Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + \cdots + 2924100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.11 | ||
Root | \(-1.98442 - 2.21794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.a.55.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.59266 | − | 3.66925i | 0.398166 | − | 0.917313i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.9268 | − | 11.6878i | −0.682928 | − | 0.730486i | ||||
\(5\) | 29.4580 | 1.17832 | 0.589160 | − | 0.808017i | \(-0.299459\pi\) | ||||
0.589160 | + | 0.808017i | \(0.299459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 32.9098i | − | 0.671628i | −0.941928 | − | 0.335814i | \(-0.890989\pi\) | ||
0.941928 | − | 0.335814i | \(-0.109011\pi\) | |||||||
\(8\) | −60.2882 | + | 21.4787i | −0.942003 | + | 0.335604i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 46.9167 | − | 108.089i | 0.469167 | − | 1.08089i | ||||
\(11\) | − | 136.639i | − | 1.12925i | −0.825348 | − | 0.564625i | \(-0.809021\pi\) | ||
0.825348 | − | 0.564625i | \(-0.190979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 164.522 | 0.973503 | 0.486751 | − | 0.873541i | \(-0.338182\pi\) | ||||
0.486751 | + | 0.873541i | \(0.338182\pi\) | |||||||
\(14\) | −120.754 | − | 52.4142i | −0.616094 | − | 0.267420i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −17.2082 | + | 255.421i | −0.0672195 | + | 0.997738i | ||||
\(17\) | −380.756 | −1.31750 | −0.658748 | − | 0.752364i | \(-0.728914\pi\) | ||||
−0.658748 | + | 0.752364i | \(0.728914\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 439.574i | − | 1.21766i | −0.793302 | − | 0.608829i | \(-0.791640\pi\) | ||
0.793302 | − | 0.608829i | \(-0.208360\pi\) | |||||||
\(20\) | −321.883 | − | 344.298i | −0.804707 | − | 0.860746i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −501.364 | − | 217.620i | −1.03588 | − | 0.449629i | ||||
\(23\) | − | 171.733i | − | 0.324636i | −0.986738 | − | 0.162318i | \(-0.948103\pi\) | ||
0.986738 | − | 0.162318i | \(-0.0518971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 242.773 | 0.388436 | ||||||||
\(26\) | 262.028 | − | 603.673i | 0.387616 | − | 0.893007i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −384.642 | + | 359.600i | −0.490615 | + | 0.458674i | ||||
\(29\) | −1041.21 | −1.23806 | −0.619029 | − | 0.785368i | \(-0.712474\pi\) | ||||
−0.619029 | + | 0.785368i | \(0.712474\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1181.17i | 1.22911i | 0.788876 | + | 0.614553i | \(0.210664\pi\) | ||||
−0.788876 | + | 0.614553i | \(0.789336\pi\) | |||||||
\(32\) | 909.798 | + | 469.941i | 0.888474 | + | 0.458927i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −606.417 | + | 1397.09i | −0.524582 | + | 1.20856i | ||||
\(35\) | − | 969.456i | − | 0.791393i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2700.79 | 1.97282 | 0.986410 | − | 0.164301i | \(-0.0525370\pi\) | ||||
0.986410 | + | 0.164301i | \(0.0525370\pi\) | |||||||
\(38\) | −1612.91 | − | 700.094i | −1.11697 | − | 0.484830i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1775.97 | + | 632.718i | −1.10998 | + | 0.395449i | ||||
\(41\) | 1556.42 | 0.925887 | 0.462944 | − | 0.886388i | \(-0.346793\pi\) | ||||
0.462944 | + | 0.886388i | \(0.346793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2218.02i | − | 1.19958i | −0.800158 | − | 0.599789i | \(-0.795251\pi\) | ||
0.800158 | − | 0.599789i | \(-0.204749\pi\) | |||||||
\(44\) | −1597.01 | + | 1493.04i | −0.824901 | + | 0.771196i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −630.130 | − | 273.512i | −0.297793 | − | 0.129259i | ||||
\(47\) | 1292.12i | 0.584934i | 0.956276 | + | 0.292467i | \(0.0944761\pi\) | ||||
−0.956276 | + | 0.292467i | \(0.905524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1317.95 | 0.548915 | ||||||||
\(50\) | 386.655 | − | 890.794i | 0.154662 | − | 0.356318i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1797.71 | − | 1922.90i | −0.664832 | − | 0.711130i | ||||
\(53\) | 1015.00 | 0.361337 | 0.180669 | − | 0.983544i | \(-0.442174\pi\) | ||||
0.180669 | + | 0.983544i | \(0.442174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4025.12i | − | 1.33062i | ||||||
\(56\) | 706.858 | + | 1984.07i | 0.225401 | + | 0.632676i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1658.29 | + | 3820.45i | −0.492952 | + | 1.13569i | ||||
\(59\) | 2434.15i | 0.699268i | 0.936886 | + | 0.349634i | \(0.113694\pi\) | ||||
−0.936886 | + | 0.349634i | \(0.886306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3839.98 | 1.03198 | 0.515988 | − | 0.856596i | \(-0.327425\pi\) | ||||
0.515988 | + | 0.856596i | \(0.327425\pi\) | |||||||
\(62\) | 4334.02 | + | 1881.21i | 1.12748 | + | 0.489388i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3173.33 | − | 2589.82i | 0.774740 | − | 0.632280i | ||||
\(65\) | 4846.48 | 1.14710 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2352.60i | − | 0.524081i | −0.965057 | − | 0.262040i | \(-0.915605\pi\) | ||
0.965057 | − | 0.262040i | \(-0.0843954\pi\) | |||||||
\(68\) | 4160.46 | + | 4450.19i | 0.899754 | + | 0.962412i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3557.18 | − | 1544.02i | −0.725955 | − | 0.315106i | ||||
\(71\) | − | 884.064i | − | 0.175375i | −0.996148 | − | 0.0876874i | \(-0.972052\pi\) | ||
0.996148 | − | 0.0876874i | \(-0.0279476\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6921.45 | 1.29883 | 0.649413 | − | 0.760436i | \(-0.275014\pi\) | ||||
0.649413 | + | 0.760436i | \(0.275014\pi\) | |||||||
\(74\) | 4301.45 | − | 9909.89i | 0.785510 | − | 1.80969i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5137.65 | + | 4803.16i | −0.889482 | + | 0.831572i | ||||
\(77\) | −4496.77 | −0.758436 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10308.0i | 1.65165i | 0.563924 | + | 0.825826i | \(0.309291\pi\) | ||||
−0.563924 | + | 0.825826i | \(0.690709\pi\) | |||||||
\(80\) | −506.918 | + | 7524.19i | −0.0792060 | + | 1.17565i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2478.85 | − | 5710.89i | 0.368657 | − | 0.849329i | ||||
\(83\) | 12322.0i | 1.78865i | 0.447417 | + | 0.894326i | \(0.352344\pi\) | ||||
−0.447417 | + | 0.894326i | \(0.647656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11216.3 | −1.55243 | ||||||||
\(86\) | −8138.47 | − | 3532.56i | −1.10039 | − | 0.477631i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2934.83 | + | 8237.73i | 0.378981 | + | 1.06376i | ||||
\(89\) | −5751.10 | −0.726057 | −0.363028 | − | 0.931778i | \(-0.618257\pi\) | ||||
−0.363028 | + | 0.931778i | \(0.618257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5414.38i | − | 0.653832i | ||||||
\(92\) | −2007.17 | + | 1876.49i | −0.237142 | + | 0.221703i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4741.11 | + | 2057.91i | 0.536568 | + | 0.232901i | ||||
\(95\) | − | 12949.0i | − | 1.43479i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8159.93 | −0.867247 | −0.433624 | − | 0.901094i | \(-0.642765\pi\) | ||||
−0.433624 | + | 0.901094i | \(0.642765\pi\) | |||||||
\(98\) | 2099.04 | − | 4835.88i | 0.218559 | − | 0.503527i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2652.74 | − | 2837.47i | −0.265274 | − | 0.283747i | ||||
\(101\) | 11440.4 | 1.12150 | 0.560749 | − | 0.827986i | \(-0.310513\pi\) | ||||
0.560749 | + | 0.827986i | \(0.310513\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11724.0i | 1.10510i | 0.833479 | + | 0.552552i | \(0.186346\pi\) | ||||
−0.833479 | + | 0.552552i | \(0.813654\pi\) | |||||||
\(104\) | −9918.73 | + | 3533.71i | −0.917043 | + | 0.326711i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1616.55 | − | 3724.28i | 0.143872 | − | 0.331460i | ||||
\(107\) | − | 21224.4i | − | 1.85382i | −0.375286 | − | 0.926909i | \(-0.622456\pi\) | ||
0.375286 | − | 0.926909i | \(-0.377544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5752.64 | −0.484188 | −0.242094 | − | 0.970253i | \(-0.577834\pi\) | ||||
−0.242094 | + | 0.970253i | \(0.577834\pi\) | |||||||
\(110\) | −14769.2 | − | 6410.66i | −1.22059 | − | 0.529806i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8405.85 | + | 566.318i | 0.670109 | + | 0.0451465i | ||||
