Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), 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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Root | \(-2.40693 + 1.48549i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.95 |
Dual form | 128.5.f.b.31.4 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.0461995 | − | 0.0461995i | 0.00513328 | − | 0.00513328i | −0.704535 | − | 0.709669i | \(-0.748845\pi\) |
0.709669 | + | 0.704535i | \(0.248845\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.04297 | − | 8.04297i | 0.321719 | − | 0.321719i | −0.527707 | − | 0.849426i | \(-0.676948\pi\) |
0.849426 | + | 0.527707i | \(0.176948\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.8797 | −1.01795 | −0.508976 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508976 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 80.9957i | 0.999947i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 84.2573 | + | 84.2573i | 0.696341 | + | 0.696341i | 0.963619 | − | 0.267278i | \(-0.0861243\pi\) |
−0.267278 | + | 0.963619i | \(0.586124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.4838 | − | 19.4838i | −0.115289 | − | 0.115289i | 0.647109 | − | 0.762398i | \(-0.275978\pi\) |
−0.762398 | + | 0.647109i | \(0.775978\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.743162i | − | 0.00330294i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 437.855 | 1.51507 | 0.757535 | − | 0.652795i | \(-0.226404\pi\) | ||||
0.757535 | + | 0.652795i | \(0.226404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −349.021 | + | 349.021i | −0.966817 | + | 0.966817i | −0.999467 | − | 0.0326494i | \(-0.989606\pi\) |
0.0326494 | + | 0.999467i | \(0.489606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.30442 | + | 2.30442i | −0.00522543 | + | 0.00522543i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −404.840 | −0.765293 | −0.382647 | − | 0.923895i | \(-0.624987\pi\) | ||||
−0.382647 | + | 0.923895i | \(0.624987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 495.621i | 0.792994i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.48412 | + | 7.48412i | 0.0102663 | + | 0.0102663i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1031.65 | + | 1031.65i | 1.22670 | + | 1.22670i | 0.965206 | + | 0.261490i | \(0.0842139\pi\) |
0.261490 | + | 0.965206i | \(0.415786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1506.15i | 1.56728i | 0.621217 | + | 0.783638i | \(0.286638\pi\) | ||||
−0.621217 | + | 0.783638i | \(0.713362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.78529 | 0.00714903 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −401.181 | + | 401.181i | −0.327494 | + | 0.327494i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 434.262 | − | 434.262i | 0.317211 | − | 0.317211i | −0.530484 | − | 0.847695i | \(-0.677990\pi\) |
0.847695 | + | 0.530484i | \(0.177990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.80028 | −0.00118362 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 696.847i | − | 0.414543i | −0.978283 | − | 0.207272i | \(-0.933542\pi\) | ||
0.978283 | − | 0.207272i | \(-0.0664584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −917.612 | − | 917.612i | −0.496275 | − | 0.496275i | 0.414002 | − | 0.910276i | \(-0.364131\pi\) |
−0.910276 | + | 0.414002i | \(0.864131\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 651.446 | + | 651.446i | 0.321702 | + | 0.321702i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 111.917i | − | 0.0506641i | −0.999679 | − | 0.0253321i | \(-0.991936\pi\) | ||
0.999679 | − | 0.0253321i | \(-0.00806431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 86.9810 | 0.0362270 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.2287 | − | 20.2287i | 0.00777728 | − | 0.00777728i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1041.19 | + | 1041.19i | −0.370663 | + | 0.370663i | −0.867719 | − | 0.497056i | \(-0.834414\pi\) |
0.497056 | + | 0.867719i | \(0.334414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1355.36 | 0.448052 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 32.2492i | 0.00992589i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1711.60 | + | 1711.60i | 0.491697 | + | 0.491697i | 0.908841 | − | 0.417144i | \(-0.136969\pi\) |
−0.417144 | + | 0.908841i | \(0.636969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3711.24 | − | 3711.24i | −0.997376 | − | 0.997376i | 0.00262076 | − | 0.999997i | \(-0.499166\pi\) |
−0.999997 | + | 0.00262076i | \(0.999166\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4040.04i | − | 1.01790i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −313.415 | −0.0741810 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1854.18 | − | 1854.18i | 0.413049 | − | 0.413049i | −0.469750 | − | 0.882799i | \(-0.655656\pi\) |
0.882799 | + | 0.469750i | \(0.155656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.7034 | + | 18.7034i | −0.00392846 | + | 0.00392846i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1161.89 | −0.230489 | −0.115244 | − | 0.993337i | \(-0.536765\pi\) | ||||
−0.115244 | + | 0.993337i | \(0.536765\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 905.295i | 0.169881i | 0.996386 | + | 0.0849404i | \(0.0270700\pi\) | ||||
−0.996386 | + | 0.0849404i | \(0.972930\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.8975 | + | 22.8975i | 0.00407066 | + | 0.00407066i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4202.72 | − | 4202.72i | −0.708842 | − | 0.708842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5869.63i | − | 0.940495i | −0.882535 | − | 0.470247i | \(-0.844165\pi\) | ||
0.882535 | − | 0.470247i | \(-0.155835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6559.96 | −0.999842 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7560.06 | − | 7560.06i | 1.09741 | − | 1.09741i | 0.102698 | − | 0.994713i | \(-0.467252\pi\) |
0.994713 | − | 0.102698i | \(-0.0327476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3521.65 | − | 3521.65i | 0.487426 | − | 0.487426i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 95.3236 | 0.0125939 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6439.80i | − | 0.813004i | −0.913650 | − | 0.406502i | \(-0.866748\pi\) | ||
0.913650 | − | 0.406502i | \(-0.133252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 971.844 | + | 971.844i | 0.117358 | + | 0.117358i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 69.5835 | + | 69.5835i | 0.00804527 | + | 0.00804527i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5614.33i | 0.622087i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −413.032 | −0.0438976 | −0.0219488 | − | 0.999759i | \(-0.506987\pi\) | ||||
−0.0219488 | + | 0.999759i | \(0.506987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6824.48 | + | 6824.48i | −0.696304 | + | 0.696304i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8460.63 | + | 8460.63i | −0.829392 | + | 0.829392i | −0.987433 | − | 0.158041i | \(-0.949482\pi\) |
0.158041 | + | 0.987433i | \(0.449482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17007.9 | 1.60316 | 0.801578 | − | 0.597891i | \(-0.203994\pi\) | ||||
0.801578 | + | 0.597891i | \(0.203994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 37.0687i | 0.00336224i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9368.65 | − | 9368.65i | −0.818294 | − | 0.818294i | 0.167567 | − | 0.985861i | \(-0.446409\pi\) |
−0.985861 | + | 0.167567i | \(0.946409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8308.73 | + | 8308.73i | 0.699329 | + | 0.699329i | 0.964266 | − | 0.264937i | \(-0.0853510\pi\) |
