Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,6,Mod(65,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.65");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.e (of order \(4\), degree \(2\), 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: | \(41.0582578721\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{14} + 68094 x^{12} - 631280 x^{10} + 1162609411 x^{8} - 7070628176 x^{6} + \cdots + 25477586689 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 65.4 | ||
Root | \(-0.0885219 - 0.618585i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.65 |
Dual form | 256.6.e.a.193.4 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.23717 | − | 1.23717i | −0.0793645 | − | 0.0793645i | 0.666310 | − | 0.745675i | \(-0.267873\pi\) |
−0.745675 | + | 0.666310i | \(0.767873\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.46137 | + | 9.46137i | −0.169250 | + | 0.169250i | −0.786650 | − | 0.617400i | \(-0.788186\pi\) |
0.617400 | + | 0.786650i | \(0.288186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 217.226i | − | 1.67558i | −0.545991 | − | 0.837791i | \(-0.683847\pi\) | ||
0.545991 | − | 0.837791i | \(-0.316153\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 239.939i | − | 0.987403i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 282.343 | − | 282.343i | 0.703550 | − | 0.703550i | −0.261621 | − | 0.965171i | \(-0.584257\pi\) |
0.965171 | + | 0.261621i | \(0.0842569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 339.858 | + | 339.858i | 0.557749 | + | 0.557749i | 0.928666 | − | 0.370917i | \(-0.120957\pi\) |
−0.370917 | + | 0.928666i | \(0.620957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 23.4106 | 0.0268649 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −473.078 | −0.397018 | −0.198509 | − | 0.980099i | \(-0.563610\pi\) | ||||
−0.198509 | + | 0.980099i | \(0.563610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 193.135 | + | 193.135i | 0.122738 | + | 0.122738i | 0.765808 | − | 0.643070i | \(-0.222340\pi\) |
−0.643070 | + | 0.765808i | \(0.722340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −268.745 | + | 268.745i | −0.132982 | + | 0.132982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1880.50i | 0.741230i | 0.928787 | + | 0.370615i | \(0.120853\pi\) | ||||
−0.928787 | + | 0.370615i | \(0.879147\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2945.96i | 0.942709i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −597.477 | + | 597.477i | −0.157729 | + | 0.157729i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5001.53 | − | 5001.53i | −1.10435 | − | 1.10435i | −0.993879 | − | 0.110473i | \(-0.964763\pi\) |
−0.110473 | − | 0.993879i | \(-0.535237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4038.97 | −0.754861 | −0.377430 | − | 0.926038i | \(-0.623192\pi\) | ||||
−0.377430 | + | 0.926038i | \(0.623192\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −698.612 | −0.111674 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2055.25 | + | 2055.25i | 0.283593 | + | 0.283593i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1878.88 | − | 1878.88i | 0.225629 | − | 0.225629i | −0.585235 | − | 0.810864i | \(-0.698998\pi\) |
0.810864 | + | 0.585235i | \(0.198998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 840.924i | − | 0.0885310i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 15340.6i | − | 1.42522i | −0.701558 | − | 0.712612i | \(-0.747512\pi\) | ||
0.701558 | − | 0.712612i | \(-0.252488\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11811.3 | − | 11811.3i | 0.974150 | − | 0.974150i | −0.0255246 | − | 0.999674i | \(-0.508126\pi\) |
0.999674 | + | 0.0255246i | \(0.00812561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2270.15 | + | 2270.15i | 0.167118 | + | 0.167118i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4380.31 | −0.289242 | −0.144621 | − | 0.989487i | \(-0.546196\pi\) | ||||
−0.144621 | + | 0.989487i | \(0.546196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30379.9 | −1.80758 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 585.278 | + | 585.278i | 0.0315092 | + | 0.0315092i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −19608.0 | + | 19608.0i | −0.958833 | + | 0.958833i | −0.999186 | − | 0.0403525i | \(-0.987152\pi\) |
0.0403525 | + | 0.999186i | \(0.487152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5342.70i | 0.238152i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 477.882i | − | 0.0194820i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 21399.1 | − | 21399.1i | 0.800323 | − | 0.800323i | −0.182822 | − | 0.983146i | \(-0.558523\pi\) |
0.983146 | + | 0.182822i | \(0.0585234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29820.9 | − | 29820.9i | −1.02612 | − | 1.02612i | −0.999650 | − | 0.0264659i | \(-0.991575\pi\) |
−0.0264659 | − | 0.999650i | \(-0.508425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −52120.8 | −1.65447 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6431.05 | −0.188798 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11258.5 | + | 11258.5i | 0.306404 | + | 0.306404i | 0.843513 | − | 0.537109i | \(-0.180484\pi\) |
−0.537109 | + | 0.843513i | \(0.680484\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2326.49 | − | 2326.49i | 0.0588273 | − | 0.0588273i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48020.3i | 1.13052i | 0.824912 | + | 0.565261i | \(0.191224\pi\) | ||||
−0.824912 | + | 0.565261i | \(0.808776\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8033.35i | 0.176437i | 0.996101 | + | 0.0882184i | \(0.0281174\pi\) | ||||
−0.996101 | + | 0.0882184i | \(0.971883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3644.66 | − | 3644.66i | 0.0748176 | − | 0.0748176i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −61332.1 | − | 61332.1i | −1.17886 | − | 1.17886i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −74631.9 | −1.34542 | −0.672708 | − | 0.739908i | \(-0.734869\pi\) | ||||
−0.672708 | + | 0.739908i | \(0.734869\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56826.8 | −0.962366 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 63073.6 | + | 63073.6i | 1.00497 | + | 1.00497i | 0.999988 | + | 0.00498026i | \(0.00158527\pi\) |
0.00498026 | + | 0.999988i | \(0.498415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4475.97 | − | 4475.97i | 0.0671954 | − | 0.0671954i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12375.5i | 0.175293i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 93498.5i | − | 1.25121i | −0.780141 | − | 0.625604i | \(-0.784852\pi\) | ||
0.780141 | − | 0.625604i | \(-0.215148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 73825.8 | − | 73825.8i | 0.934555 | − | 0.934555i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4996.90 | + | 4996.90i | 0.0599091 | + | 0.0599091i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3654.65 | −0.0415467 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −158815. | −1.71381 | −0.856907 | − | 0.515472i | \(-0.827617\pi\) | ||||
−0.856907 | + | 0.515472i | \(0.827617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −67745.0 | − | 67745.0i | −0.694687 | − | 0.694687i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −109401. | + | 109401.i | −1.06713 | + | 1.06713i | −0.0695559 | + | 0.997578i | \(0.522158\pi\) |
−0.997578 | + | 0.0695559i | \(0.977842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 56607.0i | − | 0.525747i | −0.964830 | − | 0.262873i | \(-0.915330\pi\) | ||
0.964830 | − | 0.262873i | \(-0.0846702\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5085.39i | − | 0.0450144i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 105092. | − | 105092.i | 0.887385 | − | 0.887385i | −0.106886 | − | 0.994271i | \(-0.534088\pi\) |