\(113\) | −6018.68 | −0.471351 | −0.235675 | − | 0.971832i | \(-0.575730\pi\) | ||||
−0.235675 | + | 0.971832i | \(0.575730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5058.90i | − | 0.382525i | ||||||
\(116\) | 11377.1 | + | 12169.4i | 0.845504 | + | 0.904384i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8931.52 | + | 3876.79i | 0.641448 | + | 0.278425i | ||||
\(119\) | 12530.6i | 0.884868i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4029.28 | −0.275205 | ||||||||
\(122\) | 6115.80 | − | 14089.9i | 0.410898 | − | 0.946646i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13805.3 | − | 12906.5i | 0.897845 | − | 0.839391i | ||||
\(125\) | −11259.6 | −0.720617 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7591.93i | 0.470700i | 0.971911 | + | 0.235350i | \(0.0756237\pi\) | ||||
−0.971911 | + | 0.235350i | \(0.924376\pi\) | |||||||
\(128\) | −4448.65 | − | 15768.5i | −0.271524 | − | 0.962432i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7718.82 | − | 17783.0i | 0.456735 | − | 1.05225i | ||||
\(131\) | 3334.49i | 0.194306i | 0.995269 | + | 0.0971532i | \(0.0309737\pi\) | ||||
−0.995269 | + | 0.0971532i | \(0.969026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14466.3 | −0.817813 | ||||||||
\(134\) | −8632.28 | − | 3746.90i | −0.480746 | − | 0.208671i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 22955.1 | − | 8178.14i | 1.24109 | − | 0.442157i | ||||
\(137\) | −11823.7 | −0.629960 | −0.314980 | − | 0.949098i | \(-0.601998\pi\) | ||||
−0.314980 | + | 0.949098i | \(0.601998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5544.34i | 0.286959i | 0.989653 | + | 0.143480i | \(0.0458292\pi\) | ||||
−0.989653 | + | 0.143480i | \(0.954171\pi\) | |||||||
\(140\) | −11330.8 | + | 10593.1i | −0.578101 | + | 0.540464i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3243.85 | − | 1408.02i | −0.160874 | − | 0.0698282i | ||||
\(143\) | − | 22480.2i | − | 1.09933i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30671.8 | −1.45883 | ||||||||
\(146\) | 11023.5 | − | 25396.5i | 0.517149 | − | 1.19143i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −29511.1 | − | 31566.2i | −1.34729 | − | 1.44112i | ||||
\(149\) | −11073.6 | −0.498790 | −0.249395 | − | 0.968402i | \(-0.580232\pi\) | ||||
−0.249395 | + | 0.968402i | \(0.580232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 27450.4i | − | 1.20391i | −0.798529 | − | 0.601956i | \(-0.794388\pi\) | ||
0.798529 | − | 0.601956i | \(-0.205612\pi\) | |||||||
\(152\) | 9441.47 | + | 26501.1i | 0.408651 | + | 1.14704i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7161.84 | + | 16499.8i | −0.301984 | + | 0.695724i | ||||
\(155\) | 34794.9i | 1.44828i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14606.6 | 0.592583 | 0.296291 | − | 0.955098i | \(-0.404250\pi\) | ||||
0.296291 | + | 0.955098i | \(0.404250\pi\) | |||||||
\(158\) | 37822.5 | + | 16417.1i | 1.51508 | + | 0.657632i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 26800.8 | + | 13843.5i | 1.04691 | + | 0.540762i | ||||
\(161\) | −5651.68 | −0.218035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 39065.5i | 1.47034i | 0.677883 | + | 0.735170i | \(0.262898\pi\) | ||||
−0.677883 | + | 0.735170i | \(0.737102\pi\) | |||||||
\(164\) | −17006.7 | − | 18191.1i | −0.632314 | − | 0.676348i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 45212.6 | + | 19624.8i | 1.64075 | + | 0.712180i | ||||
\(167\) | − | 3123.15i | − | 0.111985i | −0.998431 | − | 0.0559926i | \(-0.982168\pi\) | ||
0.998431 | − | 0.0559926i | \(-0.0178323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1493.53 | −0.0522925 | ||||||||
\(170\) | −17863.8 | + | 41155.5i | −0.618125 | + | 1.42407i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −25923.7 | + | 24235.9i | −0.876274 | + | 0.819225i | ||||
\(173\) | 50749.6 | 1.69567 | 0.847834 | − | 0.530262i | \(-0.177907\pi\) | ||||
0.847834 | + | 0.530262i | \(0.177907\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7989.60i | − | 0.260885i | ||||||
\(176\) | 34900.5 | + | 2351.31i | 1.12670 | + | 0.0759076i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9159.56 | + | 21102.2i | −0.289091 | + | 0.666022i | ||||
\(179\) | 4456.66i | 0.139092i | 0.997579 | + | 0.0695462i | \(0.0221551\pi\) | ||||
−0.997579 | + | 0.0695462i | \(0.977845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8462.68 | −0.258316 | −0.129158 | − | 0.991624i | \(-0.541227\pi\) | ||||
−0.129158 | + | 0.991624i | \(0.541227\pi\) | |||||||
\(182\) | −19866.7 | − | 8623.29i | −0.599769 | − | 0.260334i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3688.59 | + | 10353.4i | 0.108949 | + | 0.305808i | ||||
\(185\) | 79559.9 | 2.32461 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52026.2i | 1.48778i | ||||||||
\(188\) | 15102.0 | − | 14118.8i | 0.427286 | − | 0.399467i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −47513.1 | − | 20623.4i | −1.31615 | − | 0.571284i | ||||
\(191\) | 17699.2i | 0.485163i | 0.970131 | + | 0.242582i | \(0.0779942\pi\) | ||||
−0.970131 | + | 0.242582i | \(0.922006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10944.5 | 0.293820 | 0.146910 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146910 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(194\) | −12996.0 | + | 29940.9i | −0.345308 | + | 0.795538i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14401.0 | − | 15403.9i | −0.374869 | − | 0.400975i | ||||
\(197\) | 10101.3 | 0.260284 | 0.130142 | − | 0.991495i | \(-0.458457\pi\) | ||||
0.130142 | + | 0.991495i | \(0.458457\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 31394.8i | − | 0.792777i | −0.918083 | − | 0.396388i | \(-0.870263\pi\) | ||
0.918083 | − | 0.396388i | \(-0.129737\pi\) | |||||||
\(200\) | −14636.3 | + | 5214.43i | −0.365908 | + | 0.130361i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18220.7 | − | 41977.8i | 0.446543 | − | 1.02877i | ||||
\(203\) | 34265.9i | 0.831515i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 45848.9 | 1.09099 | ||||||||
\(206\) | 43018.5 | + | 18672.5i | 1.01373 | + | 0.440015i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2831.12 | + | 42022.4i | −0.0654383 | + | 0.971301i | ||||
\(209\) | −60063.1 | −1.37504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 83361.8i | − | 1.87241i | −0.351448 | − | 0.936207i | \(-0.614311\pi\) | ||
0.351448 | − | 0.936207i | \(-0.385689\pi\) | |||||||
\(212\) | −11090.7 | − | 11863.1i | −0.246767 | − | 0.263952i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −77877.6 | − | 33803.3i | −1.70053 | − | 0.738127i | ||||
\(215\) | − | 65338.3i | − | 1.41349i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 38872.1 | 0.825503 | ||||||||
\(218\) | −9162.02 | + | 21107.9i | −0.192787 | + | 0.444152i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −47044.7 | + | 43981.8i | −0.971997 | + | 0.908715i | ||||
\(221\) | −62642.8 | −1.28259 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13301.4i | − | 0.267478i | −0.991017 | − | 0.133739i | \(-0.957302\pi\) | ||
0.991017 | − | 0.133739i | \(-0.0426983\pi\) | |||||||
\(224\) | 15465.7 | − | 29941.2i | 0.308228 | − | 0.596724i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9585.73 | + | 22084.1i | −0.187676 | + | 0.432377i | ||||
\(227\) | 50075.5i | 0.971792i | 0.874017 | + | 0.485896i | \(0.161507\pi\) | ||||
−0.874017 | + | 0.485896i | \(0.838493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 60039.8 | 1.14490 | 0.572451 | − | 0.819939i | \(-0.305993\pi\) | ||||
0.572451 | + | 0.819939i | \(0.305993\pi\) | |||||||
\(230\) | −18562.4 | − | 8057.12i | −0.350895 | − | 0.152308i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 62772.5 | − | 22363.7i | 1.16625 | − | 0.415497i | ||||
\(233\) | −31252.0 | −0.575659 | −0.287830 | − | 0.957682i | \(-0.592934\pi\) | ||||
−0.287830 | + | 0.957682i | \(0.592934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38063.2i | 0.689239i | ||||||||
