Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.336831 + 2.80830i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.31 |
Dual form | 128.5.f.a.95.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −7.86839 | − | 7.86839i | −0.874266 | − | 0.874266i | 0.118668 | − | 0.992934i | \(-0.462138\pi\) |
−0.992934 | + | 0.118668i | \(0.962138\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −27.2309 | − | 27.2309i | −1.08924 | − | 1.08924i | −0.995607 | − | 0.0936308i | \(-0.970153\pi\) |
−0.0936308 | − | 0.995607i | \(-0.529847\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −50.3097 | −1.02673 | −0.513365 | − | 0.858171i | \(-0.671601\pi\) | ||||
−0.513365 | + | 0.858171i | \(0.671601\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 42.8233i | 0.528682i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −53.1047 | + | 53.1047i | −0.438881 | + | 0.438881i | −0.891635 | − | 0.452754i | \(-0.850442\pi\) |
0.452754 | + | 0.891635i | \(0.350442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 125.128 | − | 125.128i | 0.740404 | − | 0.740404i | −0.232252 | − | 0.972656i | \(-0.574609\pi\) |
0.972656 | + | 0.232252i | \(0.0746094\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 428.528i | 1.90457i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 286.271 | 0.990557 | 0.495279 | − | 0.868734i | \(-0.335066\pi\) | ||||
0.495279 | + | 0.868734i | \(0.335066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −99.5010 | − | 99.5010i | −0.275626 | − | 0.275626i | 0.555734 | − | 0.831360i | \(-0.312437\pi\) |
−0.831360 | + | 0.555734i | \(0.812437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 395.857 | + | 395.857i | 0.897635 | + | 0.897635i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 100.505 | 0.189991 | 0.0949957 | − | 0.995478i | \(-0.469716\pi\) | ||||
0.0949957 | + | 0.995478i | \(0.469716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 858.049i | 1.37288i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −300.390 | + | 300.390i | −0.412057 | + | 0.412057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −343.872 | + | 343.872i | −0.408885 | + | 0.408885i | −0.881350 | − | 0.472465i | \(-0.843364\pi\) |
0.472465 | + | 0.881350i | \(0.343364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 208.400i | − | 0.216858i | −0.994104 | − | 0.108429i | \(-0.965418\pi\) | ||
0.994104 | − | 0.108429i | \(-0.0345820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 835.697 | 0.767398 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1369.98 | + | 1369.98i | 1.11835 | + | 1.11835i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1159.47 | + | 1159.47i | 0.846946 | + | 0.846946i | 0.989751 | − | 0.142805i | \(-0.0456122\pi\) |
−0.142805 | + | 0.989751i | \(0.545612\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1969.12 | −1.29462 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2335.63i | − | 1.38943i | −0.719286 | − | 0.694714i | \(-0.755531\pi\) | ||
0.719286 | − | 0.694714i | \(-0.244469\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2079.41 | + | 2079.41i | −1.12461 | + | 1.12461i | −0.133575 | + | 0.991039i | \(0.542646\pi\) |
−0.991039 | + | 0.133575i | \(0.957354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1166.12 | − | 1166.12i | 0.575861 | − | 0.575861i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1054.04i | 0.477159i | 0.971123 | + | 0.238580i | \(0.0766818\pi\) | ||||
−0.971123 | + | 0.238580i | \(0.923318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 130.069 | 0.0541728 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2252.49 | − | 2252.49i | −0.866011 | − | 0.866011i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2136.46 | − | 2136.46i | −0.760576 | − | 0.760576i | 0.215850 | − | 0.976426i | \(-0.430748\pi\) |
−0.976426 | + | 0.215850i | \(0.930748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2892.18 | 0.956092 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1565.83i | 0.481941i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3721.44 | − | 3721.44i | 1.06907 | − | 1.06907i | 0.0716407 | − | 0.997431i | \(-0.477177\pi\) |
0.997431 | − | 0.0716407i | \(-0.0228235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2496.46 | + | 2496.46i | −0.670912 | + | 0.670912i | −0.957926 | − | 0.287014i | \(-0.907337\pi\) |
0.287014 | + | 0.957926i | \(0.407337\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2154.43i | − | 0.542814i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6814.72 | −1.61295 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −329.116 | − | 329.116i | −0.0733162 | − | 0.0733162i | 0.669498 | − | 0.742814i | \(-0.266509\pi\) |
−0.742814 | + | 0.669498i | \(0.766509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −790.817 | − | 790.817i | −0.166103 | − | 0.166103i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1040.71 | 0.206449 | 0.103225 | − | 0.994658i | \(-0.467084\pi\) | ||||
0.103225 | + | 0.994658i | \(0.467084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2673.24i | 0.501639i | 0.968034 | + | 0.250820i | \(0.0807001\pi\) | ||||