0.994271 | + | 0.106886i | \(0.0340881\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −35671.6 | − | 35671.6i | −0.287579 | − | 0.287579i | 0.548543 | − | 0.836122i | \(-0.315183\pi\) |
−0.836122 | + | 0.548543i | \(0.815183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4648.98 | −0.0358138 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 78832.7 | 0.580779 | 0.290389 | − | 0.956909i | \(-0.406215\pi\) | ||||
0.290389 | + | 0.956909i | \(0.406215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17792.1 | − | 17792.1i | −0.125453 | − | 0.125453i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 81545.1 | − | 81545.1i | 0.550723 | − | 0.550723i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 102765.i | 0.665237i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1616.01i | 0.0100342i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18978.9 | + | 18978.9i | −0.113112 | + | 0.113112i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −57439.7 | − | 57439.7i | −0.328804 | − | 0.328804i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −146680. | −0.806977 | −0.403488 | − | 0.914985i | \(-0.632202\pi\) | ||||
−0.403488 | + | 0.914985i | \(0.632202\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −29225.1 | −0.154626 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 163028. | + | 163028.i | 0.830011 | + | 0.830011i | 0.987518 | − | 0.157507i | \(-0.0503458\pi\) |
−0.157507 | + | 0.987518i | \(0.550346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41953.9 | − | 41953.9i | 0.205657 | − | 0.205657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 11305.9i | − | 0.0533914i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 129663.i | 0.590221i | 0.955463 | + | 0.295111i | \(0.0953565\pi\) | ||||
−0.955463 | + | 0.295111i | \(0.904644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −293683. | + | 293683.i | −1.28927 | + | 1.28927i | −0.354032 | + | 0.935233i | \(0.615190\pi\) |
−0.935233 | + | 0.354032i | \(0.884810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5419.19 | + | 5419.19i | 0.0229555 | + | 0.0229555i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 191913. | 0.784809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 94642.6 | 0.373824 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 37585.1 | + | 37585.1i | 0.143457 | + | 0.143457i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27828.6 | − | 27828.6i | 0.102690 | − | 0.102690i | −0.653895 | − | 0.756585i | \(-0.726866\pi\) |
0.756585 | + | 0.653895i | \(0.226866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 81358.3i | 0.290375i | 0.989404 | + | 0.145188i | \(0.0463785\pi\) | ||||
−0.989404 | + | 0.145188i | \(0.953621\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 113510.i | 0.392017i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 38214.2 | − | 38214.2i | 0.127760 | − | 0.127760i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 202745. | + | 202745.i | 0.656448 | + | 0.656448i | 0.954538 | − | 0.298090i | \(-0.0963495\pi\) |
−0.298090 | + | 0.954538i | \(0.596349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 48516.8 | 0.152195 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 408492. | 1.24199 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −383196. | − | 383196.i | −1.12967 | − | 1.12967i | −0.990230 | − | 0.139440i | \(-0.955470\pi\) |
−0.139440 | − | 0.990230i | \(-0.544530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6609.83 | − | 6609.83i | 0.0189008 | − | 0.0189008i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 523932.i | − | 1.45373i | −0.686781 | − | 0.726865i | \(-0.740977\pi\) | ||
0.686781 | − | 0.726865i | \(-0.259023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 140286.i | − | 0.377832i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46340.7 | − | 46340.7i | 0.121191 | − | 0.121191i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 447412. | + | 447412.i | 1.13656 | + | 1.13656i | 0.989062 | + | 0.147497i | \(0.0471217\pi\) |
0.147497 | + | 0.989062i | \(0.452878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 639939. | 1.57959 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −52948.6 | −0.127035 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −196974. | − | 196974.i | −0.459489 | − | 0.459489i | 0.438998 | − | 0.898488i | \(-0.355333\pi\) |
−0.898488 | + | 0.438998i | \(0.855333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −259968. | + | 259968.i | −0.589826 | + | 0.589826i | −0.937584 | − | 0.347758i | \(-0.886943\pi\) |
0.347758 | + | 0.937584i | \(0.386943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 73787.1i | 0.162874i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 35553.5i | 0.0763754i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −133570. | + | 133570.i | −0.279322 | + | 0.279322i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 129787. | + | 129787.i | 0.264288 | + | 0.264288i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 187212. | 0.371322 | 0.185661 | − | 0.982614i | \(-0.440557\pi\) | ||||
0.185661 | + | 0.982614i | \(0.440557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 592251. | 1.14449 | 0.572246 | − | 0.820082i | \(-0.306072\pi\) | ||||
0.572246 | + | 0.820082i | \(0.306072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7956.29 | + | 7956.29i | 0.0149839 | + | 0.0149839i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 718774. | − | 718774.i | 1.31955 | − | 1.31955i | 0.405425 | − | 0.914128i | \(-0.367124\pi\) |
0.914128 | − | 0.405425i | \(-0.132876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 285135.i | − | 0.510408i | −0.966887 | − | 0.255204i | \(-0.917857\pi\) | ||
0.966887 | − | 0.255204i | \(-0.0821426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 27857.4i | − | 0.0486351i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.08646e6 | + | 1.08646e6i | −1.85043 | + | 1.85043i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 145143. | + | 145143.i | 0.241219 | + | 0.241219i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 451204. | 0.731893 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 109061. | 0.172704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 679372. | + | 679372.i | 1.05051 | + | 1.05051i | 0.998654 | + | 0.0518587i | \(0.0165145\pi\) |
0.0518587 | + | 0.998654i | \(0.483485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 59409.2 | − | 59409.2i | 0.0897232 | − | 0.0897232i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 223502.i | 0.329750i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 877368.i | 1.26483i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9938.61 | − | 9938.61i | 0.0140028 | − | 0.0140028i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −160779. | − | 160779.i | −0.221437 | − | 0.221437i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20550.5 | 0.0276732 | 0.0138366 | − | 0.999904i | \(-0.495596\pi\) | ||||
0.0138366 | + | 0.999904i | \(0.495596\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 706851. | 0.930833 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −939376. | − | 939376.i | −1.20997 | − | 1.20997i | −0.971035 | − | 0.238936i | \(-0.923201\pi\) |
−0.238936 | − | 0.971035i | \(-0.576799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −80627.5 | + | 80627.5i | −0.101600 | + | 0.101600i | −0.756080 | − | 0.654480i | \(-0.772888\pi\) |
0.654480 | + | 0.756080i | \(0.272888\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 151756.i | 0.187119i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 293436.i | 0.354098i | 0.984202 | + | 0.177049i | \(0.0566551\pi\) | ||||