−0.264937 | + | 0.964266i | \(0.585351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 40.1254i | − | 0.00325667i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5814.63 | 0.455371 | 0.227685 | − | 0.973735i | \(-0.426884\pi\) | ||||
0.227685 | + | 0.973735i | \(0.426884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3256.12 | + | 3256.12i | −0.246209 | + | 0.246209i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1578.10 | − | 1578.10i | 0.115283 | − | 0.115283i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21840.1 | −1.54227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 442.428i | − | 0.0302185i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32.1940 | − | 32.1940i | −0.00212797 | − | 0.00212797i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9013.12 | + | 9013.12i | 0.576840 | + | 0.576840i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20367.1i | 1.26276i | 0.775472 | + | 0.631382i | \(0.217512\pi\) | ||||
−0.775472 | + | 0.631382i | \(0.782488\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −84.7864 | −0.00509503 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4414.52 | + | 4414.52i | −0.257242 | + | 0.257242i | −0.823931 | − | 0.566690i | \(-0.808224\pi\) |
0.566690 | + | 0.823931i | \(0.308224\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17409.1 | − | 17409.1i | 0.984174 | − | 0.984174i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 120.389 | 0.00660571 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11018.7i | 0.587067i | 0.955949 | + | 0.293533i | \(0.0948312\pi\) | ||||
−0.955949 | + | 0.293533i | \(0.905169\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14957.2 | + | 14957.2i | 0.774140 | + | 0.774140i | 0.978827 | − | 0.204688i | \(-0.0656178\pi\) |
−0.204688 | + | 0.978827i | \(0.565618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.17051 | − | 5.17051i | −0.000260073 | − | 0.000260073i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3283.30i | − | 0.160560i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16595.1 | 0.789302 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.01848 | − | 4.01848i | 0.000185963 | − | 0.000185963i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15393.9 | + | 15393.9i | −0.693388 | + | 0.693388i | −0.962976 | − | 0.269588i | \(-0.913112\pi\) |
0.269588 | + | 0.962976i | \(0.413112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16971.9 | −0.744347 | −0.372174 | − | 0.928163i | \(-0.621387\pi\) | ||||
−0.372174 | + | 0.928163i | \(0.621387\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 35464.4i | 1.51499i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12113.9 | + | 12113.9i | 0.504222 | + | 0.504222i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1167.73 | − | 1167.73i | −0.0473744 | − | 0.0473744i | 0.683023 | − | 0.730397i | \(-0.260665\pi\) |
−0.730397 | + | 0.683023i | \(0.760665\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 96.2051i | 0.00380543i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20193.3 | 0.779032 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −28076.2 | + | 28076.2i | −1.05673 | + | 1.05673i | −0.0584383 | + | 0.998291i | \(0.518612\pi\) |
−0.998291 | + | 0.0584383i | \(0.981388\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 62.6168 | − | 62.6168i | 0.00229998 | − | 0.00229998i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2929.82 | −0.105053 | −0.0525264 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525264 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 27801.8i | − | 0.973417i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28269.2 | − | 28269.2i | −0.966767 | − | 0.966767i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8560.97 | − | 8560.97i | −0.286043 | − | 0.286043i | 0.549470 | − | 0.835513i | \(-0.314829\pi\) |
−0.835513 | + | 0.549470i | \(0.814829\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 24721.4i | − | 0.807230i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 158.150 | 0.00504804 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24420.1 | − | 24420.1i | 0.762153 | − | 0.762153i | −0.214558 | − | 0.976711i | \(-0.568831\pi\) |
0.976711 | + | 0.214558i | \(0.0688311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10946.5 | − | 10946.5i | 0.334133 | − | 0.334133i | −0.520021 | − | 0.854154i | \(-0.674076\pi\) |
0.854154 | + | 0.520021i | \(0.174076\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −342.915 | −0.0102396 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6985.52i | − | 0.204106i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36892.5 | + | 36892.5i | 1.05501 | + | 1.05501i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −373.306 | − | 373.306i | −0.0104506 | − | 0.0104506i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22384.9i | 0.613604i | 0.951773 | + | 0.306802i | \(0.0992590\pi\) | ||||
−0.951773 | + | 0.306802i | \(0.900741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −30429.5 | −0.816920 | −0.408460 | − | 0.912776i | \(-0.633934\pi\) | ||||
−0.408460 | + | 0.912776i | \(0.633934\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.4796 | + | 14.4796i | −0.000380792 | + | 0.000380792i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19093.9 | + | 19093.9i | −0.491997 | + | 0.491997i | −0.908935 | − | 0.416938i | \(-0.863103\pi\) |
0.416938 | + | 0.908935i | \(0.363103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 67963.8 | 1.71621 | 0.858107 | − | 0.513470i | \(-0.171640\pi\) | ||||
0.858107 | + | 0.513470i | \(0.171640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 171.324i | − | 0.00424060i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −51458.4 | − | 51458.4i | −1.24872 | − | 1.24872i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5604.72 | − | 5604.72i | −0.133366 | − | 0.133366i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 32790.3i | − | 0.765253i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −58815.1 | −1.34647 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 55219.8 | − | 55219.8i | 1.24031 | − | 1.24031i | 0.280438 | − | 0.959872i | \(-0.409520\pi\) |
0.959872 | − | 0.280438i | \(-0.0904797\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −53.6790 | + | 53.6790i | −0.00118316 | + | 0.00118316i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14760.6 | −0.319322 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 75126.4i | − | 1.59541i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 41.8242 | + | 41.8242i | 0.000872046 | + | 0.000872046i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8531.07 | − | 8531.07i | −0.174670 | − | 0.174670i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 40417.5i | 0.812754i | 0.913705 | + | 0.406377i | \(0.133208\pi\) | ||||
−0.913705 | + | 0.406377i | \(0.866792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −40143.2 | −0.792952 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1672.85 | − | 1672.85i | 0.0324643 | − | 0.0324643i | −0.690688 | − | 0.723153i | \(-0.742692\pi\) |
0.723153 | + | 0.690688i | \(0.242692\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26519.0 | − | 26519.0i | 0.505691 | − | 0.505691i | −0.407510 | − | 0.913201i | \(-0.633603\pi\) |
0.913201 | + | 0.407510i | \(0.133603\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −388.328 | −0.00727737 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24163.3i | 0.445087i | 0.974923 | + | 0.222543i | \(0.0714359\pi\) | ||||
−0.974923 | + | 0.222543i | \(0.928564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −900.145 | − | 900.145i | −0.0162996 | − | 0.0162996i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −271.174 | − | 271.174i | −0.00482782 | − | 0.00482782i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 76356.4i | − | 1.33675i | −0.743825 | − | 0.668374i | \(-0.766990\pi\) | ||