−0.968034 | + | 0.250820i | \(0.919300\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6751.46 | − | 6751.46i | 1.20026 | − | 1.20026i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2671.68 | − | 2671.68i | 0.450612 | − | 0.450612i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4475.80i | − | 0.717161i | −0.933499 | − | 0.358580i | \(-0.883261\pi\) | ||
0.933499 | − | 0.358580i | \(-0.116739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8195.85 | 1.24918 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1457.69 | + | 1457.69i | 0.211597 | + | 0.211597i | 0.804945 | − | 0.593349i | \(-0.202195\pi\) |
−0.593349 | + | 0.804945i | \(0.702195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7795.43 | − | 7795.43i | −1.07895 | − | 1.07895i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5411.44 | 0.714948 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1146.97i | − | 0.144801i | −0.997376 | − | 0.0724003i | \(-0.976934\pi\) | ||
0.997376 | − | 0.0724003i | \(-0.0230659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6295.17 | + | 6295.17i | −0.760194 | + | 0.760194i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1639.78 | + | 1639.78i | −0.189592 | + | 0.189592i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5419.01i | 0.600444i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13101.5 | −1.39244 | −0.696222 | − | 0.717826i | \(-0.745137\pi\) | ||||
−0.696222 | + | 0.717826i | \(0.745137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2274.11 | − | 2274.11i | −0.232029 | − | 0.232029i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7488.18 | + | 7488.18i | 0.734063 | + | 0.734063i | 0.971422 | − | 0.237359i | \(-0.0762818\pi\) |
−0.237359 | + | 0.971422i | \(0.576282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7141.23 | −0.673129 | −0.336565 | − | 0.941660i | \(-0.609265\pi\) | ||||
−0.336565 | + | 0.941660i | \(0.609265\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 21559.1i | − | 1.95547i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1794.26 | − | 1794.26i | 0.156718 | − | 0.156718i | −0.624393 | − | 0.781111i | \(-0.714654\pi\) |
0.781111 | + | 0.624393i | \(0.214654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5362.57 | + | 5362.57i | −0.451357 | + | 0.451357i | −0.895805 | − | 0.444448i | \(-0.853400\pi\) |
0.444448 | + | 0.895805i | \(0.353400\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 18246.3i | − | 1.48091i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5165.40 | −0.404527 | −0.202263 | − | 0.979331i | \(-0.564830\pi\) | ||||
−0.202263 | + | 0.979331i | \(0.564830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2736.86 | − | 2736.86i | −0.206946 | − | 0.206946i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5358.40 | + | 5358.40i | 0.391438 | + | 0.391438i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14402.2 | −1.01703 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9000.79i | 0.614766i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18377.6 | + | 18377.6i | −1.21473 | + | 1.21473i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6346.13 | − | 6346.13i | 0.406152 | − | 0.406152i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22886.9i | 1.41899i | 0.704711 | + | 0.709495i | \(0.251077\pi\) | ||||
−0.704711 | + | 0.709495i | \(0.748923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32723.3 | 1.96642 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19202.2 | + | 19202.2i | 1.11894 | + | 1.11894i | 0.991897 | + | 0.127048i | \(0.0405502\pi\) |
0.127048 | + | 0.991897i | \(0.459450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5005.87 | + | 5005.87i | 0.282993 | + | 0.282993i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16359.8 | 0.897656 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 33680.5i | 1.79448i | 0.441547 | + | 0.897238i | \(0.354430\pi\) | ||||
−0.441547 | + | 0.897238i | \(0.645570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11747.9 | − | 11747.9i | 0.608036 | − | 0.608036i | −0.334397 | − | 0.942432i | \(-0.608532\pi\) |
0.942432 | + | 0.334397i | \(0.108532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8293.64 | − | 8293.64i | 0.417164 | − | 0.417164i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13289.8i | 0.649899i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18727.9 | 0.890746 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1023.43 | − | 1023.43i | −0.0473615 | − | 0.0473615i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14877.7 | + | 14877.7i | 0.670136 | + | 0.670136i | 0.957747 | − | 0.287611i | \(-0.0928611\pi\) |
−0.287611 | + | 0.957747i | \(0.592861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8005.74 | 0.351114 | 0.175557 | − | 0.984469i | \(-0.443827\pi\) | ||||
0.175557 | + | 0.984469i | \(0.443827\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12259.1i | 0.523690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5674.94 | + | 5674.94i | −0.236210 | + | 0.236210i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12150.9 | + | 12150.9i | −0.492958 | + | 0.492958i | −0.909237 | − | 0.416279i | \(-0.863334\pi\) |