−0.984202 | + | 0.177049i | \(0.943345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41443.8 | − | 41443.8i | 0.0489542 | − | 0.0489542i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 92332.3 | + | 92332.3i | 0.106778 | + | 0.106778i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −109538. | −0.124042 | −0.0620211 | − | 0.998075i | \(-0.519755\pi\) | ||||
−0.0620211 | + | 0.998075i | \(0.519755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 734422. | 0.814522 | 0.407261 | − | 0.913312i | \(-0.366484\pi\) | ||||
0.407261 | + | 0.913312i | \(0.366484\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 215491. | + | 215491.i | 0.234107 | + | 0.234107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 287436. | − | 287436.i | 0.305933 | − | 0.305933i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 131277.i | 0.136914i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 156065.i | − | 0.159517i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 689488. | − | 689488.i | 0.690784 | − | 0.690784i | −0.271620 | − | 0.962405i | \(-0.587559\pi\) |
0.962405 | + | 0.271620i | \(0.0875594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 530945. | + | 530945.i | 0.521493 | + | 0.521493i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11075.1 | −0.0106659 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.75709e6 | −1.65944 | −0.829719 | − | 0.558181i | \(-0.811499\pi\) | ||||
−0.829719 | + | 0.558181i | \(0.811499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −408140. | − | 408140.i | −0.378059 | − | 0.378059i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.20006e6 | + | 1.20006e6i | −1.09044 | + | 1.09044i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.72852e6i | − | 1.54094i | −0.637478 | − | 0.770468i | \(-0.720022\pi\) | ||
0.637478 | − | 0.770468i | \(-0.279978\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 371037.i | − | 0.324565i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −115674. | + | 115674.i | −0.0993015 | + | 0.0993015i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 198893. | + | 198893.i | 0.167587 | + | 0.167587i | 0.785918 | − | 0.618331i | \(-0.212191\pi\) |
−0.618331 | + | 0.785918i | \(0.712191\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.61535e6 | 1.33612 | 0.668059 | − | 0.744109i | \(-0.267126\pi\) | ||||
0.668059 | + | 0.744109i | \(0.267126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −182670. | −0.148341 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 831772. | + | 831772.i | 0.663243 | + | 0.663243i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 418236. | − | 418236.i | 0.327508 | − | 0.327508i | −0.524130 | − | 0.851638i | \(-0.675610\pi\) |
0.851638 | + | 0.524130i | \(0.175610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 969107.i | 0.745352i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.87424e6i | − | 1.41599i | −0.706219 | − | 0.707994i | \(-0.749601\pi\) | ||
0.706219 | − | 0.707994i | \(-0.250399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.11383e6 | − | 1.11383e6i | 0.826706 | − | 0.826706i | −0.160353 | − | 0.987060i | \(-0.551263\pi\) |
0.987060 | + | 0.160353i | \(0.0512634\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4521.42 | + | 4521.42i | 0.00329733 | + | 0.00329733i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.33237e6 | −2.38808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.19605e6 | −0.842376 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 196482. | + | 196482.i | 0.136016 | + | 0.136016i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 488382. | − | 488382.i | 0.332346 | − | 0.332346i | −0.521131 | − | 0.853477i | \(-0.674490\pi\) |
0.853477 | + | 0.521131i | \(0.174490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 404930.i | 0.270910i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 337387.i | 0.221941i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −639102. | + | 639102.i | −0.413421 | + | 0.413421i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.56571e6 | − | 2.56571e6i | −1.63227 | − | 1.63227i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 270696. | 0.169385 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 564294. | 0.347341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 396811. | + | 396811.i | 0.240291 | + | 0.240291i | 0.816971 | − | 0.576679i | \(-0.195652\pi\) |
−0.576679 | + | 0.816971i | \(0.695652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −70032.4 | + | 70032.4i | −0.0417256 | + | 0.0417256i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.80244e6i | 1.05672i | 0.849020 | + | 0.528361i | \(0.177193\pi\) | ||||
−0.849020 | + | 0.528361i | \(0.822807\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 346574.i | 0.199956i | 0.994990 | + | 0.0999780i | \(0.0318773\pi\) | ||||
−0.994990 | + | 0.0999780i | \(0.968123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 493135. | − | 493135.i | 0.280020 | − | 0.280020i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.44830e6 | − | 1.44830e6i | −0.809487 | − | 0.809487i | 0.175069 | − | 0.984556i | \(-0.443985\pi\) |
−0.984556 | + | 0.175069i | \(0.943985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.82429e6 | −1.55393 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −260034. | −0.140854 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −91368.1 | − | 91368.1i | −0.0487291 | − | 0.0487291i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00121e6 | + | 1.00121e6i | −0.525795 | + | 0.525795i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 88263.8i | 0.0456471i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 951516.i | 0.484648i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 881414. | − | 881414.i | 0.442191 | − | 0.442191i | −0.450557 | − | 0.892748i | \(-0.648775\pi\) |
0.892748 | + | 0.450557i | \(0.148775\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −450816. | − | 450816.i | −0.222786 | − | 0.222786i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −213042. | −0.103718 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.66445e6 | −1.27801 | −0.639003 | − | 0.769205i | \(-0.720653\pi\) | ||||
−0.639003 | + | 0.769205i | \(0.720653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −97529.5 | − | 97529.5i | −0.0460932 | − | 0.0460932i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.14038e6 | + | 1.14038e6i | −0.531083 | + | 0.531083i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.94839e6i | 1.35316i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 44023.7i | 0.0199131i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.42569e6 | − | 1.42569e6i | 0.635626 | − | 0.635626i | −0.313848 | − | 0.949473i | \(-0.601618\pi\) |
0.949473 | + | 0.313848i | \(0.101618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 297231. | + | 297231.i | 0.130626 | + | 0.130626i | 0.769397 | − | 0.638771i | \(-0.220557\pi\) |
−0.638771 | + | 0.769397i | \(0.720557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −406115. | −0.175947 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.12097e6 | −0.478804 | −0.239402 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239402 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −454338. | − | 454338.i | −0.191341 | − | 0.191341i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 127137. | − | 127137.i | 0.0527962 | − | 0.0527962i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 3.31336e6i | − | 1.35685i | −0.734669 | − | 0.678426i | \(-0.762663\pi\) | ||
0.734669 | − | 0.678426i | \(-0.237337\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 2.40150e6i | − | 0.969871i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1999.28 | − | 1999.28i | 0.000796356 | − | 0.000796356i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −76006.5 | − | 76006.5i | −0.0298620 | − | 0.0298620i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.22043e6 | −0.472986 | −0.236493 | − | 0.971633i | \(-0.575998\pi\) | ||||
