0884150i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 215242. | + | 372810.i | 0.428188 | + | 0.741643i | 0.996712 | − | 0.0810236i | \(-0.0258189\pi\) |
−0.568525 | + | 0.822666i | \(0.692486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −136961. | + | 79074.7i | −0.269413 | + | 0.155546i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −457183. | + | 791864.i | −0.894289 | + | 1.54895i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 435311.i | 0.842059i | 0.907047 | + | 0.421029i | \(0.138331\pi\) | ||||
−0.907047 | + | 0.421029i | \(0.861669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22625.1 | −0.0435231 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 256709. | + | 148211.i | 0.488388 | + | 0.281971i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3053.98 | + | 5289.64i | 0.00577826 | + | 0.0100082i | 0.868900 | − | 0.494988i | \(-0.164827\pi\) |
−0.863122 | + | 0.504996i | \(0.831494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −868.916 | + | 501.669i | −0.00162608 | + | 0.000938820i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 184878. | − | 320218.i | 0.344094 | − | 0.595989i | −0.641094 | − | 0.767462i | \(-0.721519\pi\) |
0.985189 | + | 0.171473i | \(0.0548526\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 74734.4i | 0.137590i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −381087. | −0.697807 | −0.348904 | − | 0.937159i | \(-0.613446\pi\) | ||||
−0.348904 | + | 0.937159i | \(0.613446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 370613. | + | 213974.i | 0.671341 | + | 0.387599i | 0.796585 | − | 0.604527i | \(-0.206638\pi\) |
−0.125243 | + | 0.992126i | \(0.539971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 165496. | + | 286647.i | 0.298177 | + | 0.516457i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −262283. | + | 151429.i | −0.467527 | + | 0.269927i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 211790. | − | 366831.i | 0.375514 | − | 0.650408i | −0.614890 | − | 0.788613i | \(-0.710800\pi\) |
0.990404 | + | 0.138204i | \(0.0441330\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 824333.i | − | 1.44614i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −910525. | −1.58891 | −0.794457 | − | 0.607321i | \(-0.792244\pi\) | ||||
−0.794457 | + | 0.607321i | \(0.792244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 612058. | + | 353372.i | 1.05687 | + | 0.610187i | 0.924566 | − | 0.381022i | \(-0.124428\pi\) |
0.132309 | + | 0.991209i | \(0.457761\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 69467.8 | + | 120322.i | 0.119326 | + | 0.206678i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 375177. | − | 216609.i | 0.637743 | − | 0.368201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −247932. | + | 429430.i | −0.419256 | + | 0.726173i | −0.995865 | − | 0.0908474i | \(-0.971042\pi\) |
0.576609 | + | 0.817021i | \(0.304376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 834415.i | − | 1.39644i | −0.715882 | − | 0.698221i | \(-0.753975\pi\) | ||
0.715882 | − | 0.698221i | \(-0.246025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −194384. | −0.323637 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 724312. | + | 418182.i | 1.19358 | + | 0.689112i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −335422. | − | 580968.i | −0.549908 | − | 0.952468i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −899478. | + | 519314.i | −1.45966 | + | 0.842734i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −64818.1 | + | 112268.i | −0.104652 | + | 0.181262i | −0.913596 | − | 0.406623i | \(-0.866706\pi\) |
0.808944 | + | 0.587886i | \(0.200039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44330.0i | 0.0708508i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.49398e6 | 2.37573 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 146748. | + | 84725.1i | 0.231024 | + | 0.133382i | 0.611044 | − | 0.791597i | \(-0.290750\pi\) |
−0.380021 | + | 0.924978i | \(0.624083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11621.3 | − | 20128.7i | −0.0182038 | − | 0.0315299i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −243154. | + | 140385.i | −0.377094 | + | 0.217716i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 241123. | − | 417637.i | 0.372089 | − | 0.644477i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 622158.i | 0.950613i | 0.879820 | + | 0.475307i | \(0.157663\pi\) | ||||
−0.879820 | + | 0.475307i | \(0.842337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 543177. | 0.825846 | 0.412923 | − | 0.910766i | \(-0.364508\pi\) | ||||