0.416279 | + | 0.909237i | \(0.363334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 33621.0i | 1.32989i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5056.40 | −0.195070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23646.5 | − | 23646.5i | −0.890002 | − | 0.890002i | 0.104520 | − | 0.994523i | \(-0.466669\pi\) |
−0.994523 | + | 0.104520i | \(0.966669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22756.8 | − | 22756.8i | −0.835879 | − | 0.835879i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −42493.7 | −1.52367 | −0.761836 | − | 0.647770i | \(-0.775702\pi\) | ||||
−0.761836 | + | 0.647770i | \(0.775702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2753.14i | − | 0.0963950i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4260.96 | − | 4260.96i | 0.145719 | − | 0.145719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16142.1 | − | 16142.1i | 0.539347 | − | 0.539347i | −0.383990 | − | 0.923337i | \(-0.625450\pi\) |
0.923337 | + | 0.383990i | \(0.125450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 43168.2i | − | 1.40957i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −58563.5 | −1.86931 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22442.0 | − | 22442.0i | −0.700415 | − | 0.700415i | 0.264084 | − | 0.964500i | \(-0.414930\pi\) |
−0.964500 | + | 0.264084i | \(0.914930\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9891.06 | + | 9891.06i | 0.301916 | + | 0.301916i | 0.841763 | − | 0.539847i | \(-0.181518\pi\) |
−0.539847 | + | 0.841763i | \(0.681518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 39286.3 | 1.17311 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 63146.9i | − | 1.84505i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15202.3 | + | 15202.3i | −0.434737 | + | 0.434737i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15112.5 | − | 15112.5i | 0.423071 | − | 0.423071i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2033.60i | − | 0.0557442i | −0.999611 | − | 0.0278721i | \(-0.991127\pi\) | ||
0.999611 | − | 0.0278721i | \(-0.00887311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 29257.4 | 0.785453 | 0.392727 | − | 0.919655i | \(-0.371532\pi\) | ||||
0.392727 | + | 0.919655i | \(0.371532\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 53620.9 | + | 53620.9i | 1.41015 | + | 1.41015i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −28194.9 | − | 28194.9i | −0.726504 | − | 0.726504i | 0.243417 | − | 0.969922i | \(-0.421732\pi\) |
−0.969922 | + | 0.243417i | \(0.921732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −54100.9 | −1.36615 | −0.683075 | − | 0.730348i | \(-0.739358\pi\) | ||||
−0.683075 | + | 0.730348i | \(0.739358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5179.24i | 0.128196i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17300.1 | − | 17300.1i | 0.419814 | − | 0.419814i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −63601.4 | + | 63601.4i | −1.51342 | + | 1.51342i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4303.97i | 0.100445i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10567.9 | 0.241934 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −31994.1 | − | 31994.1i | −0.718630 | − | 0.718630i | 0.249694 | − | 0.968325i | \(-0.419670\pi\) |
−0.968325 | + | 0.249694i | \(0.919670\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8188.73 | − | 8188.73i | −0.180492 | − | 0.180492i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 113249. | 2.44994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10484.6i | 0.222654i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21034.1 | − | 21034.1i | 0.438566 | − | 0.438566i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35820.6 | − | 35820.6i | 0.733412 | − | 0.733412i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 94185.8i | − | 1.89398i | −0.321261 | − | 0.946991i | \(-0.604107\pi\) | ||
0.321261 | − | 0.946991i | \(-0.395893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −36744.4 | −0.725816 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 62683.9 | + | 62683.9i | 1.21648 | + | 1.21648i | 0.968857 | + | 0.247622i | \(0.0796490\pi\) |
0.247622 | + | 0.968857i | \(0.420351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19781.9 | + | 19781.9i | 0.377221 | + | 0.377221i | 0.870099 | − | 0.492877i | \(-0.164055\pi\) |
−0.492877 | + | 0.870099i | \(0.664055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −42043.7 | −0.787910 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 25062.1i | − | 0.461642i | −0.972996 | − | 0.230821i | \(-0.925859\pi\) | ||
0.972996 | − | 0.230821i | \(-0.0741412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28702.6 | − | 28702.6i | 0.519740 | − | 0.519740i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35217.4 | + | 35217.4i | −0.626989 | + | 0.626989i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 93041.8i | − | 1.62885i | −0.580265 | − | 0.814427i | \(-0.697051\pi\) | ||
0.580265 | − | 0.814427i | \(-0.302949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −80981.9 | −1.39429 | −0.697146 | − | 0.716929i | \(-0.745547\pi\) | ||||