−0.236493 | + | 0.971633i | \(0.575998\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.68081e6 | −1.40727 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.25935e6 | + | 4.25935e6i | 1.60660 | + | 1.60660i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.20408e6 | + | 1.20408e6i | −0.448109 | + | 0.448109i | −0.894725 | − | 0.446617i | \(-0.852629\pi\) |
0.446617 | + | 0.894725i | \(0.352629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 142125.i | 0.0521907i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.39962e6i | − | 1.23190i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.81398e6 | − | 2.81398e6i | 1.00629 | − | 1.00629i | 0.00630982 | − | 0.999980i | \(-0.497992\pi\) |
0.999980 | − | 0.00630982i | \(-0.00200849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 181468. | + | 181468.i | 0.0640453 | + | 0.0640453i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −432846. | −0.150777 | −0.0753887 | − | 0.997154i | \(-0.524020\pi\) | ||||
−0.0753887 | + | 0.997154i | \(0.524020\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.16057e6 | 0.399043 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.83398e6 | − | 2.83398e6i | −0.961878 | − | 0.961878i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.69223e6 | − | 1.69223e6i | 0.567002 | − | 0.567002i | −0.364286 | − | 0.931287i | \(-0.618687\pi\) |
0.931287 | + | 0.364286i | \(0.118687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 889622.i | − | 0.294282i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 403386.i | − | 0.131747i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 706120. | − | 706120.i | 0.227712 | − | 0.227712i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05447e6 | + | 2.05447e6i | 0.654221 | + | 0.654221i | 0.954007 | − | 0.299786i | \(-0.0969151\pi\) |
−0.299786 | + | 0.954007i | \(0.596915\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −103808. | −0.0326437 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.95627e6 | 0.918087 | 0.459043 | − | 0.888414i | \(-0.348192\pi\) | ||||
0.459043 | + | 0.888414i | \(0.348192\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.37268e6 | − | 1.37268e6i | −0.421023 | − | 0.421023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 537659. | − | 537659.i | 0.162881 | − | 0.162881i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.06098e6i | − | 0.317482i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.47118e6i | 1.32164i | 0.750544 | + | 0.660821i | \(0.229792\pi\) | ||||
−0.750544 | + | 0.660821i | \(0.770208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 160415. | − | 160415.i | 0.0468426 | − | 0.0468426i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.64843e6 | − | 4.64843e6i | −1.34101 | − | 1.34101i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.19353e6 | −0.340182 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 726672. | 0.204644 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.61373e6 | + | 2.61373e6i | 0.727321 | + | 0.727321i | 0.970085 | − | 0.242765i | \(-0.0780543\pi\) |
−0.242765 | + | 0.970085i | \(0.578054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −295751. | + | 295751.i | −0.0813244 | + | 0.0813244i | −0.746599 | − | 0.665274i | \(-0.768315\pi\) |
0.665274 | + | 0.746599i | \(0.268315\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.05101e6i | 0.285598i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.39367e6i | − | 0.374273i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.47786e6 | + | 6.47786e6i | −1.71934 | + | 1.71934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −237429. | − | 237429.i | −0.0622860 | − | 0.0622860i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.14971e6 | 1.07603 | 0.538016 | − | 0.842935i | \(-0.319174\pi\) | ||||
0.538016 | + | 0.842935i | \(0.319174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.48115e6 | −0.379647 | −0.189823 | − | 0.981818i | \(-0.560792\pi\) | ||||
−0.189823 | + | 0.981818i | \(0.560792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −117089. | − | 117089.i | −0.0296683 | − | 0.0296683i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −363190. | + | 363190.i | −0.0909768 | + | 0.0909768i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.98071e6i | 0.985824i | 0.870079 | + | 0.492912i | \(0.164068\pi\) | ||||
−0.870079 | + | 0.492912i | \(0.835932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.28932e6i | 1.78481i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −713863. | + | 713863.i | −0.172825 | + | 0.172825i | −0.788219 | − | 0.615395i | \(-0.788997\pi\) |
0.615395 | + | 0.788219i | \(0.288997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 884624. | + | 884624.i | 0.211767 | + | 0.211767i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −68857.5 | −0.0162998 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.43383e6 | 0.803827 | 0.401913 | − | 0.915678i | \(-0.368345\pi\) | ||||
0.401913 | + | 0.915678i | \(0.368345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.33131e6 | − | 4.33131e6i | −1.00272 | − | 1.00272i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 100654. | − | 100654.i | 0.0230455 | − | 0.0230455i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.39699e6i | 0.316347i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.19382e6i | 0.267393i | 0.991022 | + | 0.133696i | \(0.0426847\pi\) | ||||
−0.991022 | + | 0.133696i | \(0.957315\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 282653. | − | 282653.i | 0.0626214 | − | 0.0626214i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.31361e6 | + | 3.31361e6i | 0.726189 | + | 0.726189i | 0.969858 | − | 0.243669i | \(-0.0783512\pi\) |
−0.243669 | + | 0.969858i | \(0.578351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.87318e6 | 0.622888 | 0.311444 | − | 0.950265i | \(-0.399187\pi\) | ||||
0.311444 | + | 0.950265i | \(0.399187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −94555.0 | −0.0202793 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.07444e6 | + | 2.07444e6i | 0.440159 | + | 0.440159i | 0.892065 | − | 0.451906i | \(-0.149256\pi\) |
−0.451906 | + | 0.892065i | \(0.649256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.44564e6 | − | 2.44564e6i | 0.513405 | − | 0.513405i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 501659.i | − | 0.104197i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.66966e6i | − | 1.37073i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −568970. | + | 568970.i | −0.115706 | + | 0.115706i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.70471e6 | + | 4.70471e6i | 0.946754 | + | 0.946754i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.37108e6 | 1.06960 | 0.534801 | − | 0.844978i | \(-0.320386\pi\) | ||||
0.534801 | + | 0.844978i | \(0.320386\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.27710e6 | 0.251688 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −505374. | − | 505374.i | −0.0985701 | − | 0.0985701i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.50261e6 | − | 1.50261e6i | 0.290063 | − | 0.290063i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.47468e6i | − | 1.23708i | −0.785755 | − | 0.618538i | \(-0.787725\pi\) | ||
0.785755 | − | 0.618538i | \(-0.212275\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 948157.i | 0.179311i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.39527e6 | + | 3.39527e6i | −0.635581 | + | 0.635581i | −0.949462 | − | 0.313881i | \(-0.898371\pi\) |