\(236\) | 28449.8 | − | 26597.6i | 0.510805 | − | 0.477549i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 45978.0 | + | 19957.0i | 0.811701 | + | 0.352324i | ||||
\(239\) | − | 62883.1i | − | 1.10087i | −0.834876 | − | 0.550437i | \(-0.814461\pi\) | ||
0.834876 | − | 0.550437i | \(-0.185539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 64613.0 | 1.11246 | 0.556232 | − | 0.831027i | \(-0.312247\pi\) | ||||
0.556232 | + | 0.831027i | \(0.312247\pi\) | |||||||
\(242\) | −6417.29 | + | 14784.5i | −0.109577 | + | 0.252450i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −41958.9 | − | 44880.9i | −0.704765 | − | 0.753844i | ||||
\(245\) | 38824.0 | 0.646797 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 72319.6i | − | 1.18539i | ||||||
\(248\) | −25370.0 | − | 71210.7i | −0.412493 | − | 1.15782i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17932.8 | + | 41314.5i | −0.286925 | + | 0.661032i | ||||
\(251\) | 78853.1i | 1.25162i | 0.779977 | + | 0.625808i | \(0.215231\pi\) | ||||
−0.779977 | + | 0.625808i | \(0.784769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23465.4 | −0.366595 | ||||||||
\(254\) | 27856.7 | + | 12091.4i | 0.431780 | + | 0.187417i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −64943.8 | − | 8790.66i | −0.990963 | − | 0.134135i | ||||
\(257\) | −25571.1 | −0.387153 | −0.193576 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193576 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 88882.5i | − | 1.32500i | ||||||
\(260\) | −52956.8 | − | 56644.6i | −0.783384 | − | 0.837938i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12235.1 | + | 5310.73i | 0.178240 | + | 0.0773662i | ||||
\(263\) | − | 110011.i | − | 1.59046i | −0.606305 | − | 0.795232i | \(-0.707349\pi\) | ||
0.606305 | − | 0.795232i | \(-0.292651\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29899.8 | 0.425771 | ||||||||
\(266\) | −23040.0 | + | 53080.5i | −0.325625 | + | 0.750191i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27496.6 | + | 25706.5i | −0.382834 | + | 0.357909i | ||||
\(269\) | −39818.1 | −0.550270 | −0.275135 | − | 0.961406i | \(-0.588723\pi\) | ||||
−0.275135 | + | 0.961406i | \(0.588723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14054.7i | 0.191375i | 0.995411 | + | 0.0956873i | \(0.0305049\pi\) | ||||
−0.995411 | + | 0.0956873i | \(0.969495\pi\) | |||||||
\(272\) | 6552.12 | − | 97253.1i | 0.0885614 | − | 1.31452i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18831.2 | + | 43384.2i | −0.250829 | + | 0.577871i | ||||
\(275\) | − | 33172.3i | − | 0.438642i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31583.7 | −0.411627 | −0.205813 | − | 0.978591i | \(-0.565984\pi\) | ||||
−0.205813 | + | 0.978591i | \(0.565984\pi\) | |||||||
\(278\) | 20343.6 | + | 8830.27i | 0.263232 | + | 0.114257i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20822.6 | + | 58446.8i | 0.265595 | + | 0.745494i | ||||
\(281\) | 66899.3 | 0.847244 | 0.423622 | − | 0.905839i | \(-0.360758\pi\) | ||||
0.423622 | + | 0.905839i | \(0.360758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 160099.i | 1.99901i | 0.0314612 | + | 0.999505i | \(0.489984\pi\) | ||||
−0.0314612 | + | 0.999505i | \(0.510016\pi\) | |||||||
\(284\) | −10332.7 | + | 9660.03i | −0.128109 | + | 0.119768i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −82485.4 | − | 35803.3i | −1.00843 | − | 0.437715i | ||||
\(287\) | − | 51221.4i | − | 0.621852i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 61454.3 | 0.735795 | ||||||||
\(290\) | −48849.9 | + | 112543.i | −0.580855 | + | 1.33820i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −75629.6 | − | 80896.3i | −0.887005 | − | 0.948775i | ||||
\(293\) | −92671.2 | −1.07947 | −0.539734 | − | 0.841836i | \(-0.681475\pi\) | ||||
−0.539734 | + | 0.841836i | \(0.681475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 71705.2i | 0.823961i | ||||||||
\(296\) | −162826. | + | 58009.4i | −1.85840 | + | 0.662087i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17636.6 | + | 40631.9i | −0.198601 | + | 0.457546i | ||||
\(299\) | − | 28253.8i | − | 0.316034i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72994.5 | −0.805670 | ||||||||
\(302\) | −100722. | − | 43719.3i | −1.10436 | − | 0.479357i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 112277. | + | 7564.28i | 1.21490 | + | 0.0818503i | ||||
\(305\) | 113118. | 1.21600 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 86852.2i | − | 0.921518i | −0.887525 | − | 0.460759i | \(-0.847577\pi\) | ||
0.887525 | − | 0.460759i | \(-0.152423\pi\) | |||||||
\(308\) | 49135.5 | + | 52557.2i | 0.517957 | + | 0.554027i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 127671. | + | 55416.6i | 1.32853 | + | 0.576656i | ||||
\(311\) | 43940.9i | 0.454306i | 0.973859 | + | 0.227153i | \(0.0729417\pi\) | ||||
−0.973859 | + | 0.227153i | \(0.927058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −100801. | −1.02890 | −0.514452 | − | 0.857519i | \(-0.672005\pi\) | ||||
−0.514452 | + | 0.857519i | \(0.672005\pi\) | |||||||
\(314\) | 23263.4 | − | 53595.2i | 0.235946 | − | 0.543584i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 120477. | − | 112634.i | 1.20651 | − | 1.12796i | ||||
\(317\) | −101986. | −1.01490 | −0.507449 | − | 0.861682i | \(-0.669411\pi\) | ||||
−0.507449 | + | 0.861682i | \(0.669411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 142270.i | 1.39808i | ||||||||
\(320\) | 93480.0 | − | 76290.9i | 0.912891 | − | 0.745028i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9001.23 | + | 20737.5i | −0.0868141 | + | 0.200006i | ||||
\(323\) | 167371.i | 1.60426i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 39941.4 | 0.378144 | ||||||||
\(326\) | 143341. | + | 62218.2i | 1.34876 | + | 0.585439i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −93833.6 | + | 33429.8i | −0.872189 | + | 0.310732i | ||||
\(329\) | 42523.4 | 0.392858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 39677.8i | − | 0.362153i | −0.983469 | − | 0.181076i | \(-0.942042\pi\) | ||
0.983469 | − | 0.181076i | \(-0.0579581\pi\) | |||||||
\(332\) | 144017. | − | 134641.i | 1.30658 | − | 1.22152i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11459.6 | − | 4974.13i | −0.102725 | − | 0.0445887i | ||||
\(335\) | − | 69302.8i | − | 0.617534i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −129324. | −1.13873 | −0.569364 | − | 0.822086i | \(-0.692810\pi\) | ||||
−0.569364 | + | 0.822086i | \(0.692810\pi\) | |||||||
\(338\) | −2378.68 | + | 5480.12i | −0.0208211 | + | 0.0479686i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 122559. | + | 131094.i | 1.06020 | + | 1.13403i | ||||
\(341\) | 161394. | 1.38797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 122390.i | − | 1.04030i | ||||||
\(344\) | 47640.1 | + | 133720.i | 0.402583 | + | 1.13001i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 80827.1 | − | 186213.i | 0.675157 | − | 1.55546i | ||||
\(347\) | 174482.i | 1.44908i | 0.689233 | + | 0.724540i | \(0.257948\pi\) | ||||
−0.689233 | + | 0.724540i | \(0.742052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −39421.3 | −0.323654 | −0.161827 | − | 0.986819i | \(-0.551739\pi\) | ||||
−0.161827 | + | 0.986819i | \(0.551739\pi\) | |||||||
\(350\) | −29315.9 | − | 12724.7i | −0.239313 | − | 0.103875i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 64212.4 | − | 124314.i | 0.518243 | − | 1.00331i | ||||
\(353\) | −123080. | −0.987733 | −0.493866 | − | 0.869538i | \(-0.664417\pi\) | ||||
−0.493866 | + | 0.869538i | \(0.664417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 26042.7i | − | 0.206647i | ||||||
\(356\) | 62841.3 | + | 67217.5i | 0.495844 | + | 0.530374i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16352.6 | + | 7097.96i | 0.127591 | + | 0.0553818i | ||||
\(359\) | 20967.0i | 0.162685i | 0.996686 | + | 0.0813424i | \(0.0259207\pi\) | ||||
−0.996686 | + | 0.0813424i | \(0.974079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −62904.6 | −0.482690 | ||||||||