−0.697146 | + | 0.716929i | \(0.745547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −40156.6 | − | 40156.6i | −0.680056 | − | 0.680056i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3541.90 | − | 3541.90i | −0.0590071 | − | 0.0590071i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24900.8 | −0.408149 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 22939.3i | − | 0.369984i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25910.0 | − | 25910.0i | 0.411264 | − | 0.411264i | −0.470915 | − | 0.882179i | \(-0.656076\pi\) |
0.882179 | + | 0.470915i | \(0.156076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5337.31 | + | 5337.31i | −0.0833837 | + | 0.0833837i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 122675.i | 1.88658i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15800.6 | 0.239225 | 0.119613 | − | 0.992821i | \(-0.461835\pi\) | ||||
0.119613 | + | 0.992821i | \(0.461835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −58332.6 | − | 58332.6i | −0.869584 | − | 0.869584i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14725.7 | − | 14725.7i | −0.216170 | − | 0.216170i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 82043.7 | 1.18613 | 0.593067 | − | 0.805153i | \(-0.297917\pi\) | ||||
0.593067 | + | 0.805153i | \(0.297917\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 116356.i | 1.65690i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9024.78 | + | 9024.78i | −0.126594 | + | 0.126594i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30820.2 | − | 30820.2i | 0.425923 | − | 0.425923i | −0.461314 | − | 0.887237i | \(-0.652622\pi\) |
0.887237 | + | 0.461314i | \(0.152622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 110808.i | 1.50880i | 0.656412 | + | 0.754402i | \(0.272073\pi\) | ||||
−0.656412 | + | 0.754402i | \(0.727927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 99065.7 | 1.32922 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −45566.4 | − | 45566.4i | −0.602531 | − | 0.602531i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25634.0 | − | 25634.0i | −0.334084 | − | 0.334084i | 0.520051 | − | 0.854135i | \(-0.325913\pi\) |
−0.854135 | + | 0.520051i | \(0.825913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8924.39 | 0.114649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 48800.5i | − | 0.618033i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.0999999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −111466. | + | 111466.i | −1.39178 | + | 1.39178i | −0.570439 | + | 0.821340i | \(0.693227\pi\) |
−0.821340 | + | 0.570439i | \(0.806773\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 42638.9 | − | 42638.9i | 0.524948 | − | 0.524948i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 117505.i | 1.42657i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1569.88 | −0.0187963 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 103088. | + | 103088.i | 1.21737 | + | 1.21737i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13093.1 | − | 13093.1i | −0.152514 | − | 0.152514i | 0.626726 | − | 0.779240i | \(-0.284395\pi\) |
−0.779240 | + | 0.626726i | \(0.784395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −202676. | −2.32895 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 31904.2i | − | 0.361688i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12576.1 | − | 12576.1i | 0.140670 | − | 0.140670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 104615. | − | 104615.i | 1.15467 | − | 1.15467i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 117840.i | − | 1.28353i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 135962. | 1.46156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25274.9 | + | 25274.9i | 0.268171 | + | 0.268171i | 0.828363 | − | 0.560192i | \(-0.189273\pi\) |
−0.560192 | + | 0.828363i | \(0.689273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 56190.0 | + | 56190.0i | 0.588494 | + | 0.588494i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −53808.0 | −0.556322 | −0.278161 | − | 0.960534i | \(-0.589725\pi\) | ||||
−0.278161 | + | 0.960534i | \(0.589725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 137345.i | 1.40192i | 0.713199 | + | 0.700961i | \(0.247245\pi\) | ||||
−0.713199 | + | 0.700961i | \(0.752755\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −58667.1 | + | 58667.1i | −0.591253 | + | 0.591253i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −115546. | + | 115546.i | −1.14984 | + | 1.14984i | −0.163252 | + | 0.986584i | \(0.552198\pi\) |
−0.986584 | + | 0.163252i | \(0.947802\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36522.4i | − | 0.358904i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28235.9 | −0.274026 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28484.2 | − | 28484.2i | −0.273023 | − | 0.273023i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 107366. | + | 107366.i | 1.01648 | + | 1.01648i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 84389.7 | 0.789213 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 53028.7i | − | 0.489913i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 68009.3 | − | 68009.3i | 0.620744 | − | 0.620744i | −0.324978 | − | 0.945722i | \(-0.605357\pi\) |