0.412923 | + | 0.910766i | \(0.364508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −574976. | − | 331962.i | −0.865634 | − | 0.499774i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24555.5 | + | 42531.3i | 0.0367878 | + | 0.0637184i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −213399. | + | 123206.i | −0.316597 | + | 0.182787i | −0.649875 | − | 0.760041i | \(-0.725179\pi\) |
0.333278 | + | 0.942829i | \(0.391845\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8586.13 | + | 14871.6i | −0.0126765 | + | 0.0219563i | −0.872294 | − | 0.488982i | \(-0.837368\pi\) |
0.859618 | + | 0.510938i | \(0.170702\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 471086.i | 0.688794i | 0.938824 | + | 0.344397i | \(0.111917\pi\) | ||||
−0.938824 | + | 0.344397i | \(0.888083\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 197808. | 0.287829 | 0.143915 | − | 0.989590i | \(-0.454031\pi\) | ||||
0.143915 | + | 0.989590i | \(0.454031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20576.7 | + | 11880.0i | 0.0296542 | + | 0.0171209i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −796542. | − | 1.37965e6i | −1.14245 | − | 1.97877i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −216362. | + | 124917.i | −0.307367 | + | 0.177458i | −0.645748 | − | 0.763551i | \(-0.723454\pi\) |
0.338381 | + | 0.941009i | \(0.390121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −309388. | + | 535876.i | −0.437433 | + | 0.757656i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.96429e6i | − | 2.75102i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 117806. | 0.164210 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.47232e6 | − | 850042.i | −2.03302 | − | 1.17376i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −96671.0 | − | 167439.i | −0.132861 | − | 0.230122i | 0.791917 | − | 0.610629i | \(-0.209083\pi\) |
−0.924778 | + | 0.380506i | \(0.875750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −860714. | + | 496934.i | −1.17192 | + | 0.676607i | −0.954131 | − | 0.299389i | \(-0.903217\pi\) |
−0.217787 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 508451. | − | 880664.i | 0.689070 | − | 1.19350i | −0.283070 | − | 0.959099i | \(-0.591353\pi\) |
0.972139 | − | 0.234404i | \(-0.0753139\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 17982.7i | − | 0.0241453i | −0.999927 | − | 0.0120727i | \(-0.996157\pi\) | ||
0.999927 | − | 0.0120727i | \(-0.00384294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −195478. | −0.261256 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −327564. | − | 189119.i | −0.433768 | − | 0.250436i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −127273. | − | 220444.i | −0.167765 | − | 0.290577i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 191333. | − | 110466.i | 0.249905 | − | 0.144282i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −267680. | + | 463636.i | −0.348030 | + | 0.602806i | −0.985899 | − | 0.167339i | \(-0.946483\pi\) |
0.637869 | + | 0.770145i | \(0.279816\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 348052.i | 0.448427i | 0.974540 | + | 0.224214i | \(0.0719813\pi\) | ||||
−0.974540 | + | 0.224214i | \(0.928019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.28216e6 | −1.64445 | −0.822227 | − | 0.569160i | \(-0.807268\pi\) | ||||
−0.822227 | + | 0.569160i | \(0.807268\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −538578. | − | 310948.i | −0.684544 | − | 0.395222i | 0.117021 | − | 0.993129i | \(-0.462666\pi\) |
−0.801565 | + | 0.597908i | \(0.795999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −72520.0 | − | 125608.i | −0.0917602 | − | 0.158933i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −985254. | + | 568837.i | −1.23551 | + | 0.713320i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −95915.0 | + | 166130.i | −0.119740 | + | 0.207396i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58038.6i | 0.0718121i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28078.1 | 0.0345874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 130469. | + | 75326.4i | 0.159298 | + | 0.0919709i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 626846. | + | 1.08573e6i | 0.761985 | + | 1.31980i | 0.941826 | + | 0.336101i | \(0.109108\pi\) |
−0.179841 | + | 0.983696i | \(0.557558\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 455921. | − | 263226.i | 0.549355 | − | 0.317170i | −0.199507 | − | 0.979896i | \(-0.563934\pi\) |
0.748862 | + | 0.662726i | \(0.230601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 244925. | − | 424223.i | 0.293827 | − | 0.508923i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 9437.09i | − | 0.0112228i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 317984. | 0.376508 | 0.188254 | − | 0.982120i | \(-0.439717\pi\) | ||||