0.743825 | − | 0.668374i | \(-0.233010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 40548.1 | 0.698130 | 0.349065 | − | 0.937099i | \(-0.386499\pi\) | ||||
0.349065 | + | 0.937099i | \(0.386499\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −909.281 | + | 909.281i | −0.0153988 | + | 0.0153988i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 699.586 | − | 699.586i | 0.0116549 | − | 0.0116549i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13600.5 | 0.222926 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 698.542i | − | 0.0112666i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10536.0 | + | 10536.0i | 0.167235 | + | 0.167235i | 0.785763 | − | 0.618528i | \(-0.212271\pi\) |
−0.618528 | + | 0.785763i | \(0.712271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34110.7 | − | 34110.7i | −0.532905 | − | 0.532905i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 325.397i | − | 0.00500419i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 37983.9 | 0.575086 | 0.287543 | − | 0.957768i | \(-0.407162\pi\) | ||||
0.287543 | + | 0.957768i | \(0.407162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21660.9 | + | 21660.9i | −0.322906 | + | 0.322906i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −83559.4 | + | 83559.4i | −1.22663 | + | 1.22663i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 37545.0 | 0.542801 | 0.271400 | − | 0.962467i | \(-0.412513\pi\) | ||||
0.271400 | + | 0.962467i | \(0.412513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16748.6i | 0.238498i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −297.516 | − | 297.516i | −0.00417338 | − | 0.00417338i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4676.63 | − | 4676.63i | −0.0646291 | − | 0.0646291i | 0.674053 | − | 0.738683i | \(-0.264552\pi\) |
−0.738683 | + | 0.674053i | \(0.764552\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2746.12i | − | 0.0373922i | −0.999825 | − | 0.0186961i | \(-0.994049\pi\) | ||
0.999825 | − | 0.0186961i | \(-0.00595149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 89.7975 | 0.00120487 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −41759.7 | + | 41759.7i | −0.552194 | + | 0.552194i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 33056.5 | − | 33056.5i | 0.430822 | − | 0.430822i | −0.458086 | − | 0.888908i | \(-0.651465\pi\) |
0.888908 | + | 0.458086i | \(0.151465\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −121992. | −1.56719 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 80033.0i | 1.01358i | 0.862071 | + | 0.506788i | \(0.169167\pi\) | ||||
−0.862071 | + | 0.506788i | \(0.830833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 72284.3 | + | 72284.3i | 0.902549 | + | 0.902549i | 0.995656 | − | 0.0931068i | \(-0.0296798\pi\) |
−0.0931068 | + | 0.995656i | \(0.529680\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 259.379 | + | 259.379i | 0.00319334 | + | 0.00319334i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34758.5i | 0.421985i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 108196. | 1.29544 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.0819 | + | 19.0819i | −0.000225339 | + | 0.000225339i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 84911.3 | − | 84911.3i | 0.989077 | − | 0.989077i | −0.0108641 | − | 0.999941i | \(-0.503458\pi\) |
0.999941 | + | 0.0108641i | \(0.00345823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27532.6 | 0.316376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1261.18i | 0.0142977i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7887.81 | + | 7887.81i | 0.0882296 | + | 0.0882296i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45770.2 | + | 45770.2i | 0.505184 | + | 0.505184i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 781.754i | 0.00851500i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −59698.7 | −0.641749 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 55472.5 | − | 55472.5i | 0.588574 | − | 0.588574i | −0.348671 | − | 0.937245i | \(-0.613367\pi\) |
0.937245 | + | 0.348671i | \(0.113367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 785.756 | − | 785.756i | 0.00822944 | − | 0.00822944i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −127048. | −1.31355 | −0.656777 | − | 0.754084i | \(-0.728081\pi\) | ||||
−0.656777 | + | 0.754084i | \(0.728081\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25469.3i | 0.259974i | 0.991516 | + | 0.129987i | \(0.0414935\pi\) | ||||
−0.991516 | + | 0.129987i | \(0.958507\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −32493.9 | − | 32493.9i | −0.327477 | − | 0.327477i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 94218.4 | + | 94218.4i | 0.937599 | + | 0.937599i | 0.998164 | − | 0.0605656i | \(-0.0192904\pi\) |
−0.0605656 | + | 0.998164i | \(0.519290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 173848.i | 1.70840i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −865.654 | −0.00840107 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −152821. | + | 152821.i | −1.46480 | + | 1.46480i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9656.57 | − | 9656.57i | 0.0914232 | − | 0.0914232i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 767.719 | 0.00717971 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5582.38i | 0.0515737i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −65141.3 | − | 65141.3i | −0.594567 | − | 0.594567i | 0.344295 | − | 0.938862i | \(-0.388118\pi\) |
−0.938862 | + | 0.344295i | \(0.888118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 35173.4 | + | 35173.4i | 0.317195 | + | 0.317195i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 29826.2i | − | 0.265771i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 135004. | 1.18874 | 0.594369 | − | 0.804193i | \(-0.297402\pi\) | ||||
0.594369 | + | 0.804193i | \(0.297402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 268.633 | − | 268.633i | 0.00233754 | − | 0.00233754i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −126904. | + | 126904.i | −1.09136 | + | 1.09136i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 115422. | 0.981075 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 300.862i | 0.00252772i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10849.2 | − | 10849.2i | −0.0901025 | − | 0.0901025i | 0.660619 | − | 0.750721i | \(-0.270294\pi\) |
−0.750721 | + | 0.660619i | \(0.770294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6073.15 | + | 6073.15i | 0.0498612 | + | 0.0498612i | 0.731598 | − | 0.681737i | \(-0.238775\pi\) |
−0.681737 | + | 0.731598i | \(0.738775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 291.638i | − | 0.00236717i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −143445. | −1.15116 | −0.575579 | − | 0.817746i | \(-0.695223\pi\) | ||||
−0.575579 | + | 0.817746i | \(0.695223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9345.08 | + | 9345.08i | −0.0741526 | + | 0.0741526i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1009.00 | + | 1009.00i | −0.00791690 | + | 0.00791690i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 124076. | 0.962718 | 0.481359 | − | 0.876523i | \(-0.340143\pi\) | ||||
0.481359 | + | 0.876523i | \(0.340143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 113310.i | − | 0.869472i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.4400 | − | 20.4400i | −0.000155120 | − | 0.000155120i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7281.26 | + | 7281.26i | 0.0546538 | + | 0.0546538i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 126240.i | 0.937268i | 0.883392 | + | 0.468634i | \(0.155254\pi\) | ||||