\(362\) | −13478.2 | + | 31051.7i | −0.102852 | + | 0.236956i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −63282.1 | + | 59162.1i | −0.477615 | + | 0.446520i | ||||
\(365\) | 203892. | 1.53043 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 58300.8i | 0.432855i | 0.976299 | + | 0.216427i | \(0.0694405\pi\) | ||||
−0.976299 | + | 0.216427i | \(0.930560\pi\) | |||||||
\(368\) | 43864.1 | + | 2955.21i | 0.323902 | + | 0.0218219i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 126712. | − | 291925.i | 0.925581 | − | 2.13240i | ||||
\(371\) | − | 33403.3i | − | 0.242684i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −79775.3 | −0.573391 | −0.286695 | − | 0.958022i | \(-0.592557\pi\) | ||||
−0.286695 | + | 0.958022i | \(0.592557\pi\) | |||||||
\(374\) | 190897. | + | 82860.3i | 1.36476 | + | 0.592384i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27753.0 | − | 77899.5i | −0.196306 | − | 0.551009i | ||||
\(377\) | −171301. | −1.20525 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 80878.2i | − | 0.563058i | −0.959553 | − | 0.281529i | \(-0.909159\pi\) | ||
0.959553 | − | 0.281529i | \(-0.0908415\pi\) | |||||||
\(380\) | −151345. | + | 141491.i | −1.04809 | + | 0.979857i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 64943.0 | + | 28188.9i | 0.445047 | + | 0.193176i | ||||
\(383\) | − | 99819.8i | − | 0.680486i | −0.940338 | − | 0.340243i | \(-0.889491\pi\) | ||
0.940338 | − | 0.340243i | \(-0.110509\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −132466. | −0.893680 | ||||||||
\(386\) | 17430.9 | − | 40158.1i | 0.116989 | − | 0.269525i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 89162.3 | + | 95371.4i | 0.592267 | + | 0.633512i | ||||
\(389\) | 15583.1 | 0.102981 | 0.0514903 | − | 0.998673i | \(-0.483603\pi\) | ||||
0.0514903 | + | 0.998673i | \(0.483603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 65388.3i | 0.427707i | ||||||||
\(392\) | −79456.6 | + | 28307.7i | −0.517080 | + | 0.184218i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16088.0 | − | 37064.4i | 0.103636 | − | 0.238762i | ||||
\(395\) | 303652.i | 1.94617i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −67256.6 | −0.426730 | −0.213365 | − | 0.976973i | \(-0.568442\pi\) | ||||
−0.213365 | + | 0.976973i | \(0.568442\pi\) | |||||||
\(398\) | −115195. | − | 50001.3i | −0.727225 | − | 0.315657i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4177.68 | + | 62009.2i | −0.0261105 | + | 0.387558i | ||||
\(401\) | 151843. | 0.944288 | 0.472144 | − | 0.881521i | \(-0.343480\pi\) | ||||
0.472144 | + | 0.881521i | \(0.343480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 194329.i | 1.19654i | ||||||||
\(404\) | −125008. | − | 133713.i | −0.765903 | − | 0.819239i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 125730. | + | 54574.0i | 0.762760 | + | 0.331081i | ||||
\(407\) | − | 369034.i | − | 2.22781i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −64170.7 | −0.383610 | −0.191805 | − | 0.981433i | \(-0.561434\pi\) | ||||
−0.191805 | + | 0.981433i | \(0.561434\pi\) | |||||||
\(410\) | 73021.9 | − | 168231.i | 0.434396 | − | 1.00078i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 137028. | − | 128107.i | 0.807262 | − | 0.754706i | ||||
\(413\) | 80107.4 | 0.469648 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 362982.i | 2.10760i | ||||||||
\(416\) | 149682. | + | 77315.6i | 0.864932 | + | 0.446766i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −95660.3 | + | 220387.i | −0.547494 | + | 1.26134i | ||||
\(419\) | 85171.9i | 0.485142i | 0.970134 | + | 0.242571i | \(0.0779907\pi\) | ||||
−0.970134 | + | 0.242571i | \(0.922009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 214896. | 1.21245 | 0.606224 | − | 0.795294i | \(-0.292683\pi\) | ||||
0.606224 | + | 0.795294i | \(0.292683\pi\) | |||||||
\(422\) | −305875. | − | 132767.i | −1.71759 | − | 0.745532i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −61192.3 | + | 21800.8i | −0.340381 | + | 0.121266i | ||||
\(425\) | −92437.2 | −0.511763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 126373.i | − | 0.693105i | ||||||
\(428\) | −248066. | + | 231915.i | −1.35419 | + | 1.26602i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −239743. | − | 104062.i | −1.29661 | − | 0.562802i | ||||
\(431\) | − | 19885.9i | − | 0.107051i | −0.998566 | − | 0.0535254i | \(-0.982954\pi\) | ||
0.998566 | − | 0.0535254i | \(-0.0170458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 103996. | 0.554679 | 0.277339 | − | 0.960772i | \(-0.410547\pi\) | ||||
0.277339 | + | 0.960772i | \(0.410547\pi\) | |||||||
\(434\) | 61910.2 | − | 142632.i | 0.328687 | − | 0.757244i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 62858.2 | + | 67235.6i | 0.330666 | + | 0.353693i | ||||
\(437\) | −75489.2 | −0.395296 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 55956.4i | − | 0.290349i | −0.989406 | − | 0.145175i | \(-0.953626\pi\) | ||
0.989406 | − | 0.145175i | \(-0.0463744\pi\) | |||||||
\(440\) | 86454.1 | + | 242667.i | 0.446561 | + | 1.25345i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −99768.9 | + | 229852.i | −0.510682 | + | 1.17653i | ||||
\(443\) | − | 22607.4i | − | 0.115198i | −0.998340 | − | 0.0575988i | \(-0.981656\pi\) | ||
0.998340 | − | 0.0575988i | \(-0.0183444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169416. | −0.855527 | ||||||||
\(446\) | −48806.2 | − | 21184.7i | −0.245361 | − | 0.106501i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −85230.4 | − | 104434.i | −0.424657 | − | 0.520337i | ||||
\(449\) | 77577.5 | 0.384807 | 0.192404 | − | 0.981316i | \(-0.438372\pi\) | ||||
0.192404 | + | 0.981316i | \(0.438372\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 212668.i | − | 1.04556i | ||||||
\(452\) | 65765.2 | + | 70345.0i | 0.321899 | + | 0.344315i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 183740. | + | 79753.4i | 0.891438 | + | 0.386934i | ||||
\(455\) | − | 159497.i | − | 0.770423i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −242860. | −1.16285 | −0.581425 | − | 0.813600i | \(-0.697505\pi\) | ||||
−0.581425 | + | 0.813600i | \(0.697505\pi\) | |||||||
\(458\) | 95623.2 | − | 220301.i | 0.455861 | − | 1.05023i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −59127.2 | + | 55277.8i | −0.279429 | + | 0.261237i | ||||
\(461\) | −199640. | −0.939391 | −0.469696 | − | 0.882828i | \(-0.655636\pi\) | ||||
−0.469696 | + | 0.882828i | \(0.655636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 63490.8i | − | 0.296175i | −0.988974 | − | 0.148088i | \(-0.952688\pi\) | ||
0.988974 | − | 0.148088i | \(-0.0473118\pi\) | |||||||
\(464\) | 17917.3 | − | 265946.i | 0.0832216 | − | 1.23526i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −49773.9 | + | 114671.i | −0.229208 | + | 0.528060i | ||||
\(467\) | − | 112982.i | − | 0.518053i | −0.965870 | − | 0.259026i | \(-0.916598\pi\) | ||
0.965870 | − | 0.259026i | \(-0.0834017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −77423.5 | −0.351987 | ||||||||
\(470\) | 139664. | + | 60621.9i | 0.632248 | + | 0.274431i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −52282.3 | − | 146751.i | −0.234677 | − | 0.658713i | ||||
\(473\) | −303068. | −1.35462 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 106717.i | − | 0.472982i | ||||||
\(476\) | 146455. | − | 136920.i | 0.646383 | − | 0.604301i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −230734. | − | 100152.i | −1.00985 | − | 0.438331i | ||||
\(479\) | − | 313437.i | − | 1.36609i | −0.730376 | − | 0.683045i | \(-0.760655\pi\) | ||
0.730376 | − | 0.683045i | \(-0.239345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 444339. | 1.92055 | ||||||||
\(482\) | 102907. | − | 237081.i | 0.442945 | − | 1.02048i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 44027.3 | + | 47093.4i | 0.187945 | + | 0.201034i | ||||
\(485\) | −240375. | −1.02189 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 64950.6i | 0.273858i | 0.990581 | + | 0.136929i | \(0.0437232\pi\) | ||||
−0.990581 | + | 0.136929i | \(0.956277\pi\) | |||||||