0.313881 | + | 0.949462i | \(0.398371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.36611e6 | + | 2.36611e6i | 0.438448 | + | 0.438448i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.28192e6 | 0.235152 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.04312e7 | 1.89428 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.47024e6 | − | 2.47024e6i | −0.444107 | − | 0.444107i | 0.449283 | − | 0.893390i | \(-0.351680\pi\) |
−0.893390 | + | 0.449283i | \(0.851680\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −648193. | + | 648193.i | −0.115374 | + | 0.115374i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9.84544e6i | − | 1.73506i | −0.497383 | − | 0.867531i | \(-0.665706\pi\) | ||
0.497383 | − | 0.867531i | \(-0.334294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.07017e6i | − | 0.361225i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −173558. | + | 173558.i | −0.0299864 | + | 0.0299864i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.92555e6 | + | 2.92555e6i | 0.500511 | + | 0.500511i | 0.911597 | − | 0.411086i | \(-0.134850\pi\) |
−0.411086 | + | 0.911597i | \(0.634850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.74505e6 | 0.295635 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −230788. | −0.0387186 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 535580. | + | 535580.i | 0.0889828 | + | 0.0889828i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.23675e6 | + | 1.23675e6i | −0.203496 | + | 0.203496i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.10705e6i | − | 0.180405i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 160551.i | 0.0259130i | 0.999916 | + | 0.0129565i | \(0.00412430\pi\) | ||||
−0.999916 | + | 0.0129565i | \(0.995876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.69862e6 | − | 2.69862e6i | 0.431408 | − | 0.431408i | −0.457699 | − | 0.889107i | \(-0.651326\pi\) |
0.889107 | + | 0.457699i | \(0.151326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −791713. | − | 791713.i | −0.125363 | − | 0.125363i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.91075e6 | 0.299694 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90007e6 | 0.450578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.13448e6 | − | 5.13448e6i | −0.790241 | − | 0.790241i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.21363e6 | − | 5.21363e6i | 0.794918 | − | 0.794918i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.98864e6i | 0.300380i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 487380.i | 0.0729343i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.57756e6 | + | 8.57756e6i | −1.27172 | + | 1.27172i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.35404e6 | + | 6.35404e6i | 0.933376 | + | 0.933376i | 0.997915 | − | 0.0645390i | \(-0.0205577\pi\) |
−0.0645390 | + | 0.997915i | \(0.520558\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 643250. | 0.0936225 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 675005. | 0.0973455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.08327e6 | + | 3.08327e6i | 0.440599 | + | 0.440599i | 0.892213 | − | 0.451614i | \(-0.149152\pi\) |
−0.451614 | + | 0.892213i | \(0.649152\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.15519e6 | + | 7.15519e6i | −1.01319 | + | 1.01319i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.93194e6i | − | 0.271091i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.62119e7i | 2.25436i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 43985.7 | − | 43985.7i | 0.00606149 | − | 0.00606149i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.15476e6 | − | 4.15476e6i | −0.567424 | − | 0.567424i | 0.363982 | − | 0.931406i | \(-0.381417\pi\) |
−0.931406 | + | 0.363982i | \(0.881417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.02831e6 | 1.08666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 330498. | 0.0443365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.09434e6 | + | 2.09434e6i | 0.278469 | + | 0.278469i | 0.832497 | − | 0.554029i | \(-0.186910\pi\) |
−0.554029 | + | 0.832497i | \(0.686910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −745866. | + | 745866.i | −0.0982969 | + | 0.0982969i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.23442e7i | 1.61252i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.46207e6i | − | 0.448286i | −0.974556 | − | 0.224143i | \(-0.928042\pi\) | ||
0.974556 | − | 0.224143i | \(-0.0719583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.29256e6 | + | 5.29256e6i | −0.679321 | + | 0.679321i | −0.959847 | − | 0.280525i | \(-0.909491\pi\) |
0.280525 | + | 0.959847i | \(0.409491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −231613. | − | 231613.i | −0.0294698 | − | 0.0294698i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.53988e6 | −0.698764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.13325e6 | 0.266749 | 0.133374 | − | 0.991066i | \(-0.457419\pi\) | ||||
0.133374 | + | 0.991066i | \(0.457419\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −732715. | − | 732715.i | −0.0908320 | − | 0.0908320i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.37012e7 | − | 1.37012e7i | 1.68391 | − | 1.68391i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.10723e7i | 1.34917i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.54306e6i | 0.186420i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.61821e6 | + | 1.61821e6i | −0.193839 | + | 0.193839i | −0.797353 | − | 0.603514i | \(-0.793767\pi\) |
0.603514 | + | 0.797353i | \(0.293767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −780069. | − | 780069.i | −0.0926498 | − | 0.0926498i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.77849e6 | −0.209451 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.12281e6 | 0.131121 | 0.0655603 | − | 0.997849i | \(-0.479117\pi\) | ||||
0.0655603 | + | 0.997849i | \(0.479117\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −972295. | − | 972295.i | −0.112591 | − | 0.112591i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −352760. | + | 352760.i | −0.0405082 | + | 0.0405082i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.37554e6i | − | 0.953774i | −0.878965 | − | 0.476887i | \(-0.841765\pi\) | ||
0.878965 | − | 0.476887i | \(-0.158235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.75444e6i | 0.423994i | 0.977270 | + | 0.211997i | \(0.0679967\pi\) | ||||
−0.977270 | + | 0.211997i | \(0.932003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.70135e6 | − | 2.70135e6i | 0.302544 | − | 0.302544i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15289.7 | − | 15289.7i | −0.00169828 | − | 0.00169828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.04209e7 | 1.14798 | 0.573988 | − | 0.818864i | \(-0.305396\pi\) | ||||
0.573988 | + | 0.818864i | \(0.305396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.68827e6 | 0.293717 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.48868e6 | − | 1.48868e6i | −0.161324 | − | 0.161324i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.21233e6 | + | 9.21233e6i | −0.990190 | + | 0.990190i | −0.999952 | − | 0.00976261i | \(-0.996892\pi\) |
0.00976261 | + | 0.999952i | \(0.496892\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 359134.i | − | 0.0382885i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.42219e7i | − | 1.50399i | −0.659167 | − | 0.751997i | \(-0.729091\pi\) | ||
0.659167 | − | 0.751997i | \(-0.270909\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.69068e6 | − | 9.69068e6i | 1.01655 | − | 1.01655i | 0.0166871 | − | 0.999861i | \(-0.494688\pi\) |