0.945722 | + | 0.324978i | \(0.105357\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −49652.2 | + | 49652.2i | −0.447765 | + | 0.447765i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17924.3i | 0.159718i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −146703. | −1.29176 | −0.645878 | − | 0.763440i | \(-0.723509\pi\) | ||||
−0.645878 | + | 0.763440i | \(0.723509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 40643.4 | + | 40643.4i | 0.353664 | + | 0.353664i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11067.0 | + | 11067.0i | 0.0951749 | + | 0.0951749i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 114250. | 0.971108 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 43069.4i | 0.361851i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −80120.9 | + | 80120.9i | −0.665406 | + | 0.665406i | −0.956649 | − | 0.291243i | \(-0.905931\pi\) |
0.291243 | + | 0.956649i | \(0.405931\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −100990. | + | 100990.i | −0.829143 | + | 0.829143i | −0.987398 | − | 0.158255i | \(-0.949413\pi\) |
0.158255 | + | 0.987398i | \(0.449413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 75174.4i | 0.610177i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 129855. | 1.04210 | 0.521052 | − | 0.853525i | \(-0.325540\pi\) | ||||
0.521052 | + | 0.853525i | \(0.325540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28339.6 | − | 28339.6i | −0.224873 | − | 0.224873i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 113322. | + | 113322.i | 0.889158 | + | 0.889158i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 55943.2 | 0.434068 | 0.217034 | − | 0.976164i | \(-0.430362\pi\) | ||||
0.217034 | + | 0.976164i | \(0.430362\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 110520.i | − | 0.848061i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 70821.8 | − | 70821.8i | 0.537469 | − | 0.537469i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 72794.8 | − | 72794.8i | 0.546405 | − | 0.546405i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 144947.i | − | 1.07616i | −0.842892 | − | 0.538082i | \(-0.819149\pi\) | ||
0.842892 | − | 0.538082i | \(-0.180851\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 100019. | 0.734566 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 107485. | + | 107485.i | 0.780906 | + | 0.780906i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24034.7 | − | 24034.7i | −0.172751 | − | 0.172751i | 0.615436 | − | 0.788187i | \(-0.288980\pi\) |
−0.788187 | + | 0.615436i | \(0.788980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −99867.8 | −0.710171 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 86056.2i | 0.605480i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27907.2 | + | 27907.2i | −0.194284 | + | 0.194284i | −0.797544 | − | 0.603260i | \(-0.793868\pi\) |
0.603260 | + | 0.797544i | \(0.293868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 180083. | − | 180083.i | 1.24057 | − | 1.24057i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 96652.7i | 0.658895i | 0.944174 | + | 0.329448i | \(0.106863\pi\) | ||||
−0.944174 | + | 0.329448i | \(0.893137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −145505. | −0.981648 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −89047.2 | − | 89047.2i | −0.594564 | − | 0.594564i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −133129. | − | 133129.i | −0.879777 | − | 0.879777i | 0.113734 | − | 0.993511i | \(-0.463719\pi\) |
−0.993511 | + | 0.113734i | \(0.963719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28771.8 | 0.188197 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 302181.i | − | 1.95651i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −121880. | + | 121880.i | −0.781159 | + | 0.781159i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33406.1 | + | 33406.1i | −0.211956 | + | 0.211956i | −0.805098 | − | 0.593142i | \(-0.797887\pi\) |
0.593142 | + | 0.805098i | \(0.297887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 78776.3i | − | 0.494823i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −87329.7 | −0.543092 | −0.271546 | − | 0.962425i | \(-0.587535\pi\) | ||||
−0.271546 | + | 0.962425i | \(0.587535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26076.8 | − | 26076.8i | −0.160562 | − | 0.160562i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −223181. | − | 223181.i | −1.36065 | − | 1.36065i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −123146. | −0.743418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 47133.9i | 0.281765i | 0.990026 | + | 0.140883i | \(0.0449940\pi\) | ||||
−0.990026 | + | 0.140883i | \(0.955006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 265012. | − | 265012.i | 1.56885 | − | 1.56885i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −187224. | + | 187224.i | −1.09765 | + | 1.09765i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 79388.5i | − | 0.460958i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −184874. | −1.06317 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −70487.1 | − | 70487.1i | −0.401497 | − | 0.401497i | 0.477264 | − | 0.878760i | \(-0.341629\pi\) |