−0.883392 | + | 0.468634i | \(0.844746\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 56441.7 | 0.414521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 51934.3 | − | 51934.3i | 0.377317 | − | 0.377317i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 95513.7 | − | 95513.7i | 0.686512 | − | 0.686512i | −0.274948 | − | 0.961459i | \(-0.588661\pi\) |
0.961459 | + | 0.274948i | \(0.0886605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 832.804 | 0.00592216 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 40200.9i | − | 0.282848i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31220.0 | + | 31220.0i | 0.217347 | + | 0.217347i | 0.807380 | − | 0.590032i | \(-0.200885\pi\) |
−0.590032 | + | 0.807380i | \(0.700885\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 940.951 | + | 940.951i | 0.00648212 | + | 0.00648212i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 253102.i | − | 1.72543i | −0.505689 | − | 0.862716i | \(-0.668762\pi\) | ||
0.505689 | − | 0.862716i | \(-0.331238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −67604.7 | −0.456095 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 74322.6 | − | 74322.6i | 0.496248 | − | 0.496248i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 43279.4 | − | 43279.4i | 0.286011 | − | 0.286011i | −0.549490 | − | 0.835500i | \(-0.685178\pi\) |
0.835500 | + | 0.549490i | \(0.185178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −177261. | −1.15947 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 407.898i | 0.00264099i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −47209.2 | − | 47209.2i | −0.302575 | − | 0.302575i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −198533. | − | 198533.i | −1.25965 | − | 1.25965i | −0.951258 | − | 0.308395i | \(-0.900208\pi\) |
−0.308395 | − | 0.951258i | \(-0.599792\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1608.58i | − | 0.0101041i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −89330.8 | −0.555536 | −0.277768 | − | 0.960648i | \(-0.589595\pi\) | ||||
−0.277768 | + | 0.960648i | \(0.589595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29345.5 | − | 29345.5i | 0.180689 | − | 0.180689i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −52761.6 | + | 52761.6i | −0.321668 | + | 0.321668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 73179.5 | 0.441775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26716.3i | − | 0.159709i | −0.996807 | − | 0.0798545i | \(-0.974554\pi\) | ||
0.996807 | − | 0.0798545i | \(-0.0254456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 509.057 | + | 509.057i | 0.00301358 | + | 0.00301358i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −85373.9 | − | 85373.9i | −0.500524 | − | 0.500524i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 121611.i | − | 0.706115i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1382.03 | 0.00794775 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 119011. | − | 119011.i | 0.677889 | − | 0.677889i | −0.281633 | − | 0.959522i | \(-0.590876\pi\) |
0.959522 | + | 0.281633i | \(0.0908761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −126967. | + | 126967.i | −0.716355 | + | 0.716355i | −0.967857 | − | 0.251502i | \(-0.919075\pi\) |
0.251502 | + | 0.967857i | \(0.419075\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9064.80 | 0.0506614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 217010.i | 1.20144i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 185115. | + | 185115.i | 1.01528 | + | 1.01528i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −151.687 | − | 151.687i | −0.000824201 | − | 0.000824201i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 82986.1i | − | 0.446736i | −0.974734 | − | 0.223368i | \(-0.928295\pi\) | ||
0.974734 | − | 0.223368i | \(-0.0717051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −153228. | −0.817265 | −0.408633 | − | 0.912699i | \(-0.633994\pi\) | ||||
−0.408633 | + | 0.912699i | \(0.633994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 766.685 | − | 766.685i | 0.00405171 | − | 0.00405171i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 141298. | − | 141298.i | 0.739899 | − | 0.739899i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 48984.2 | 0.254172 | 0.127086 | − | 0.991892i | \(-0.459438\pi\) | ||||
0.127086 | + | 0.991892i | \(0.459438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7045.09i | 0.0362251i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5464.01 | − | 5464.01i | −0.0278422 | − | 0.0278422i | 0.693049 | − | 0.720891i | \(-0.256267\pi\) |
−0.720891 | + | 0.693049i | \(0.756267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −51795.1 | − | 51795.1i | −0.261559 | − | 0.261559i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1422.38i | 0.00711870i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 140068. | 0.694776 | 0.347388 | − | 0.937721i | \(-0.387069\pi\) | ||||
0.347388 | + | 0.937721i | \(0.387069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58714.4 | − | 58714.4i | 0.288664 | − | 0.288664i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −784.092 | + | 784.092i | −0.00382094 | + | 0.00382094i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15633.0 | 0.0755127 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 219788.i | − | 1.05238i | −0.850368 | − | 0.526188i | \(-0.823621\pi\) | ||
0.850368 | − | 0.526188i | \(-0.176379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3276.96 | + | 3276.96i | 0.0155541 | + | 0.0155541i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −124163. | − | 124163.i | −0.584239 | − | 0.584239i | 0.351826 | − | 0.936065i | \(-0.385561\pi\) |
−0.936065 | + | 0.351826i | \(0.885561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 236566.i | − | 1.10354i | −0.833995 | − | 0.551772i | \(-0.813952\pi\) | ||
0.833995 | − | 0.551772i | \(-0.186048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1119.32 | 0.00517663 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −73415.5 | + | 73415.5i | −0.336631 | + | 0.336631i | −0.855098 | − | 0.518467i | \(-0.826503\pi\) |
0.518467 | + | 0.855098i | \(0.326503\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −92485.8 | + | 92485.8i | −0.420465 | + | 0.420465i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −107.897 | −0.000486372 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 154631.i | − | 0.691153i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −172982. | − | 172982.i | −0.766681 | − | 0.766681i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −84332.1 | − | 84332.1i | −0.370643 | − | 0.370643i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 212004.i | 0.924003i | 0.886879 | + | 0.462002i | \(0.152869\pi\) | ||||
−0.886879 | + | 0.462002i | \(0.847131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16922.1 | −0.0731417 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 932.920 | − | 932.920i | 0.00399899 | − | 0.00399899i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3322.01 | + | 3322.01i | −0.0141227 | + | 0.0141227i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26716.3 | 0.112647 | 0.0563234 | − | 0.998413i | \(-0.482062\pi\) | ||||
0.0563234 | + | 0.998413i | \(0.482062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2594.22i | 0.0108490i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −99544.8 | − | 99544.8i | −0.412910 | − | 0.412910i | 0.469841 | − | 0.882751i | \(-0.344311\pi\) |