\(488\) | −231506. | + | 82477.7i | −0.972125 | + | 0.346336i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 61833.6 | − | 142455.i | 0.257533 | − | 0.593316i | ||||
\(491\) | 358585.i | 1.48741i | 0.668510 | + | 0.743703i | \(0.266932\pi\) | ||||
−0.668510 | + | 0.743703i | \(0.733068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 396446. | 1.63114 | ||||||||
\(494\) | −265359. | − | 115181.i | −1.08738 | − | 0.471983i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −301696. | − | 20325.8i | −1.22633 | − | 0.0826198i | ||||
\(497\) | −29094.4 | −0.117787 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12696.3i | 0.0509890i | 0.999675 | + | 0.0254945i | \(0.00811603\pi\) | ||||
−0.999675 | + | 0.0254945i | \(0.991884\pi\) | |||||||
\(500\) | 123032. | + | 131600.i | 0.492130 | + | 0.526401i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 289332. | + | 125586.i | 1.14812 | + | 0.498351i | ||||
\(503\) | 114739.i | 0.453498i | 0.973953 | + | 0.226749i | \(0.0728097\pi\) | ||||
−0.973953 | + | 0.226749i | \(0.927190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 337011. | 1.32148 | ||||||||
\(506\) | −37372.5 | + | 86100.5i | −0.145966 | + | 0.336283i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 88732.8 | − | 82955.8i | 0.343840 | − | 0.321454i | ||||
\(509\) | −44847.2 | −0.173101 | −0.0865505 | − | 0.996247i | \(-0.527584\pi\) | ||||
−0.0865505 | + | 0.996247i | \(0.527584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 227783.i | − | 0.872329i | ||||||
\(512\) | −135689. | + | 224295.i | −0.517611 | + | 0.855616i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −40726.1 | + | 93826.7i | −0.154151 | + | 0.355141i | ||||
\(515\) | 345367.i | 1.30216i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 176554. | 0.660536 | ||||||||
\(518\) | −326132. | − | 141560.i | −1.21544 | − | 0.527571i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −292186. | + | 104096.i | −1.08057 | + | 0.384970i | ||||
\(521\) | 285591. | 1.05213 | 0.526065 | − | 0.850444i | \(-0.323667\pi\) | ||||
0.526065 | + | 0.850444i | \(0.323667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 164178.i | 0.600220i | 0.953905 | + | 0.300110i | \(0.0970234\pi\) | ||||
−0.953905 | + | 0.300110i | \(0.902977\pi\) | |||||||
\(524\) | 38972.8 | − | 36435.5i | 0.141938 | − | 0.132697i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −403658. | − | 175210.i | −1.45895 | − | 0.633269i | ||||
\(527\) | − | 449738.i | − | 1.61934i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 250349. | 0.894611 | ||||||||
\(530\) | 47620.3 | − | 109710.i | 0.169527 | − | 0.390565i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 158071. | + | 169079.i | 0.558507 | + | 0.597401i | ||||
\(533\) | 256065. | 0.901354 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 625227.i | − | 2.18439i | ||||||
\(536\) | 50530.7 | + | 141834.i | 0.175884 | + | 0.493686i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −63416.9 | + | 146103.i | −0.219099 | + | 0.504770i | ||||
\(539\) | − | 180083.i | − | 0.619863i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −300448. | −1.02654 | −0.513269 | − | 0.858228i | \(-0.671566\pi\) | ||||
−0.513269 | + | 0.858228i | \(0.671566\pi\) | |||||||
\(542\) | 51570.4 | + | 22384.5i | 0.175551 | + | 0.0761989i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −346411. | − | 178933.i | −1.17056 | − | 0.604634i | ||||
\(545\) | −169461. | −0.570528 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 74251.6i | 0.248160i | 0.992272 | + | 0.124080i | \(0.0395979\pi\) | ||||
−0.992272 | + | 0.124080i | \(0.960402\pi\) | |||||||
\(548\) | 129196. | + | 138193.i | 0.430217 | + | 0.460177i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −121717. | − | 52832.3i | −0.402372 | − | 0.174652i | ||||
\(551\) | 457688.i | 1.50753i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 339233. | 1.10930 | ||||||||
\(554\) | −50302.2 | + | 115889.i | −0.163896 | + | 0.377591i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 64801.0 | − | 60582.1i | 0.209620 | − | 0.195972i | ||||
\(557\) | 193413. | 0.623411 | 0.311705 | − | 0.950179i | \(-0.399100\pi\) | ||||
0.311705 | + | 0.950179i | \(0.399100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 364913.i | − | 1.16779i | ||||||
\(560\) | 247619. | + | 16682.6i | 0.789603 | + | 0.0531970i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 106548. | − | 245470.i | 0.337344 | − | 0.777188i | ||||
\(563\) | − | 177354.i | − | 0.559530i | −0.960068 | − | 0.279765i | \(-0.909743\pi\) | ||
0.960068 | − | 0.279765i | \(-0.0902566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −177298. | −0.555402 | ||||||||
\(566\) | 587443. | + | 254983.i | 1.83372 | + | 0.795938i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18988.5 | + | 53298.6i | 0.0588565 | + | 0.165204i | ||||
\(569\) | 590091. | 1.82261 | 0.911306 | − | 0.411730i | \(-0.135075\pi\) | ||||
0.911306 | + | 0.411730i | \(0.135075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 524012.i | 1.60720i | 0.595172 | + | 0.803598i | \(0.297084\pi\) | ||||
−0.595172 | + | 0.803598i | \(0.702916\pi\) | |||||||
\(572\) | −262743. | + | 245637.i | −0.803044 | + | 0.750761i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −187944. | − | 81578.4i | −0.570433 | − | 0.247600i | ||||
\(575\) | − | 41692.0i | − | 0.126100i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −337273. | −1.01305 | −0.506523 | − | 0.862226i | \(-0.669070\pi\) | ||||
−0.506523 | + | 0.862226i | \(0.669070\pi\) | |||||||
\(578\) | 97876.1 | − | 225492.i | 0.292969 | − | 0.674955i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 335146. | + | 358486.i | 0.996273 | + | 1.06565i | ||||
\(581\) | 405515. | 1.20131 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 138688.i | − | 0.408040i | ||||||
\(584\) | −417282. | + | 148663.i | −1.22350 | + | 0.435892i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −147594. | + | 340034.i | −0.429807 | + | 0.990210i | ||||
\(587\) | 4289.71i | 0.0124495i | 0.999981 | + | 0.00622475i | \(0.00198141\pi\) | ||||
−0.999981 | + | 0.00622475i | \(0.998019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 519212. | 1.49663 | ||||||||
\(590\) | 263105. | + | 114202.i | 0.755830 | + | 0.328073i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −46475.7 | + | 689839.i | −0.132612 | + | 1.96836i | ||||
\(593\) | 150227. | 0.427207 | 0.213604 | − | 0.976920i | \(-0.431480\pi\) | ||||
0.213604 | + | 0.976920i | \(0.431480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 369126.i | 1.04266i | ||||||||
\(596\) | 121000. | + | 129426.i | 0.340637 | + | 0.364359i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −103670. | − | 44998.8i | −0.289902 | − | 0.125834i | ||||
\(599\) | 473108.i | 1.31858i | 0.751888 | + | 0.659290i | \(0.229143\pi\) | ||||
−0.751888 | + | 0.659290i | \(0.770857\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −83320.1 | −0.230675 | −0.115338 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115338 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(602\) | −116256. | + | 267835.i | −0.320790 | + | 0.739052i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −320834. | + | 299946.i | −0.879441 | + | 0.822185i | ||||
\(605\) | −118695. | −0.324280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 143905.i | 0.390570i | 0.980747 | + | 0.195285i | \(0.0625632\pi\) | ||||
−0.980747 | + | 0.195285i | \(0.937437\pi\) | |||||||
\(608\) | 206574. | − | 399924.i | 0.558816 | − | 1.08186i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 180159. | − | 415059.i | 0.484169 | − | 1.11545i | ||||
\(611\) | 212582.i | 0.569435i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5563.04 | −0.0148044 | −0.00740221 | − | 0.999973i | \(-0.502356\pi\) | ||||
−0.00740221 | + | 0.999973i | \(0.502356\pi\) | |||||||
\(614\) | −318683. | − | 138326.i | −0.845321 | − | 0.366917i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 271102. | − | 96584.6i | 0.714449 | − | 0.254534i | ||||
\(617\) | −300749. | −0.790012 | −0.395006 | − | 0.918679i | \(-0.629257\pi\) | ||||