0.188254 | + | 0.982120i | \(0.439717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.97879e6 | + | 1.14245e6i | 2.32271 | + | 1.34102i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.04480e6 | − | 1.80965e6i | −1.22110 | − | 2.11500i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.27158e6 | − | 734148.i | 1.47337 | − | 0.850652i | 0.473822 | − | 0.880621i | \(-0.342874\pi\) |
0.999551 | + | 0.0299688i | \(0.00954081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 581497. | − | 1.00718e6i | 0.670885 | − | 1.16201i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35789.3i | 0.0409383i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −672991. | −0.766532 | −0.383266 | − | 0.923638i | \(-0.625201\pi\) | ||||
−0.383266 | + | 0.923638i | \(0.625201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 75861.4 | + | 43798.6i | 0.0856725 | + | 0.0494631i | 0.542224 | − | 0.840234i | \(-0.317582\pi\) |
−0.456552 | + | 0.889697i | \(0.650916\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 636243. | + | 1.10200e6i | 0.715483 | + | 1.23925i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −786357. | + | 454003.i | −0.876839 | + | 0.506243i | −0.869615 | − | 0.493731i | \(-0.835633\pi\) |
−0.00722389 | + | 0.999974i | \(0.502299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 478153. | − | 828185.i | 0.530927 | − | 0.919592i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 747370.i | 0.822905i | 0.911431 | + | 0.411452i | \(0.134978\pi\) | ||||
−0.911431 | + | 0.411452i | \(0.865022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −418630. | −0.459011 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −409473. | − | 236410.i | −0.445234 | − | 0.257056i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 442731. | + | 766832.i | 0.479394 | + | 0.830335i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.50689e6 | − | 870001.i | 1.61818 | − | 0.934254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −162017. | + | 280622.i | −0.173264 | + | 0.300102i | −0.939559 | − | 0.342387i | \(-0.888765\pi\) |
0.766295 | + | 0.642489i | \(0.222098\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 873822.i | 0.926797i | 0.886150 | + | 0.463398i | \(0.153370\pi\) | ||||
−0.886150 | + | 0.463398i | \(0.846630\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −82500.5 | −0.0871427 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 246498. | + | 142316.i | 0.258240 | + | 0.149095i | 0.623532 | − | 0.781798i | \(-0.285697\pi\) |
−0.365291 | + | 0.930893i | \(0.619031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 344343. | + | 596419.i | 0.359274 | + | 0.622280i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 306.104 | − | 176.729i | 0.000316783 | − | 0.000182895i | −0.499842 | − | 0.866117i | \(-0.666608\pi\) |
0.500158 | + | 0.865934i | \(0.333275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00464e6 | + | 1.74009e6i | −1.03547 | + | 1.79349i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 74719.9i | 0.0763913i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.22572e6 | 1.24808 | 0.624041 | − | 0.781392i | \(-0.285490\pi\) | ||||
0.624041 | + | 0.781392i | \(0.285490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −265505. | − | 153290.i | −0.268180 | − | 0.154834i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 663483. | + | 1.14919e6i | 0.667482 | + | 1.15611i | 0.978606 | + | 0.205744i | \(0.0659613\pi\) |
−0.311124 | + | 0.950369i | \(0.600705\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 108.5.g.a.17.4 | 8 | ||
3.2 | odd | 2 | 36.5.g.a.5.2 | ✓ | 8 | ||
4.3 | odd | 2 | 432.5.q.c.17.4 | 8 | |||
9.2 | odd | 6 | inner | 108.5.g.a.89.4 | 8 | ||
9.4 | even | 3 | 324.5.c.a.161.1 | 8 | |||
9.5 | odd | 6 | 324.5.c.a.161.8 | 8 | |||
9.7 | even | 3 | 36.5.g.a.29.2 | yes | 8 | ||
12.11 | even | 2 | 144.5.q.c.113.3 | 8 | |||
36.7 | odd | 6 | 144.5.q.c.65.3 | 8 | |||
36.11 | even | 6 | 432.5.q.c.305.4 | 8 | |||
36.23 | even | 6 | 1296.5.e.g.161.8 | 8 | |||
36.31 | odd | 6 | 1296.5.e.g.161.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.g.a.5.2 | ✓ | 8 | 3.2 | odd | 2 | ||
36.5.g.a.29.2 | yes | 8 | 9.7 | even | 3 | ||
108.5.g.a.17.4 | 8 | 1.1 | even | 1 | trivial | ||
108.5.g.a.89.4 | 8 | 9.2 | odd | 6 | inner | ||
144.5.q.c.65.3 | 8 | 36.7 | odd | 6 | |||
144.5.q.c.113.3 | 8 | 12.11 | even | 2 | |||
324.5.c.a.161.1 | 8 | 9.4 | even | 3 | |||
324.5.c.a.161.8 | 8 | 9.5 | odd | 6 | |||
432.5.q.c.17.4 | 8 | 4.3 | odd | 2 | |||
432.5.q.c.305.4 | 8 | 36.11 | even | 6 | |||
1296.5.e.g.161.1 | 8 | 36.31 | odd | 6 | |||
1296.5.e.g.161.8 | 8 | 36.23 | even | 6 |