−0.882751 | + | 0.469841i | \(0.844311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 451714. | + | 451714.i | 1.85853 | + | 1.85853i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 109778.i | 0.448028i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 57954.9 | 0.234627 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −189887. | + | 189887.i | −0.762597 | + | 0.762597i | −0.976791 | − | 0.214194i | \(-0.931287\pi\) |
0.214194 | + | 0.976791i | \(0.431287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −135.356 | + | 135.356i | −0.000539265 | + | 0.000539265i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 188872. | 0.746502 | 0.373251 | − | 0.927730i | \(-0.378243\pi\) | ||||
0.373251 | + | 0.927730i | \(0.378243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 136097.i | 0.533662i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1284.43 | − | 1284.43i | −0.00499682 | − | 0.00499682i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14343.5 | + | 14343.5i | 0.0553629 | + | 0.0553629i | 0.734246 | − | 0.678883i | \(-0.237536\pi\) |
−0.678883 | + | 0.734246i | \(0.737536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 45155.8i | − | 0.172931i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5224.23 | −0.0198513 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 136794. | − | 136794.i | 0.515765 | − | 0.515765i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9429.82 | − | 9429.82i | 0.0352795 | − | 0.0352795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −791.025 | −0.00293667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 65377.4i | 0.240853i | 0.992722 | + | 0.120427i | \(0.0384262\pi\) | ||||
−0.992722 | + | 0.120427i | \(0.961574\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 143634. | + | 143634.i | 0.525113 | + | 0.525113i | 0.919111 | − | 0.393998i | \(-0.128908\pi\) |
−0.393998 | + | 0.919111i | \(0.628908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1142.12 | − | 1142.12i | −0.00414374 | − | 0.00414374i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 659477.i | 2.37453i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −115946. | −0.414327 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −138632. | + | 138632.i | −0.491671 | + | 0.491671i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13577.2 | + | 13577.2i | −0.0477921 | + | 0.0477921i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −150704. | −0.526521 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2256.40i | − | 0.00782469i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7328.78 | + | 7328.78i | 0.0252263 | + | 0.0252263i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 275122. | + | 275122.i | 0.940007 | + | 0.940007i | 0.998300 | − | 0.0582928i | \(-0.0185657\pi\) |
−0.0582928 | + | 0.998300i | \(0.518566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1011.45i | − | 0.00343039i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 133654. | 0.449975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1032.53 | − | 1032.53i | 0.00345087 | − | 0.00345087i | −0.705379 | − | 0.708830i | \(-0.749223\pi\) |
0.708830 | + | 0.705379i | \(0.249223\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 300594. | − | 300594.i | 0.997323 | − | 0.997323i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −720136. | −2.37198 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 292775.i | 0.957379i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −322.727 | − | 322.727i | −0.00104773 | − | 0.00104773i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 223266. | + | 223266.i | 0.719635 | + | 0.719635i | 0.968530 | − | 0.248895i | \(-0.0800674\pi\) |
−0.248895 | + | 0.968530i | \(0.580067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35757.1i | 0.114430i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3408.83 | 0.0108313 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −191551. | + | 191551.i | −0.604322 | + | 0.604322i | −0.941457 | − | 0.337134i | \(-0.890542\pi\) |
0.337134 | + | 0.941457i | \(0.390542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46766.9 | − | 46766.9i | 0.146501 | − | 0.146501i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 327209. | 1.01779 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 119746.i | − | 0.369858i | −0.982752 | − | 0.184929i | \(-0.940795\pi\) | ||
0.982752 | − | 0.184929i | \(-0.0592055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −375516. | − | 375516.i | −1.15175 | − | 1.15175i | −0.986202 | − | 0.165544i | \(-0.947062\pi\) |
−0.165544 | − | 0.986202i | \(-0.552938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1034.17 | + | 1034.17i | 0.00314980 | + | 0.00314980i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 200647.i | − | 0.606873i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 185281. | 0.556518 | 0.278259 | − | 0.960506i | \(-0.410243\pi\) | ||||
0.278259 | + | 0.960506i | \(0.410243\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1405.83 | + | 1405.83i | −0.00419348 | + | 0.00419348i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −377093. | + | 377093.i | −1.11711 | + | 1.11711i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −175456. | −0.516216 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 25385.3i | − | 0.0741771i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 483071. | + | 483071.i | 1.40196 | + | 1.40196i | 0.793875 | + | 0.608081i | \(0.208060\pi\) |
0.608081 | + | 0.793875i | \(0.291940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −525679. | − | 525679.i | −1.51527 | − | 1.51527i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1764.26i | 0.00505112i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 636299. | 1.80947 | 0.904736 | − | 0.425973i | \(-0.140068\pi\) | ||||
0.904736 | + | 0.425973i | \(0.140068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −175659. | + | 175659.i | −0.496177 | + | 0.496177i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3139.90 | − | 3139.90i | 0.00880981 | − | 0.00880981i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 410280. | 1.14347 | 0.571737 | − | 0.820437i | \(-0.306270\pi\) | ||||
0.571737 | + | 0.820437i | \(0.306270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 531872.i | 1.47251i | 0.676704 | + | 0.736255i | \(0.263408\pi\) | ||||
−0.676704 | + | 0.736255i | \(0.736592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 150181. | + | 150181.i | 0.413028 | + | 0.413028i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3558.44 | − | 3558.44i | −0.00972184 | − | 0.00972184i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 505448.i | − | 1.37182i | −0.727684 | − | 0.685912i | \(-0.759403\pi\) | ||
0.727684 | − | 0.685912i | \(-0.240597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4754.71 | −0.0128200 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2180.57 | + | 2180.57i | −0.00584099 | + | 0.00584099i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31334.4 | − | 31334.4i | 0.0833873 | − | 0.0833873i | −0.664183 | − | 0.747570i | \(-0.731220\pi\) |
0.747570 | + | 0.664183i | \(0.231220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −517.871 | −0.00136921 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 481833.i | − | 1.26569i | −0.774280 | − | 0.632844i | \(-0.781888\pi\) | ||
0.774280 | − | 0.632844i | \(-0.218112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −55035.5 | − | 55035.5i | −0.143635 | − | 0.143635i | 0.631632 | − | 0.775268i | \(-0.282385\pi\) |