−0.395006 | + | 0.918679i | \(0.629257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 158539.i | − | 0.413767i | −0.978366 | − | 0.206883i | \(-0.933668\pi\) | ||
0.978366 | − | 0.206883i | \(-0.0663321\pi\) | |||||||
\(620\) | 406675. | − | 380199.i | 1.05795 | − | 0.989070i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 161230. | + | 69983.1i | 0.416741 | + | 0.180889i | ||||
\(623\) | 189267.i | 0.487640i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −483419. | −1.23755 | ||||||||
\(626\) | −160542. | + | 369863.i | −0.409675 | + | 0.943828i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −159604. | − | 170718.i | −0.404691 | − | 0.432873i | ||||
\(629\) | −1.02834e6 | −2.59918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 557374.i | 1.39987i | 0.714206 | + | 0.699936i | \(0.246788\pi\) | ||||
−0.714206 | + | 0.699936i | \(0.753212\pi\) | |||||||
\(632\) | −221401. | − | 621449.i | −0.554301 | − | 1.55586i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −162429. | + | 374213.i | −0.404098 | + | 0.930979i | ||||
\(635\) | 223643.i | 0.554635i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 216831. | 0.534370 | ||||||||
\(638\) | 522023. | + | 226588.i | 1.28247 | + | 0.556667i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −131048. | − | 464508.i | −0.319942 | − | 1.13405i | ||||
\(641\) | 101106. | 0.246071 | 0.123036 | − | 0.992402i | \(-0.460737\pi\) | ||||
0.123036 | + | 0.992402i | \(0.460737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 406950.i | − | 0.984281i | −0.870516 | − | 0.492141i | \(-0.836215\pi\) | ||
0.870516 | − | 0.492141i | \(-0.163785\pi\) | |||||||
\(644\) | 61755.1 | + | 66055.6i | 0.148902 | + | 0.159271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 614126. | + | 266565.i | 1.47161 | + | 0.638761i | ||||
\(647\) | − | 427706.i | − | 1.02173i | −0.859660 | − | 0.510866i | \(-0.829325\pi\) | ||
0.859660 | − | 0.510866i | \(-0.170675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 332601. | 0.789648 | ||||||||
\(650\) | 63613.3 | − | 146555.i | 0.150564 | − | 0.346876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 456588. | − | 426862.i | 1.07406 | − | 1.00414i | ||||
\(653\) | 430055. | 1.00855 | 0.504275 | − | 0.863543i | \(-0.331760\pi\) | ||||
0.504275 | + | 0.863543i | \(0.331760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 98227.4i | 0.228955i | ||||||||
\(656\) | −26783.1 | + | 397542.i | −0.0622377 | + | 0.923793i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 67725.4 | − | 156029.i | 0.156423 | − | 0.360374i | ||||
\(659\) | 179686.i | 0.413755i | 0.978367 | + | 0.206878i | \(0.0663302\pi\) | ||||
−0.978367 | + | 0.206878i | \(0.933670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −539348. | −1.23443 | −0.617214 | − | 0.786795i | \(-0.711739\pi\) | ||||
−0.617214 | + | 0.786795i | \(0.711739\pi\) | |||||||
\(662\) | −145588. | − | 63193.4i | −0.332208 | − | 0.144197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −264660. | − | 742872.i | −0.600279 | − | 1.68492i | ||||
\(665\) | −426148. | −0.963645 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 178809.i | 0.401918i | ||||||||
\(668\) | −36502.7 | + | 34126.2i | −0.0818036 | + | 0.0764777i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −254290. | − | 110376.i | −0.566473 | − | 0.245881i | ||||
\(671\) | − | 524693.i | − | 1.16536i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −758520. | −1.67470 | −0.837350 | − | 0.546667i | \(-0.815896\pi\) | ||||
−0.837350 | + | 0.546667i | \(0.815896\pi\) | |||||||
\(674\) | −205970. | + | 474523.i | −0.453403 | + | 1.04457i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16319.5 | + | 17456.0i | 0.0357120 | + | 0.0381989i | ||||
\(677\) | −394155. | −0.859982 | −0.429991 | − | 0.902833i | \(-0.641483\pi\) | ||||
−0.429991 | + | 0.902833i | \(0.641483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 268542.i | 0.582468i | ||||||||
\(680\) | 676211. | − | 240911.i | 1.46239 | − | 0.521002i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 257047. | − | 592197.i | 0.552642 | − | 1.27320i | ||||
\(683\) | − | 483705.i | − | 1.03691i | −0.855106 | − | 0.518453i | \(-0.826508\pi\) | ||
0.855106 | − | 0.518453i | \(-0.173492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −348303. | −0.742294 | ||||||||
\(686\) | −449079. | − | 194926.i | −0.954277 | − | 0.414210i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 566528. | + | 38168.1i | 1.19686 | + | 0.0806349i | ||||
\(689\) | 166989. | 0.351763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 136607.i | 0.286098i | 0.989716 | + | 0.143049i | \(0.0456907\pi\) | ||||
−0.989716 | + | 0.143049i | \(0.954309\pi\) | |||||||
\(692\) | −554533. | − | 593150.i | −1.15802 | − | 1.23866i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 640219. | + | 277891.i | 1.32926 | + | 0.576974i | ||||
\(695\) | 163325.i | 0.338130i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −592615. | −1.21985 | ||||||||
\(698\) | −62784.9 | + | 144647.i | −0.128868 | + | 0.296892i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −93380.6 | + | 87301.1i | −0.190573 | + | 0.178165i | ||||
\(701\) | 878847. | 1.78845 | 0.894226 | − | 0.447617i | \(-0.147727\pi\) | ||||
0.894226 | + | 0.447617i | \(0.147727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.18720e6i | − | 2.40222i | ||||||
\(704\) | −353871. | − | 433602.i | −0.714002 | − | 0.874875i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −196026. | + | 451613.i | −0.393282 | + | 0.906061i | ||||
\(707\) | − | 376502.i | − | 0.753231i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 445304. | 0.885857 | 0.442929 | − | 0.896557i | \(-0.353939\pi\) | ||||
0.442929 | + | 0.896557i | \(0.353939\pi\) | |||||||
\(710\) | −95557.4 | − | 41477.3i | −0.189560 | − | 0.0822800i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 346723. | − | 123526.i | 0.683948 | − | 0.243668i | ||||
\(713\) | 202846. | 0.399012 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 662220.i | − | 1.29536i | ||||||
\(716\) | 52088.4 | − | 48697.2i | 0.101605 | − | 0.0949900i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 76933.2 | + | 33393.4i | 0.149233 | + | 0.0647756i | ||||
\(719\) | − | 731078.i | − | 1.41418i | −0.707121 | − | 0.707092i | \(-0.750007\pi\) | ||
0.707121 | − | 0.707092i | \(-0.249993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 385836. | 0.742219 | ||||||||
\(722\) | −100186. | + | 230813.i | −0.192191 | + | 0.442778i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 92470.3 | + | 98909.8i | 0.176411 | + | 0.188696i | ||||
\(725\) | −252776. | −0.480906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 992100.i | 1.87710i | 0.345147 | + | 0.938549i | \(0.387829\pi\) | ||||
−0.345147 | + | 0.938549i | \(0.612171\pi\) | |||||||
\(728\) | 116294. | + | 326423.i | 0.219429 | + | 0.615912i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 324731. | − | 748131.i | 0.609366 | − | 1.40389i | ||||
\(731\) | 844524.i | 1.58044i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −121286. | −0.225737 | −0.112868 | − | 0.993610i | \(-0.536004\pi\) | ||||
−0.112868 | + | 0.993610i | \(0.536004\pi\) | |||||||
\(734\) | 213920. | + | 92853.6i | 0.397064 | + | 0.172348i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 80704.2 | − | 156242.i | 0.148984 | − | 0.288431i | ||||
\(737\) | −321457. | −0.591818 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 273800.i | 0.501355i | 0.968071 | + | 0.250677i | \(0.0806534\pi\) | ||||
−0.968071 | + | 0.250677i | \(0.919347\pi\) | |||||||
\(740\) | −869338. | − | 929878.i | −1.58754 | − | 1.69810i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −122565. | − | 53200.3i | −0.222618 | − | 0.0966287i | ||||
\(743\) | 389402.i | 0.705376i | 0.935741 | + | 0.352688i | \(0.114732\pi\) | ||||
−0.935741 | + | 0.352688i | \(0.885268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −326207. | −0.587733 | ||||||||