−0.878760 | + | 0.477264i | \(0.841629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −109929. | − | 109929.i | −0.620225 | − | 0.620225i | 0.325364 | − | 0.945589i | \(-0.394513\pi\) |
−0.945589 | + | 0.325364i | \(0.894513\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −45137.6 | −0.252266 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 245634.i | 1.35991i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 125596. | − | 125596.i | 0.688845 | − | 0.688845i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 104569. | − | 104569.i | 0.568184 | − | 0.568184i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8391.44i | 0.0451733i | 0.999745 | + | 0.0225867i | \(0.00719017\pi\) | ||||
−0.999745 | + | 0.0225867i | \(0.992810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 112221. | 0.598545 | 0.299272 | − | 0.954168i | \(-0.403256\pi\) | ||||
0.299272 | + | 0.954168i | \(0.403256\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −147359. | − | 147359.i | −0.778749 | − | 0.778749i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10000.4 | − | 10000.4i | −0.0523666 | − | 0.0523666i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 95834.1 | 0.497269 | 0.248634 | − | 0.968597i | \(-0.420018\pi\) | ||||
0.248634 | + | 0.968597i | \(0.420018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5569.98i | 0.0286402i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 48800.8 | − | 48800.8i | 0.248668 | − | 0.248668i | −0.571756 | − | 0.820424i | \(-0.693738\pi\) |
0.820424 | + | 0.571756i | \(0.193738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31233.0 | + | 31233.0i | −0.157722 | + | 0.157722i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 234127.i | − | 1.17175i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −246669. | −1.22355 | −0.611776 | − | 0.791031i | \(-0.709545\pi\) | ||||
−0.611776 | + | 0.791031i | \(0.709545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 124033. | + | 124033.i | 0.609794 | + | 0.609794i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −62992.3 | − | 62992.3i | −0.306967 | − | 0.306967i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 342847. | 1.65606 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6030.04i | − | 0.0288727i | −0.999896 | − | 0.0144364i | \(-0.995405\pi\) | ||
0.999896 | − | 0.0144364i | \(-0.00459540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −85992.8 | + | 85992.8i | −0.408166 | + | 0.408166i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13122.6 | + | 13122.6i | −0.0617473 | + | 0.0617473i | −0.737306 | − | 0.675559i | \(-0.763902\pi\) |
0.675559 | + | 0.737306i | \(0.263902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 408077.i | 1.90362i | 0.306689 | + | 0.951810i | \(0.400779\pi\) | ||||
−0.306689 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 89305.3 | 0.413020 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −108240. | − | 108240.i | −0.496311 | − | 0.496311i | 0.413977 | − | 0.910288i | \(-0.364140\pi\) |
−0.910288 | + | 0.413977i | \(0.864140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16557.8 | + | 16557.8i | 0.0752759 | + | 0.0752759i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 191216. | 0.861953 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 220853.i | − | 0.987144i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 85376.7 | − | 85376.7i | 0.378401 | − | 0.378401i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 91490.1 | − | 91490.1i | 0.402103 | − | 0.402103i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 223150.i | − | 0.972583i | −0.873797 | − | 0.486291i | \(-0.838349\pi\) | ||
0.873797 | − | 0.486291i | \(-0.161651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 290165. | 1.25416 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 39785.8 | + | 39785.8i | 0.170543 | + | 0.170543i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 356767. | + | 356767.i | 1.51670 | + | 1.51670i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −225880. | −0.952399 | −0.476200 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476200 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 372120.i | 1.55620i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −101698. | + | 101698.i | −0.421842 | + | 0.421842i | −0.885837 | − | 0.463996i | \(-0.846415\pi\) |
0.463996 | + | 0.885837i | \(0.346415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −98440.7 | + | 98440.7i | −0.405024 | + | 0.405024i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 123853.i | 0.505469i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −52357.9 | −0.211968 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 226481. | + | 226481.i | 0.909559 | + | 0.909559i | 0.996236 | − | 0.0866770i | \(-0.0276248\pi\) |
−0.0866770 | + | 0.996236i | \(0.527625\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 334357. | + | 334357.i | 1.33209 | + | 1.33209i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −125734. | −0.496956 | −0.248478 | − | 0.968637i | \(-0.579930\pi\) | ||||
−0.248478 | + | 0.968637i | \(0.579930\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 407820.i | − | 1.59914i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21662.8 | + | 21662.8i | −0.0842749 | + | 0.0842749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 82499.2 | − | 82499.2i | 0.318430 | − | 0.318430i | −0.529734 | − | 0.848164i | \(-0.677708\pi\) |