0.999861 | − | 0.0166871i | \(-0.00531192\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.12355e6 | − | 1.12355e6i | −0.116914 | − | 0.116914i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.03103e7 | −2.09650 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.11922e6 | −0.831409 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −134927. | − | 134927.i | −0.0137066 | − | 0.0137066i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −888856. | + | 888856.i | −0.0895787 | + | 0.0895787i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.49041e7i | − | 1.49016i | −0.666974 | − | 0.745081i | \(-0.732411\pi\) | ||
0.666974 | − | 0.745081i | \(-0.267589\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.68100e6i | − | 0.166747i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.38779e6 | − | 1.38779e6i | 0.136581 | − | 0.136581i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.03249e7 | − | 1.03249e7i | −1.00817 | − | 1.00817i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.15219e7 | 1.11628 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.23159e7 | −1.18391 | −0.591956 | − | 0.805970i | \(-0.701644\pi\) | ||||
−0.591956 | + | 0.805970i | \(0.701644\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.66909e6 | + | 4.66909e6i | 0.445353 | + | 0.445353i | 0.893806 | − | 0.448453i | \(-0.148025\pi\) |
−0.448453 | + | 0.893806i | \(0.648025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 276510. | − | 276510.i | 0.0261704 | − | 0.0261704i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.22769e7i | − | 1.15299i | −0.817100 | − | 0.576496i | \(-0.804419\pi\) | ||
0.817100 | − | 0.576496i | \(-0.195581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.20838e7i | − | 1.12614i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.08545e6 | − | 1.08545e6i | 0.100383 | − | 0.100383i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.63324e6 | + | 5.63324e6i | 0.516982 | + | 0.516982i | 0.916657 | − | 0.399675i | \(-0.130877\pi\) |
−0.399675 | + | 0.916657i | \(0.630877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.08494e6 | −0.280959 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.92751e6 | 0.174214 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.13854e6 | + | 3.13854e6i | 0.281523 | + | 0.281523i | 0.833716 | − | 0.552193i | \(-0.186209\pi\) |
−0.552193 | + | 0.833716i | \(0.686209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.25214e6 | + | 2.25214e6i | −0.200489 | + | 0.200489i | −0.800210 | − | 0.599720i | \(-0.795278\pi\) |
0.599720 | + | 0.800210i | \(0.295278\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 397823.i | 0.0351484i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 793884.i | 0.0696150i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.40536e6 | − | 9.40536e6i | 0.818579 | − | 0.818579i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25424.4 | − | 25424.4i | −0.00219627 | − | 0.00219627i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.68394e7 | −1.44385 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.80254e6 | −0.493834 | −0.246917 | − | 0.969037i | \(-0.579417\pi\) | ||||
−0.246917 | + | 0.969037i | \(0.579417\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.76015e6 | − | 1.76015e6i | −0.148693 | − | 0.148693i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.37302e6 | − | 5.37302e6i | 0.450554 | − | 0.450554i | −0.444984 | − | 0.895538i | \(-0.646791\pi\) |
0.895538 | + | 0.444984i | \(0.146791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.44988e7i | 2.87163i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.32434e6i | 0.192057i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.95020e6 | − | 7.95020e6i | 0.652118 | − | 0.652118i | −0.301384 | − | 0.953503i | \(-0.597449\pi\) |
0.953503 | + | 0.301384i | \(0.0974488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.22679e6 | − | 1.22679e6i | −0.0998950 | − | 0.0998950i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 199500. | 0.0161269 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.33278e7 | −1.06958 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.10073e7 | − | 1.10073e7i | −0.876968 | − | 0.876968i | 0.116251 | − | 0.993220i | \(-0.462912\pi\) |
−0.993220 | + | 0.116251i | \(0.962912\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.47159e7 | + | 1.47159e7i | −1.16401 | + | 1.16401i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.55729e6i | − | 0.436417i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.25731e6i | 0.565840i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 363030. | − | 363030.i | 0.0281028 | − | 0.0281028i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.83300e6 | − | 9.83300e6i | −0.755772 | − | 0.755772i | 0.219778 | − | 0.975550i | \(-0.429467\pi\) |
−0.975550 | + | 0.219778i | \(0.929467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 725755. | 0.0553862 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −102546. | −0.00777045 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.37647e7 | + | 2.37647e7i | 1.78807 | + | 1.78807i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.04507e6 | + | 6.04507e6i | −0.451633 | + | 0.451633i | −0.895896 | − | 0.444263i | \(-0.853465\pi\) |
0.444263 | + | 0.895896i | \(0.353465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.79071e7i | 1.32847i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.59528e6i | − | 0.559526i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.81576e6 | + | 1.81576e6i | −0.132829 | + | 0.132829i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 135517. | + | 135517.i | 0.00984454 | + | 0.00984454i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.40812e7 | −1.73722 | −0.868611 | − | 0.495495i | \(-0.834987\pi\) | ||||
−0.868611 | + | 0.495495i | \(0.834987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.22965e7 | −0.880932 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −908604. | − | 908604.i | −0.0646441 | − | 0.0646441i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.47343e7 | − | 1.47343e7i | 1.04108 | − | 1.04108i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.30046e6i | 0.371944i | 0.982555 | + | 0.185972i | \(0.0595434\pi\) | ||||
−0.982555 | + | 0.185972i | \(0.940457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.32757e7i | 0.925207i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.58766e6 | + | 5.58766e6i | −0.386755 | + | 0.386755i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.14793e7 | − | 1.14793e7i | −0.789143 | − | 0.789143i | 0.192210 | − | 0.981354i | \(-0.438434\pi\) |
−0.981354 | + | 0.192210i | \(0.938434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −711214. | −0.0485604 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.35752e6 | 0.431141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.10488e6 | − | 1.10488e6i | −0.0744226 | − | 0.0744226i | 0.668916 | − | 0.743338i | \(-0.266759\pi\) |
−0.743338 | + | 0.668916i | \(0.766759\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 162412. | − | 162412.i | 0.0108661 | − | 0.0108661i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.73631e6i | − | 0.181842i | −0.995858 | − | 0.0909209i | \(-0.971019\pi\) | ||
0.995858 | − | 0.0909209i | \(-0.0289810\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 526594.i | 0.0347605i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.51338e7 | − | 1.51338e7i | 0.992308 | − | 0.992308i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.28288e7 | − | 2.28288e7i | −1.48689 | − | 1.48689i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.79880e7 | −1.81080 | −0.905402 | − | 0.424555i | \(-0.860430\pi\) | ||||
−0.905402 | + | 0.424555i | \(0.860430\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.70603e6 | −0.109647 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −769761. | − | 769761.i | −0.0491460 | − | 0.0491460i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.52053e7 | + | 1.52053e7i | −0.964393 | + | 0.964393i | −0.999388 | − | 0.0349946i | \(-0.988859\pi\) |