−0.775268 | + | 0.631632i | \(0.782385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3029.87 | − | 3029.87i | −0.00785672 | − | 0.00785672i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 321215.i | 0.827599i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −164779. | −0.421834 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2717.23 | + | 2717.23i | −0.00691180 | + | 0.00691180i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 190144. | − | 190144.i | 0.480597 | − | 0.480597i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −188802. | −0.474184 | −0.237092 | − | 0.971487i | \(-0.576194\pi\) | ||||
−0.237092 | + | 0.971487i | \(0.576194\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5102.26i | − | 0.0127337i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 163812. | + | 163812.i | 0.406255 | + | 0.406255i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1694.72 | − | 1694.72i | −0.00417656 | − | 0.00417656i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 94108.5i | − | 0.230477i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −442081. | −1.07593 | −0.537967 | − | 0.842966i | \(-0.680807\pi\) | ||||
−0.537967 | + | 0.842966i | \(0.680807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 246339. | − | 246339.i | 0.595814 | − | 0.595814i | −0.343382 | − | 0.939196i | \(-0.611573\pi\) |
0.939196 | + | 0.343382i | \(0.111573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −681.935 | + | 681.935i | −0.00163917 | + | 0.00163917i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −54549.4 | −0.130311 | −0.0651555 | − | 0.997875i | \(-0.520754\pi\) | ||||
−0.0651555 | + | 0.997875i | \(0.520754\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 288429.i | 0.684778i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3470.80 | − | 3470.80i | −0.00818970 | − | 0.00818970i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −231745. | − | 231745.i | −0.543481 | − | 0.543481i | 0.381066 | − | 0.924548i | \(-0.375557\pi\) |
−0.924548 | + | 0.381066i | \(0.875557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 71011.8i | 0.165519i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −73325.0 | −0.169872 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 479757. | − | 479757.i | 1.10472 | − | 1.10472i | 0.110883 | − | 0.993833i | \(-0.464632\pi\) |
0.993833 | − | 0.110883i | \(-0.0353678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −515798. | + | 515798.i | −1.18053 | + | 1.18053i | −0.200922 | + | 0.979607i | \(0.564394\pi\) |
−0.979607 | + | 0.200922i | \(0.935606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −788.263 | −0.00179326 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 280041.i | − | 0.633254i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −417654. | − | 417654.i | −0.938782 | − | 0.938782i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1867.27 | + | 1867.27i | 0.00417210 | + | 0.00417210i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 625397.i | − | 1.38903i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −505551. | −1.11618 | −0.558090 | − | 0.829780i | \(-0.688466\pi\) | ||||
−0.558090 | + | 0.829780i | \(0.688466\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3709.29 | + | 3709.29i | −0.00814111 | + | 0.00814111i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 460825. | − | 460825.i | 1.00545 | − | 1.00545i | 0.00546007 | − | 0.999985i | \(-0.498262\pi\) |
0.999985 | − | 0.00546007i | \(-0.00173800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20601.9 | 0.0446857 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 154.570i | − | 0.000333297i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −120242. | − | 120242.i | −0.257761 | − | 0.257761i | 0.566382 | − | 0.824143i | \(-0.308343\pi\) |
−0.824143 | + | 0.566382i | \(0.808343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 88622.7 | + | 88622.7i | 0.188870 | + | 0.188870i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2450.33i | − | 0.00519171i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40572.7 | 0.0854664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −166965. | + | 166965.i | −0.349678 | + | 0.349678i | −0.859990 | − | 0.510311i | \(-0.829530\pi\) |
0.510311 | + | 0.859990i | \(0.329530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 340403. | − | 340403.i | 0.708805 | − | 0.708805i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 240600. | 0.498111 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 305118.i | − | 0.628062i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1116.33 | + | 1116.33i | 0.00228475 | + | 0.00228475i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39689.8 | − | 39689.8i | −0.0807687 | − | 0.0807687i | 0.665568 | − | 0.746337i | \(-0.268189\pi\) |
−0.746337 | + | 0.665568i | \(0.768189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 303133.i | 0.613371i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −83.1725 | −0.000167341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 422013. | − | 422013.i | 0.844281 | − | 0.844281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −250742. | + | 250742.i | −0.498809 | + | 0.498809i | −0.911067 | − | 0.412258i | \(-0.864740\pi\) |
0.412258 | + | 0.911067i | \(0.364740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 475415. | 0.940445 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 609751.i | − | 1.19943i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26407.5 | − | 26407.5i | −0.0516553 | − | 0.0516553i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3527.63 | − | 3527.63i | −0.00686190 | − | 0.00686190i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 133454.i | 0.258152i | 0.991635 | + | 0.129076i | \(0.0412011\pi\) | ||||
−0.991635 | + | 0.129076i | \(0.958799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −848347. | −1.63194 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1873.30 | − | 1873.30i | 0.00358370 | − | 0.00358370i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −511309. | + | 511309.i | −0.972763 | + | 0.972763i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 583370. | 1.10376 | 0.551881 | − | 0.833923i | \(-0.313910\pi\) | ||||
0.551881 | + | 0.833923i | \(0.313910\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 531273.i | − | 0.999684i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −401781. | − | 401781.i | −0.751891 | − | 0.751891i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −534516. | − | 534516.i | −0.994838 | − | 0.994838i | 0.00514857 | − | 0.999987i | \(-0.498361\pi\) |
−0.999987 | + | 0.00514857i | \(0.998361\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 64.6410i | − | 0.000119656i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 312456. | 0.575247 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 91929.4 | − | 91929.4i | 0.168332 | − | 0.168332i | −0.617914 | − | 0.786246i | \(-0.712022\pi\) |
0.786246 | + | 0.617914i | \(0.212022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 628.336 | − | 628.336i | 0.00114434 | − | 0.00114434i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 83329.2 | 0.150945 | 0.0754727 | − | 0.997148i | \(-0.475953\pi\) | ||||
0.0754727 | + | 0.997148i | \(0.475953\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 247625.i | 0.446151i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 612333. | + | 612333.i | 1.09735 | + | 1.09735i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 467305. | + | 467305.i | 0.832985 | + | 0.832985i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 318689.i | − | 0.565051i | −0.959260 | − | 0.282525i | \(-0.908828\pi\) | ||