0.848164 | + | 0.529734i | \(0.177708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 134490.i | − | 0.515048i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 59778.1 | 0.227147 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 194462. | + | 194462.i | 0.733198 | + | 0.733198i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −55974.7 | − | 55974.7i | −0.209416 | − | 0.209416i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −254025. | −0.943066 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 225057.i | − | 0.829120i | −0.910022 | − | 0.414560i | \(-0.863936\pi\) | ||
0.910022 | − | 0.414560i | \(-0.136064\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −230384. | + | 230384.i | −0.842264 | + | 0.842264i | −0.989153 | − | 0.146889i | \(-0.953074\pi\) |
0.146889 | + | 0.989153i | \(0.453074\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −339664. | + | 339664.i | −1.23234 | + | 1.23234i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 59659.0i | − | 0.214810i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −269740. | −0.963903 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 159364. | + | 159364.i | 0.565199 | + | 0.565199i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −292253. | − | 292253.i | −1.02874 | − | 1.02874i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −97718.9 | −0.341406 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 353165.i | 1.22470i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6907.27 | + | 6907.27i | −0.0237755 | + | 0.0237755i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 183995. | − | 183995.i | 0.628655 | − | 0.628655i | −0.319074 | − | 0.947730i | \(-0.603372\pi\) |
0.947730 | + | 0.319074i | \(0.103372\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 155654.i | − | 0.527909i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 292056. | 0.983271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −416851. | − | 416851.i | −1.39318 | − | 1.39318i | −0.818100 | − | 0.575075i | \(-0.804973\pi\) |
−0.575075 | − | 0.818100i | \(-0.695027\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −106907. | − | 106907.i | −0.354699 | − | 0.354699i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 68431.2 | 0.225399 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 225176.i | 0.736330i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −496864. | + | 496864.i | −1.61307 | + | 1.61307i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 233211. | − | 233211.i | 0.751691 | − | 0.751691i | −0.223104 | − | 0.974795i | \(-0.571619\pi\) |
0.974795 | + | 0.223104i | \(0.0716189\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 520386.i | 1.66534i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 239236. | 0.760152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −82256.5 | − | 82256.5i | −0.259510 | − | 0.259510i | 0.565345 | − | 0.824855i | \(-0.308743\pi\) |
−0.824855 | + | 0.565345i | \(0.808743\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 140659. | + | 140659.i | 0.440626 | + | 0.440626i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −412331. | −1.28257 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 130218.i | 0.402203i | 0.979570 | + | 0.201102i | \(0.0644522\pi\) | ||||
−0.979570 | + | 0.201102i | \(0.935548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 62508.2 | − | 62508.2i | 0.191719 | − | 0.191719i | −0.604720 | − | 0.796438i | \(-0.706715\pi\) |
0.796438 | + | 0.604720i | \(0.206715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16001.2 | + | 16001.2i | −0.0487353 | + | 0.0487353i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 86238.6i | 0.260835i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 522256. | 1.56867 | 0.784336 | − | 0.620336i | \(-0.213004\pi\) | ||||
0.784336 | + | 0.620336i | \(0.213004\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −230208. | − | 230208.i | −0.686695 | − | 0.686695i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −73336.0 | − | 73336.0i | −0.217252 | − | 0.217252i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 226912. | 0.667606 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 291829.i | − | 0.852739i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 309702. | − | 309702.i | 0.898811 | − | 0.898811i | −0.0965202 | − | 0.995331i | \(-0.530771\pi\) |
0.995331 | + | 0.0965202i | \(0.0307712\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20736.0 | + | 20736.0i | −0.0597717 | + | 0.0597717i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 443697.i | 1.27032i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −447350. | −1.27215 | −0.636075 | − | 0.771628i | \(-0.719443\pi\) | ||||
−0.636075 | + | 0.771628i | \(0.719443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 392186. | + | 392186.i | 1.10779 | + | 1.10779i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 425687. | + | 425687.i | 1.19438 | + | 1.19438i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −462149. | −1.28804 | −0.644019 | − | 0.765009i | \(-0.722734\pi\) | ||||