0.0349946 | + | 0.999388i | \(0.488859\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.31374e6i | − | 0.0827760i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.28357e7i | − | 0.803448i | −0.915761 | − | 0.401724i | \(-0.868411\pi\) | ||
0.915761 | − | 0.401724i | \(-0.131589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.74879e6 | + | 7.74879e6i | −0.481862 | + | 0.481862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.07396e6 | − | 1.07396e6i | −0.0663490 | − | 0.0663490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.45453e7 | 0.892760 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 479067. | 0.0292133 | 0.0146066 | − | 0.999893i | \(-0.495350\pi\) | ||||
0.0146066 | + | 0.999893i | \(0.495350\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.17382e6 | + | 2.17382e6i | 0.131700 | + | 0.131700i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.26917e6 | − | 7.26917e6i | 0.437558 | − | 0.437558i | −0.453631 | − | 0.891190i | \(-0.649872\pi\) |
0.891190 | + | 0.453631i | \(0.149872\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.18987e7i | − | 0.711614i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00988e6i | 0.0600089i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.96282e6 | − | 2.96282e6i | 0.174929 | − | 0.174929i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.35582e7 | + | 1.35582e7i | 0.795378 | + | 0.795378i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.97660e6 | 0.348377 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.83649e6 | −0.222208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 924212. | + | 924212.i | 0.0531906 | + | 0.0531906i | 0.733202 | − | 0.680011i | \(-0.238025\pi\) |
−0.680011 | + | 0.733202i | \(0.738025\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.13847e6 | + | 2.13847e6i | −0.122296 | + | 0.122296i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.71245e7i | − | 0.973142i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.02697e7i | − | 1.14463i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −459035. | + | 459035.i | −0.0257590 | + | 0.0257590i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.36584e6 | + | 4.36584e6i | 0.243457 | + | 0.243457i | 0.818279 | − | 0.574822i | \(-0.194929\pi\) |
−0.574822 | + | 0.818279i | \(0.694929\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.07223e6 | 0.114834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.24339e7 | −1.23545 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.26816e6 | + | 2.26816e6i | 0.124132 | + | 0.124132i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.86489e6 | + | 3.86489e6i | −0.210207 | + | 0.210207i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 492129.i | − | 0.0266008i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.80829e7i | − | 0.971396i | −0.874127 | − | 0.485698i | \(-0.838565\pi\) | ||
0.874127 | − | 0.485698i | \(-0.161435\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.29179e7 | − | 2.29179e7i | 1.22355 | − | 1.22355i | 0.257191 | − | 0.966361i | \(-0.417203\pi\) |
0.966361 | − | 0.257191i | \(-0.0827969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.99847e6 | − | 1.99847e6i | −0.106040 | − | 0.106040i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.25112e6 | 0.382394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.56235e6 | 0.239130 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.77137e7 | − | 1.77137e7i | −0.922782 | − | 0.922782i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.13555e6 | − | 4.13555e6i | 0.214129 | − | 0.214129i | −0.591890 | − | 0.806019i | \(-0.701618\pi\) |
0.806019 | + | 0.591890i | \(0.201618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.35656e7i | 0.698133i | 0.937098 | + | 0.349067i | \(0.113501\pi\) | ||||
−0.937098 | + | 0.349067i | \(0.886499\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.05809e6i | − | 0.105276i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.05917e6 | + | 2.05917e6i | −0.104696 | + | 0.104696i | −0.757514 | − | 0.652819i | \(-0.773586\pi\) |
0.652819 | + | 0.757514i | \(0.273586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.41770e7 | + | 2.41770e7i | 1.22185 | + | 1.22185i | 0.966975 | + | 0.254871i | \(0.0820329\pi\) |
0.254871 | + | 0.966975i | \(0.417967\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.03486e6 | −0.0519850 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.43721e7 | 0.717641 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.95711e6 | + | 4.95711e6i | 0.246044 | + | 0.246044i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.41320e6 | − | 2.41320e6i | 0.119064 | − | 0.119064i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.89108e6i | 0.485108i | 0.970138 | + | 0.242554i | \(0.0779852\pi\) | ||||
−0.970138 | + | 0.242554i | \(0.922015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.95194e7i | 1.43919i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.31875e6 | + | 2.31875e6i | −0.112379 | + | 0.112379i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.32730e6 | + | 1.32730e6i | 0.0639481 | + | 0.0639481i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 351039. | 0.0168131 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.75598e6 | −0.131222 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.53322e6 | + | 3.53322e6i | 0.167243 | + | 0.167243i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.10564e7 | − | 1.10564e7i | 0.520284 | − | 0.520284i | −0.397373 | − | 0.917657i | \(-0.630078\pi\) |
0.917657 | + | 0.397373i | \(0.130078\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 876893.i | 0.0410234i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.52495e7i | − | 0.709257i | −0.935007 | − | 0.354628i | \(-0.884607\pi\) | ||
0.935007 | − | 0.354628i | \(-0.115393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.20409e7 | + | 1.20409e7i | −0.556768 | + | 0.556768i | −0.928386 | − | 0.371617i | \(-0.878803\pi\) |
0.371617 | + | 0.928386i | \(0.378803\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.12271e6 | + | 4.12271e6i | 0.189529 | + | 0.189529i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.08994e7 | 1.41229 | 0.706145 | − | 0.708067i | \(-0.250433\pi\) | ||||
0.706145 | + | 0.708067i | \(0.250433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.46626e6 | −0.384726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.47972e6 | + | 1.47972e6i | 0.0668548 | + | 0.0668548i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.10718e7 | + | 2.10718e7i | −0.946568 | + | 0.946568i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.65259e6i | 0.341793i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.81060e7i | 1.69222i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.24774e7 | + | 1.24774e7i | −0.550938 | + | 0.550938i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.33320e7 | − | 2.33320e7i | −1.02436 | − | 1.02436i | −0.999696 | − | 0.0246672i | \(-0.992147\pi\) |
−0.0246672 | − | 0.999696i | \(-0.507853\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.20842e6 | −0.0527529 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.57739e7 | 1.55284 | 0.776419 | − | 0.630218i | \(-0.217034\pi\) | ||||
0.776419 | + | 0.630218i | \(0.217034\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.50070e7 | − | 2.50070e7i | −1.07935 | − | 1.07935i | −0.996568 | − | 0.0827776i | \(-0.973621\pi\) |
−0.0827776 | − | 0.996568i | \(-0.526379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 500967. | − | 500967.i | 0.0215006 | − | 0.0215006i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.34384e7i | − | 1.42704i | −0.700633 | − | 0.713521i | \(-0.747099\pi\) | ||