0.959260 | − | 0.282525i | \(-0.0911722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 973.515 | 0.00171693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −136504. | + | 136504.i | −0.239470 | + | 0.239470i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 428881. | − | 428881.i | 0.748419 | − | 0.748419i | −0.225763 | − | 0.974182i | \(-0.572488\pi\) |
0.974182 | + | 0.225763i | \(0.0724875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3151.80 | −0.00547110 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 718933.i | 1.24142i | 0.784040 | + | 0.620711i | \(0.213156\pi\) | ||||
−0.784040 | + | 0.620711i | \(0.786844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −414437. | − | 414437.i | −0.711884 | − | 0.711884i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 285239. | + | 285239.i | 0.487401 | + | 0.487401i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 66696.8i | − | 0.113374i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 421326. | 0.712468 | 0.356234 | − | 0.934397i | \(-0.384061\pi\) | ||||
0.356234 | + | 0.934397i | \(0.384061\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1754.84 | − | 1754.84i | 0.00295208 | − | 0.00295208i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −455325. | + | 455325.i | −0.762013 | + | 0.762013i | −0.976686 | − | 0.214673i | \(-0.931132\pi\) |
0.214673 | + | 0.976686i | \(0.431132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −746482. | −1.24284 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2001.44i | 0.00331513i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 243214. | + | 243214.i | 0.400788 | + | 0.400788i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −97898.1 | − | 97898.1i | −0.160499 | − | 0.160499i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15442.0i | 0.0251872i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18784.0 | −0.0304825 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −541211. | + | 541211.i | −0.873811 | + | 0.873811i | −0.992885 | − | 0.119074i | \(-0.962007\pi\) |
0.119074 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1734.56 | − | 1734.56i | 0.00278635 | − | 0.00278635i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −290032. | −0.463546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 144618.i | 0.229972i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 773.775 | + | 773.775i | 0.00122428 | + | 0.00122428i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −481291. | − | 481291.i | −0.757690 | − | 0.757690i | 0.218212 | − | 0.975901i | \(-0.429978\pi\) |
−0.975901 | + | 0.218212i | \(0.929978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49003.4i | − | 0.0767597i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 521597. | 0.812961 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −76277.7 | + | 76277.7i | −0.118295 | + | 0.118295i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 162414. | − | 162414.i | 0.250629 | − | 0.250629i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −432.116 | −0.000663518 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 34438.5i | − | 0.0526195i | −0.999654 | − | 0.0263097i | \(-0.991624\pi\) | ||
0.999654 | − | 0.0263097i | \(-0.00837562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −227480. | − | 227480.i | −0.345862 | − | 0.345862i | 0.512704 | − | 0.858566i | \(-0.328644\pi\) |
−0.858566 | + | 0.512704i | \(0.828644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −126.869 | − | 126.869i | −0.000191944 | − | 0.000191944i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 451633.i | 0.679939i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 640532. | 0.959614 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −78715.2 | + | 78715.2i | −0.117352 | + | 0.117352i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 807677. | − | 807677.i | 1.19826 | − | 1.19826i | 0.223573 | − | 0.974687i | \(-0.428228\pi\) |
0.974687 | − | 0.223573i | \(-0.0717722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −703593. | −1.03878 | −0.519388 | − | 0.854539i | \(-0.673840\pi\) | ||||
−0.519388 | + | 0.854539i | \(0.673840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3858.56i | 0.00566914i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 775918. | + | 775918.i | 1.13450 | + | 1.13450i | 0.989420 | + | 0.145081i | \(0.0463444\pi\) |
0.145081 | + | 0.989420i | \(0.453656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 804056. | + | 804056.i | 1.16998 | + | 1.16998i | 0.982214 | + | 0.187763i | \(0.0601236\pi\) |
0.187763 | + | 0.982214i | \(0.439876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 3054.39i | − | 0.00442305i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38085.1 | 0.0548864 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23564.4 | + | 23564.4i | −0.0337974 | + | 0.0337974i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11272.2 | + | 11272.2i | −0.0160901 | + | 0.0160901i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −248652. | −0.353239 | −0.176619 | − | 0.984279i | \(-0.556516\pi\) | ||||
−0.176619 | + | 0.984279i | \(0.556516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.42133e6i | 2.00957i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3697.49 | + | 3697.49i | 0.00520297 | + | 0.00520297i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −223609. | − | 223609.i | −0.313166 | − | 0.313166i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22068.2i | 0.0307610i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6679.00 | 0.00926608 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −175807. | + | 175807.i | −0.242760 | + | 0.242760i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −779867. | + | 779867.i | −1.07182 | + | 1.07182i | −0.0746081 | + | 0.997213i | \(0.523771\pi\) |
−0.997213 | + | 0.0746081i | \(0.976229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −454737. | −0.622054 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 481792.i | 0.655992i | 0.944679 | + | 0.327996i | \(0.106373\pi\) | ||||
−0.944679 | + | 0.327996i | \(0.893627\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 947889. | + | 947889.i | 1.28461 | + | 1.28461i | 0.938015 | + | 0.346594i | \(0.112662\pi\) |
0.346594 | + | 0.938015i | \(0.387338\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1605.83 | + | 1605.83i | 0.00216617 | + | 0.00216617i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.00011e6i | 1.34284i | 0.741077 | + | 0.671421i | \(0.234316\pi\) | ||||
−0.741077 | + | 0.671421i | \(0.765684\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −137711. | −0.184051 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4998.61 | − | 4998.61i | 0.00664984 | − | 0.00664984i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 494559. | − | 494559.i | 0.654905 | − | 0.654905i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72252.8 | −0.0952398 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 33453.9i | − | 0.0438953i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −449571. | − | 449571.i | −0.587195 | − | 0.587195i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 747906. | + | 747906.i | 0.972406 | + | 0.972406i | 0.999629 | − | 0.0272234i | \(-0.00866655\pi\) |
−0.0272234 | + | 0.999629i | \(0.508667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 7845.72i | − | 0.0101544i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53961.8 | −0.0695240 | −0.0347620 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347620 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 629494. | − | 629494.i | 0.807366 | − | 0.807366i | −0.176869 | − | 0.984234i | \(-0.556597\pi\) |