\(746\) | −127055. | + | 292716.i | −0.228305 | + | 0.525979i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 608071. | − | 568483.i | 1.08680 | − | 1.01605i | ||||
\(749\) | −698489. | −1.24508 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 430569.i | 0.763419i | 0.924282 | + | 0.381710i | \(0.124665\pi\) | ||||
−0.924282 | + | 0.381710i | \(0.875335\pi\) | |||||||
\(752\) | −330034. | − | 22235.0i | −0.583611 | − | 0.0393189i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −272825. | + | 628548.i | −0.479891 | + | 1.10559i | ||||
\(755\) | − | 808633.i | − | 1.41859i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.04226e6 | −1.81880 | −0.909401 | − | 0.415920i | \(-0.863460\pi\) | ||||
−0.909401 | + | 0.415920i | \(0.863460\pi\) | |||||||
\(758\) | −296762. | − | 128812.i | −0.516500 | − | 0.224190i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 278127. | + | 780670.i | 0.481521 | + | 1.35158i | ||||
\(761\) | −117139. | −0.202271 | −0.101135 | − | 0.994873i | \(-0.532248\pi\) | ||||
−0.101135 | + | 0.994873i | \(0.532248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 189318.i | 0.325195i | ||||||||
\(764\) | 206865. | − | 193397.i | 0.354405 | − | 0.331331i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −366264. | − | 158979.i | −0.624219 | − | 0.270946i | ||||
\(767\) | 400471.i | 0.680739i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −104458. | −0.176639 | −0.0883197 | − | 0.996092i | \(-0.528150\pi\) | ||||
−0.0883197 | + | 0.996092i | \(0.528150\pi\) | |||||||
\(770\) | −210973. | + | 486050.i | −0.355833 | + | 0.819785i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −119589. | − | 127917.i | −0.200658 | − | 0.214631i | ||||
\(773\) | 34677.2 | 0.0580343 | 0.0290172 | − | 0.999579i | \(-0.490762\pi\) | ||||
0.0290172 | + | 0.999579i | \(0.490762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 286756.i | 0.477429i | ||||||||
\(776\) | 491948. | − | 175264.i | 0.816950 | − | 0.291052i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24818.7 | − | 57178.4i | 0.0410034 | − | 0.0944654i | ||||
\(779\) | − | 684161.i | − | 1.12741i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −120798. | −0.198042 | ||||||||
\(782\) | 239926. | + | 104142.i | 0.392341 | + | 0.170298i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22679.4 | + | 336631.i | −0.0368978 | + | 0.547674i | ||||
\(785\) | 430280. | 0.698252 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.08172e6i | 1.74649i | 0.487285 | + | 0.873243i | \(0.337987\pi\) | ||||
−0.487285 | + | 0.873243i | \(0.662013\pi\) | |||||||
\(788\) | −110376. | − | 118062.i | −0.177755 | − | 0.190133i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.11418e6 | + | 483615.i | 1.78525 | + | 0.774900i | ||||
\(791\) | 198074.i | 0.316573i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 631762. | 1.00463 | ||||||||
\(794\) | −107117. | + | 246781.i | −0.169910 | + | 0.391446i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −366935. | + | 343046.i | −0.579112 | + | 0.541409i | ||||
\(797\) | −370822. | −0.583779 | −0.291889 | − | 0.956452i | \(-0.594284\pi\) | ||||
−0.291889 | + | 0.956452i | \(0.594284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 491982.i | − | 0.770648i | ||||||
\(800\) | 220874. | + | 114089.i | 0.345116 | + | 0.178264i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 241834. | − | 557149.i | 0.375983 | − | 0.866208i | ||||
\(803\) | − | 945741.i | − | 1.46670i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −166487. | −0.256915 | ||||||||
\(806\) | 713041. | + | 309500.i | 1.09760 | + | 0.476421i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −689722. | + | 245725.i | −1.05646 | + | 0.376380i | ||||
\(809\) | −763253. | −1.16620 | −0.583098 | − | 0.812402i | \(-0.698160\pi\) | ||||
−0.583098 | + | 0.812402i | \(0.698160\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 976424.i | − | 1.48456i | −0.670091 | − | 0.742279i | \(-0.733745\pi\) | ||
0.670091 | − | 0.742279i | \(-0.266255\pi\) | |||||||
\(812\) | 400492. | − | 374418.i | 0.607410 | − | 0.567864i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.35408e6 | − | 587747.i | −2.04360 | − | 0.887037i | ||||
\(815\) | 1.15079e6i | 1.73253i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −974984. | −1.46067 | ||||||||
\(818\) | −102202. | + | 235459.i | −0.152741 | + | 0.351891i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −500984. | − | 535872.i | −0.745068 | − | 0.796954i | ||||
\(821\) | 1.05933e6 | 1.57162 | 0.785808 | − | 0.618470i | \(-0.212247\pi\) | ||||
0.785808 | + | 0.618470i | \(0.212247\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 649256.i | 0.958553i | 0.877664 | + | 0.479277i | \(0.159101\pi\) | ||||
−0.877664 | + | 0.479277i | \(0.840899\pi\) | |||||||
\(824\) | −251817. | − | 706821.i | −0.370877 | − | 1.04101i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 127584. | − | 293934.i | 0.186998 | − | 0.430815i | ||||
\(827\) | 1.23981e6i | 1.81278i | 0.422439 | + | 0.906391i | \(0.361174\pi\) | ||||
−0.422439 | + | 0.906391i | \(0.638826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 656712. | 0.955577 | 0.477788 | − | 0.878475i | \(-0.341439\pi\) | ||||
0.477788 | + | 0.878475i | \(0.341439\pi\) | |||||||
\(830\) | 1.33187e6 | + | 578108.i | 1.93333 | + | 0.839175i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 522083. | − | 426082.i | 0.754211 | − | 0.615526i | ||||
\(833\) | −501816. | −0.723194 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 92001.8i | − | 0.131954i | ||||||
\(836\) | 656300. | + | 702004.i | 0.939053 | + | 1.00445i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 312517. | + | 135650.i | 0.445027 | + | 0.193167i | ||||
\(839\) | 895246.i | 1.27180i | 0.771772 | + | 0.635899i | \(0.219371\pi\) | ||||
−0.771772 | + | 0.635899i | \(0.780629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 376830. | 0.532787 | ||||||||
\(842\) | 342257. | − | 788507.i | 0.482756 | − | 1.11220i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −974314. | + | 910881.i | −1.36777 | + | 1.27872i | ||||
\(845\) | −43996.2 | −0.0616172 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 132603.i | 0.184836i | ||||||||
\(848\) | −17466.2 | + | 259251.i | −0.0242889 | + | 0.360520i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −147221. | + | 339176.i | −0.203767 | + | 0.469447i | ||||
\(851\) | − | 463814.i | − | 0.640449i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.15283e6 | 1.58441 | 0.792206 | − | 0.610254i | \(-0.208933\pi\) | ||||
0.792206 | + | 0.610254i | \(0.208933\pi\) | |||||||
\(854\) | −463695. | − | 201270.i | −0.635794 | − | 0.275971i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 455871. | + | 1.27958e6i | 0.622149 | + | 1.74630i | ||||
\(857\) | 576402. | 0.784809 | 0.392404 | − | 0.919793i | \(-0.371643\pi\) | ||||
0.392404 | + | 0.919793i | \(0.371643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 365493.i | − | 0.495327i | −0.968846 | − | 0.247664i | \(-0.920337\pi\) | ||
0.968846 | − | 0.247664i | \(-0.0796628\pi\) | |||||||
\(860\) | −763660. | + | 713942.i | −1.03253 | + | 0.965308i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −72966.3 | − | 31671.5i | −0.0981992 | − | 0.0426240i | ||||
\(863\) | 233229.i | 0.313156i | 0.987666 | + | 0.156578i | \(0.0500463\pi\) | ||||
−0.987666 | + | 0.156578i | \(0.949954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.49498e6 | 1.99804 | ||||||||
\(866\) | 165631. | − | 381588.i | 0.220854 | − | 0.508814i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −424749. | − | 454328.i | −0.563759 | − | 0.603018i | ||||
\(869\) | 1.40847e6 | 1.86513 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 387054.i | − | 0.510194i | ||||||
\(872\) | 346816. | − | 123559.i | 0.456107 | − | 0.162496i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −120229. | + | 276989.i | −0.157393 | + | 0.362610i | ||||
\(875\) | 370553.i | 0.483987i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −939899. | −1.22203 | −0.611015 | − | 0.791619i | \(-0.709238\pi\) | ||||