0.700633 | − | 0.713521i | \(-0.252901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.18626e7i | 1.35216i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.60446e7 | + | 1.60446e7i | −0.677073 | + | 0.677073i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −845993. | − | 845993.i | −0.0355008 | − | 0.0355008i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.72728e6 | 0.155537 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.58135e6 | 0.0656218 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.02010e7 | + | 2.02010e7i | 0.833632 | + | 0.833632i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.27610e6 | − | 9.27610e6i | 0.380674 | − | 0.380674i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.34844e6i | 0.259088i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.91931e6i | − | 0.199656i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.53434e7 | + | 1.53434e7i | −0.619304 | + | 0.619304i | −0.945353 | − | 0.326049i | \(-0.894283\pi\) |
0.326049 | + | 0.945353i | \(0.394283\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.62496e7 | + | 2.62496e7i | 1.05369 | + | 1.05369i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −479747. | −0.0191521 | −0.00957604 | − | 0.999954i | \(-0.503048\pi\) | ||||
−0.00957604 | + | 0.999954i | \(0.503048\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.56167e7 | 1.41409 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −698127. | − | 698127.i | −0.0275665 | − | 0.0275665i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.54138e7 | − | 3.54138e7i | 1.39075 | − | 1.39075i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 9.26403e6i | − | 0.361835i | −0.983498 | − | 0.180918i | \(-0.942093\pi\) | ||
0.983498 | − | 0.180918i | \(-0.0579068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 981845.i | − | 0.0381412i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.63201e7 | + | 1.63201e7i | −0.630547 | + | 0.630547i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.53511e6 | + | 5.53511e6i | 0.212702 | + | 0.212702i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.35822e7 | −0.519124 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.65567e7 | 1.38972 | 0.694861 | − | 0.719144i | \(-0.255466\pi\) | ||||
0.694861 | + | 0.719144i | \(0.255466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.86744e6 | − | 5.86744e6i | −0.221858 | − | 0.221858i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.22993e6 | − | 2.22993e6i | 0.0838662 | − | 0.0838662i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.52752e6i | − | 0.0945507i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.48280e6i | − | 0.315639i | −0.987468 | − | 0.157819i | \(-0.949554\pi\) | ||
0.987468 | − | 0.157819i | \(-0.0504464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 428770. | − | 428770.i | 0.0158694 | − | 0.0158694i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.36732e7 | − | 1.36732e7i | −0.503379 | − | 0.503379i | 0.409107 | − | 0.912486i | \(-0.365840\pi\) |
−0.912486 | + | 0.409107i | \(0.865840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.88480e7 | 1.05642 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.45593e6 | −0.0894617 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.62841e7 | + | 2.62841e7i | 0.952399 | + | 0.952399i | 0.998917 | − | 0.0465186i | \(-0.0148127\pi\) |
−0.0465186 | + | 0.998917i | \(0.514813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.73020e6 | + | 2.73020e6i | −0.0984075 | + | 0.0984075i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.58358e6i | 0.128489i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.85225e6i | − | 0.101732i | −0.998705 | − | 0.0508658i | \(-0.983802\pi\) | ||
0.998705 | − | 0.0508658i | \(-0.0161981\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.77128e6 | + | 1.77128e6i | −0.0628463 | + | 0.0628463i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.49413e6 | + | 3.49413e6i | 0.123327 | + | 0.123327i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.81661e7 | 0.988964 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.23158e7 | −0.430185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.52158e7 | − | 2.52158e7i | −0.876206 | − | 0.876206i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.60351e6 | + | 5.60351e6i | −0.193705 | + | 0.193705i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.35407e6i | 0.0809568i | 0.999180 | + | 0.0404784i | \(0.0128882\pi\) | ||||
−0.999180 | + | 0.0404784i | \(0.987112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 226076.i | 0.00773472i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.13394e6 | − | 3.13394e6i | 0.106670 | − | 0.106670i | −0.651757 | − | 0.758427i | \(-0.725968\pi\) |
0.758427 | + | 0.651757i | \(0.225968\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.37955e7 | + | 6.37955e7i | 2.16027 | + | 2.16027i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.47733e6 | 0.0834589 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 574910. | 0.0192692 | 0.00963460 | − | 0.999954i | \(-0.496933\pi\) | ||||
0.00963460 | + | 0.999954i | \(0.496933\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.63986e7 | − | 2.63986e7i | −0.880288 | − | 0.880288i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.55901e6 | + | 8.55901e6i | −0.283956 | + | 0.283956i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.93611e7i | − | 0.969145i | −0.874751 | − | 0.484572i | \(-0.838975\pi\) | ||
0.874751 | − | 0.484572i | \(-0.161025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.36012e7i | 0.446669i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.17719e6 | − | 1.17719e6i | 0.0384638 | − | 0.0384638i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.22111e7 | + | 2.22111e7i | 0.722069 | + | 0.722069i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.12370e7 | 1.65730 | 0.828648 | − | 0.559770i | \(-0.189111\pi\) | ||||
0.828648 | + | 0.559770i | \(0.189111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.18092e6 | −0.0701885 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.69776e6 | + | 2.69776e6i | 0.0863866 | + | 0.0863866i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.85202e7 | − | 1.85202e7i | 0.590076 | − | 0.590076i | −0.347576 | − | 0.937652i | \(-0.612995\pi\) |
0.937652 | + | 0.347576i | \(0.112995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.24517e6i | 0.0711764i |
(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 | 256.6.e.a.65.4 | ✓ | 16 | |
4.3 | odd | 2 | inner | 256.6.e.a.65.5 | yes | 16 | |
8.3 | odd | 2 | 256.6.e.b.65.4 | yes | 16 | ||
8.5 | even | 2 | 256.6.e.b.65.5 | yes | 16 | ||
16.3 | odd | 4 | 256.6.e.b.193.4 | yes | 16 | ||
16.5 | even | 4 | inner | 256.6.e.a.193.4 | yes | 16 | |
16.11 | odd | 4 | inner | 256.6.e.a.193.5 | yes | 16 | |
16.13 | even | 4 | 256.6.e.b.193.5 | yes | 16 | ||
32.5 | even | 8 | 1024.6.a.e.1.5 | 8 | |||
32.11 | odd | 8 | 1024.6.a.e.1.6 | 8 | |||
32.21 | even | 8 | 1024.6.a.d.1.4 | 8 | |||
32.27 | odd | 8 | 1024.6.a.d.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
256.6.e.a.65.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
256.6.e.a.65.5 | yes | 16 | 4.3 | odd | 2 | inner | |
256.6.e.a.193.4 | yes | 16 | 16.5 | even | 4 | inner | |
256.6.e.a.193.5 | yes | 16 | 16.11 | odd | 4 | inner | |
256.6.e.b.65.4 | yes | 16 | 8.3 | odd | 2 | ||
256.6.e.b.65.5 | yes | 16 | 8.5 | even | 2 | ||
256.6.e.b.193.4 | yes | 16 | 16.3 | odd | 4 | ||
256.6.e.b.193.5 | yes | 16 | 16.13 | even | 4 | ||
1024.6.a.d.1.3 | 8 | 32.27 | odd | 8 | |||
1024.6.a.d.1.4 | 8 | 32.21 | even | 8 | |||
1024.6.a.e.1.5 | 8 | 32.5 | even | 8 | |||
1024.6.a.e.1.6 | 8 | 32.11 | odd | 8 |