0.984234 | + | 0.176869i | \(0.0565968\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1271.99 | − | 1271.99i | 0.00162405 | − | 0.00162405i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 880807. | 1.11952 | 0.559762 | − | 0.828653i | \(-0.310893\pi\) | ||||
0.559762 | + | 0.828653i | \(0.310893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.01590e6i | − | 1.28543i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −552724. | − | 552724.i | −0.696231 | − | 0.696231i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39061.4 | + | 39061.4i | 0.0489829 | + | 0.0489829i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 392821.i | − | 0.490398i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 728.826 | 0.000905814 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.55383e6 | + | 1.55383e6i | −1.92257 | + | 1.92257i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −455891. | + | 455891.i | −0.561580 | + | 0.561580i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4229.12 | 0.00518650 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 176085.i | − | 0.214994i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −662568. | − | 662568.i | −0.805408 | − | 0.805408i | 0.178527 | − | 0.983935i | \(-0.442867\pi\) |
−0.983935 | + | 0.178527i | \(0.942867\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −685275. | − | 685275.i | −0.829348 | − | 0.829348i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 817906.i | − | 0.985522i | −0.870165 | − | 0.492761i | \(-0.835988\pi\) | ||
0.870165 | − | 0.492761i | \(-0.164012\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.27398e6 | 1.52834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2758.05 | + | 2758.05i | −0.00329428 | + | 0.00329428i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 220195. | − | 220195.i | 0.261860 | − | 0.261860i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33891.9 | −0.0401296 | −0.0200648 | − | 0.999799i | \(-0.506387\pi\) | ||||
−0.0200648 | + | 0.999799i | \(0.506387\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 5125.61i | − | 0.00604263i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22638.1 | + | 22638.1i | 0.0265728 | + | 0.0265728i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 215230. | + | 215230.i | 0.251547 | + | 0.251547i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.37757e6i | 1.60307i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −207783. | −0.240757 | −0.120378 | − | 0.992728i | \(-0.538411\pi\) | ||||
−0.120378 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30358.2 | + | 30358.2i | −0.0350249 | + | 0.0350249i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5869.57 | + | 5869.57i | −0.00674284 | + | 0.00674284i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 593450. | 0.678830 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.12361e6i | − | 1.27979i | −0.768464 | − | 0.639893i | \(-0.778978\pi\) | ||
0.768464 | − | 0.639893i | \(-0.221022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1176.67 | + | 1176.67i | 0.00133452 | + | 0.00133452i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 856765. | + | 856765.i | 0.967570 | + | 0.967570i | 0.999490 | − | 0.0319200i | \(-0.0101622\pi\) |
−0.0319200 | + | 0.999490i | \(0.510162\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 282112.i | 0.317247i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6004.97 | −0.00672430 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 246666. | − | 246666.i | 0.275048 | − | 0.275048i | −0.556080 | − | 0.831129i | \(-0.687695\pi\) |
0.831129 | + | 0.556080i | \(0.187695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17638.6 | − | 17638.6i | 0.0195853 | − | 0.0195853i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8705.68 | 0.00962591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 219446.i | 0.241625i | 0.992675 | + | 0.120812i | \(0.0385500\pi\) | ||||
−0.992675 | + | 0.120812i | \(0.961450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 180041. | + | 180041.i | 0.197408 | + | 0.197408i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8031.71 | + | 8031.71i | 0.00876968 | + | 0.00876968i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 549607.i | − | 0.597606i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.34498e6 | −1.45636 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 758821. | − | 758821.i | 0.818251 | − | 0.818251i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −244743. | + | 244743.i | −0.262819 | + | 0.262819i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 650799. | 0.695975 | 0.347988 | − | 0.937499i | \(-0.386865\pi\) | ||||
0.347988 | + | 0.937499i | \(0.386865\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14120.5i | 0.0150384i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −790825. | − | 790825.i | −0.838768 | − | 0.838768i | 0.149929 | − | 0.988697i | \(-0.452096\pi\) |
−0.988697 | + | 0.149929i | \(0.952096\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −746058. | − | 746058.i | −0.788037 | − | 0.788037i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 892.258i | − | 0.000938602i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.40812e6 | −1.47520 | −0.737600 | − | 0.675237i | \(-0.764041\pi\) | ||||
−0.737600 | + | 0.675237i | \(0.764041\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 542600. | − | 542600.i | 0.566128 | − | 0.566128i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −672972. | + | 672972.i | −0.699292 | + | 0.699292i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −208227. | −0.215491 | −0.107746 | − | 0.994179i | \(-0.534363\pi\) | ||||
−0.107746 | + | 0.994179i | \(0.534363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 307144.i | 0.316569i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 257.903 | + | 257.903i | 0.000264742 | + | 0.000264742i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 371486. | + | 371486.i | 0.379796 | + | 0.379796i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 170063.i | − | 0.173166i | −0.996245 | − | 0.0865831i | \(-0.972405\pi\) | ||
0.996245 | − | 0.0865831i | \(-0.0275948\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6019.00 | −0.00610416 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 546631. | − | 546631.i | 0.552138 | − | 0.552138i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 917799. | − | 917799.i | 0.923331 | − | 0.923331i | −0.0739326 | − | 0.997263i | \(-0.523555\pi\) |
0.997263 | + | 0.0739326i | \(0.0235550\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6500.15 | 0.00651317 |
(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 | 128.5.f.b.95.4 | 14 | ||
4.3 | odd | 2 | 128.5.f.a.95.4 | 14 | |||
8.3 | odd | 2 | 64.5.f.a.47.4 | 14 | |||
8.5 | even | 2 | 16.5.f.a.3.7 | ✓ | 14 | ||
16.3 | odd | 4 | 16.5.f.a.11.7 | yes | 14 | ||
16.5 | even | 4 | 128.5.f.a.31.4 | 14 | |||
16.11 | odd | 4 | inner | 128.5.f.b.31.4 | 14 | ||
16.13 | even | 4 | 64.5.f.a.15.4 | 14 | |||
24.5 | odd | 2 | 144.5.m.a.19.1 | 14 | |||
24.11 | even | 2 | 576.5.m.a.559.5 | 14 | |||
48.29 | odd | 4 | 576.5.m.a.271.5 | 14 | |||
48.35 | even | 4 | 144.5.m.a.91.1 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.7 | ✓ | 14 | 8.5 | even | 2 | ||
16.5.f.a.11.7 | yes | 14 | 16.3 | odd | 4 | ||
64.5.f.a.15.4 | 14 | 16.13 | even | 4 | |||
64.5.f.a.47.4 | 14 | 8.3 | odd | 2 | |||
128.5.f.a.31.4 | 14 | 16.5 | even | 4 | |||
128.5.f.a.95.4 | 14 | 4.3 | odd | 2 | |||
128.5.f.b.31.4 | 14 | 16.11 | odd | 4 | inner | ||
128.5.f.b.95.4 | 14 | 1.1 | even | 1 | trivial | ||
144.5.m.a.19.1 | 14 | 24.5 | odd | 2 | |||
144.5.m.a.91.1 | 14 | 48.35 | even | 4 | |||
576.5.m.a.271.5 | 14 | 48.29 | odd | 4 | |||
576.5.m.a.559.5 | 14 | 24.11 | even | 2 |