−0.611015 | + | 0.791619i | \(0.709238\pi\) | |||||||
\(878\) | −205318. | − | 89119.8i | −0.266341 | − | 0.115607i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.02810e6 | + | 69264.9i | 1.32761 | + | 0.0894434i | ||||
\(881\) | 918880. | 1.18388 | 0.591939 | − | 0.805983i | \(-0.298363\pi\) | ||||
0.591939 | + | 0.805983i | \(0.298363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 842123.i | − | 1.08008i | −0.841641 | − | 0.540038i | \(-0.818410\pi\) | ||
0.841641 | − | 0.540038i | \(-0.181590\pi\) | |||||||
\(884\) | 684488. | + | 732155.i | 0.875913 | + | 0.936911i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −82952.3 | − | 36006.0i | −0.105672 | − | 0.0458677i | ||||
\(887\) | − | 255495.i | − | 0.324740i | −0.986730 | − | 0.162370i | \(-0.948086\pi\) | ||
0.986730 | − | 0.162370i | \(-0.0519138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 249849. | 0.316136 | ||||||||
\(890\) | −269822. | + | 621629.i | −0.340642 | + | 0.784786i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −155464. | + | 145342.i | −0.195389 | + | 0.182668i | ||||
\(893\) | 567982. | 0.712249 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 131284.i | 0.163895i | ||||||||
\(896\) | −518937. | + | 146404.i | −0.646396 | + | 0.182363i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 123555. | − | 284651.i | 0.153217 | − | 0.352989i | ||||
\(899\) | − | 1.22984e6i | − | 1.52170i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −386466. | −0.476060 | ||||||||
\(902\) | −780331. | − | 338708.i | −0.959105 | − | 0.416306i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 362855. | − | 129273.i | 0.444014 | − | 0.158187i | ||||
\(905\) | −249293. | −0.304378 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.42137e6i | − | 1.72780i | −0.503663 | − | 0.863900i | \(-0.668014\pi\) | ||
0.503663 | − | 0.863900i | \(-0.331986\pi\) | |||||||
\(908\) | 585271. | − | 547167.i | 0.709880 | − | 0.663664i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −585234. | − | 254025.i | −0.706719 | − | 0.306756i | ||||
\(911\) | − | 42728.5i | − | 0.0514851i | −0.999669 | − | 0.0257425i | \(-0.991805\pi\) | ||
0.999669 | − | 0.0257425i | \(-0.00819501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.68367e6 | 2.01983 | ||||||||
\(914\) | −386794. | + | 891115.i | −0.463007 | + | 1.06670i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −656045. | − | 701731.i | −0.781885 | − | 0.836334i | ||||
\(917\) | 109737. | 0.130502 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 32211.9i | − | 0.0381404i | −0.999818 | − | 0.0190702i | \(-0.993929\pi\) | ||
0.999818 | − | 0.0190702i | \(-0.00607060\pi\) | |||||||
\(920\) | 108658. | + | 304992.i | 0.128377 | + | 0.360340i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −317960. | + | 732531.i | −0.374034 | + | 0.861716i | ||||
\(923\) | − | 145448.i | − | 0.170728i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 655678. | 0.766315 | ||||||||
\(926\) | −232964. | − | 101120.i | −0.271686 | − | 0.117927i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −947287. | − | 489306.i | −1.09998 | − | 0.568178i | ||||
\(929\) | −1.39589e6 | −1.61741 | −0.808706 | − | 0.588214i | \(-0.799831\pi\) | ||||
−0.808706 | + | 0.588214i | \(0.799831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 579335.i | − | 0.668391i | ||||||
\(932\) | 341485. | + | 365266.i | 0.393134 | + | 0.420511i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −414558. | − | 179942.i | −0.475217 | − | 0.206271i | ||||
\(935\) | 1.53259e6i | 1.75308i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −525528. | −0.598572 | −0.299286 | − | 0.954163i | \(-0.596749\pi\) | ||||
−0.299286 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(938\) | −123310. | + | 284087.i | −0.140149 | + | 0.322883i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 444874. | − | 415911.i | 0.503479 | − | 0.470700i | ||||
\(941\) | −1.40325e6 | −1.58473 | −0.792364 | − | 0.610048i | \(-0.791150\pi\) | ||||
−0.792364 | + | 0.610048i | \(0.791150\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 267287.i | − | 0.300577i | ||||||
\(944\) | −621733. | − | 41887.3i | −0.697686 | − | 0.0470044i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −482686. | + | 1.11203e6i | −0.539365 | + | 1.24261i | ||||
\(947\) | − | 1.40028e6i | − | 1.56140i | −0.624905 | − | 0.780701i | \(-0.714862\pi\) | ||
0.624905 | − | 0.780701i | \(-0.285138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.13873e6 | 1.26441 | ||||||||
\(950\) | −391570. | − | 169964.i | −0.433873 | − | 0.188325i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −269141. | − | 755448.i | −0.296965 | − | 0.833548i | ||||
\(953\) | 537716. | 0.592062 | 0.296031 | − | 0.955178i | \(-0.404337\pi\) | ||||
0.296031 | + | 0.955178i | \(0.404337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 521384.i | 0.571677i | ||||||||
\(956\) | −734963. | + | 687113.i | −0.804174 | + | 0.751818i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.15008e6 | − | 499200.i | −1.25313 | − | 0.543931i | ||||
\(959\) | 389116.i | 0.423099i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −471644. | −0.510701 | ||||||||
\(962\) | 707683. | − | 1.63039e6i | 0.764696 | − | 1.76174i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −706016. | − | 755182.i | −0.759732 | − | 0.812639i | ||||
\(965\) | 322403. | 0.346213 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 153678.i | − | 0.164346i | −0.996618 | − | 0.0821732i | \(-0.973814\pi\) | ||
0.996618 | − | 0.0821732i | \(-0.0261861\pi\) | |||||||
\(968\) | 242918. | − | 86543.6i | 0.259244 | − | 0.0923601i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −382837. | + | 881997.i | −0.406884 | + | 0.937397i | ||||
\(971\) | − | 36471.1i | − | 0.0386821i | −0.999813 | − | 0.0193411i | \(-0.993843\pi\) | ||
0.999813 | − | 0.0193411i | \(-0.00615683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 182463. | 0.192730 | ||||||||
\(974\) | 238320. | + | 103444.i | 0.251214 | + | 0.109041i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −66079.2 | + | 980813.i | −0.0693689 | + | 1.02964i | ||||
\(977\) | 1.18898e6 | 1.24562 | 0.622811 | − | 0.782373i | \(-0.285991\pi\) | ||||
0.622811 | + | 0.782373i | \(0.285991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 785825.i | 0.819900i | ||||||||
\(980\) | −424224. | − | 453766.i | −0.441716 | − | 0.472476i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.31574e6 | + | 571106.i | 1.36442 | + | 0.592235i | ||||
\(983\) | 890220.i | 0.921277i | 0.887588 | + | 0.460639i | \(0.152380\pi\) | ||||
−0.887588 | + | 0.460639i | \(0.847620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 297565. | 0.306697 | ||||||||
\(986\) | 631405. | − | 1.45466e6i | 0.649463 | − | 1.49626i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −845256. | + | 790225.i | −0.865913 | + | 0.809538i | ||||
\(989\) | −380906. | −0.389426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 844659.i | 0.860070i | 0.902812 | + | 0.430035i | \(0.141499\pi\) | ||||
−0.902812 | + | 0.430035i | \(0.858501\pi\) | |||||||
\(992\) | −555081. | + | 1.07463e6i | −0.564070 | + | 1.09203i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −46337.5 | + | 106755.i | −0.0468986 | + | 0.108047i | ||||
\(995\) | − | 924826.i | − | 0.934144i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.30909e6 | 1.31698 | 0.658492 | − | 0.752587i | \(-0.271194\pi\) | ||||
0.658492 | + | 0.752587i | \(0.271194\pi\) | |||||||
\(998\) | 46586.0 | + | 20221.0i | 0.0467729 | + | 0.0203021i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.d.a.55.11 | yes | 16 | |
3.2 | odd | 2 | inner | 108.5.d.a.55.6 | yes | 16 | |
4.3 | odd | 2 | inner | 108.5.d.a.55.12 | yes | 16 | |
12.11 | even | 2 | inner | 108.5.d.a.55.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.a.55.5 | ✓ | 16 | 12.11 | even | 2 | inner | |
108.5.d.a.55.6 | yes | 16 | 3.2 | odd | 2 | inner | |
108.5.d.a.55.11 | yes | 16 | 1.1 | even | 1 | trivial | |
108.5.d.a.55.12 | yes | 16 | 4.3 | odd | 2 | inner |