−0.644019 | + | 0.765009i | \(0.722734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 374481.i | − | 1.03677i | −0.855149 | − | 0.518383i | \(-0.826534\pi\) | ||
0.855149 | − | 0.518383i | \(-0.173466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14093.8 | − | 14093.8i | 0.0387610 | − | 0.0387610i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 245100. | − | 245100.i | 0.669627 | − | 0.669627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 86755.6i | 0.235462i | 0.993046 | + | 0.117731i | \(0.0375620\pi\) | ||||
−0.993046 | + | 0.117731i | \(0.962438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −272248. | −0.734058 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 131891. | + | 131891.i | 0.353290 | + | 0.353290i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 112325. | + | 112325.i | 0.298920 | + | 0.298920i | 0.840591 | − | 0.541671i | \(-0.182208\pi\) |
−0.541671 | + | 0.840591i | \(0.682208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.00088e6 | 2.64626 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 602706.i | 1.58320i | 0.611041 | + | 0.791599i | \(0.290751\pi\) | ||||
−0.611041 | + | 0.791599i | \(0.709249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −150969. | + | 150969.i | −0.394010 | + | 0.394010i | −0.876114 | − | 0.482104i | \(-0.839873\pi\) |
0.482104 | + | 0.876114i | \(0.339873\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30190.8 | + | 30190.8i | −0.0782873 | + | 0.0782873i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 57703.6i | 0.148671i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 190658. | 0.488084 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −83152.6 | − | 83152.6i | −0.211515 | − | 0.211515i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 331922. | + | 331922.i | 0.838948 | + | 0.838948i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 693714. | 1.74230 | 0.871148 | − | 0.491020i | \(-0.163376\pi\) | ||||
0.871148 | + | 0.491020i | \(0.163376\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 503485.i | 1.25655i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 623231. | − | 623231.i | 1.54562 | − | 1.54562i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16275.3 | − | 16275.3i | 0.0401098 | − | 0.0401098i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 44566.7i | 0.109146i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17843.0 | −0.0434261 | −0.0217131 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217131 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −230136. | − | 230136.i | −0.556626 | − | 0.556626i | 0.371719 | − | 0.928345i | \(-0.378768\pi\) |
−0.928345 | + | 0.371719i | \(0.878768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −891085. | − | 891085.i | −2.14190 | − | 2.14190i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −568528. | −1.35814 | −0.679068 | − | 0.734075i | \(-0.737616\pi\) | ||||
−0.679068 | + | 0.734075i | \(0.737616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 395251.i | 0.938391i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 82496.7 | − | 82496.7i | 0.194659 | − | 0.194659i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −371799. | + | 371799.i | −0.871932 | + | 0.871932i | −0.992683 | − | 0.120751i | \(-0.961470\pi\) |
0.120751 | + | 0.992683i | \(0.461470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.04579e6i | − | 2.43759i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −114477. | −0.265208 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −71107.3 | − | 71107.3i | −0.163736 | − | 0.163736i | 0.620484 | − | 0.784219i | \(-0.286936\pi\) |
−0.784219 | + | 0.620484i | \(0.786936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −570193. | − | 570193.i | −1.30502 | − | 1.30502i | −0.924960 | − | 0.380065i | \(-0.875902\pi\) |
−0.380065 | − | 0.924960i | \(-0.624098\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −563701. | −1.28239 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 272629.i | − | 0.616494i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34561.0 | + | 34561.0i | −0.0776846 | + | 0.0776846i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −741091. | + | 741091.i | −1.65584 | + | 1.65584i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 265148.i | − | 0.588901i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −57084.2 | −0.126033 | −0.0630167 | − | 0.998012i | \(-0.520072\pi\) | ||||
−0.0630167 | + | 0.998012i | \(0.520072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −257749. | − | 257749.i | −0.565704 | − | 0.565704i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 107264. | + | 107264.i | 0.234032 | + | 0.234032i | 0.814373 | − | 0.580341i | \(-0.197081\pi\) |
−0.580341 | + | 0.814373i | \(0.697081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 659134. | 1.42966 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 986444.i | − | 2.12705i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41763.8 | − | 41763.8i | 0.0895280 | − | 0.0895280i | −0.660924 | − | 0.750452i | \(-0.729836\pi\) |
0.750452 | + | 0.660924i | \(0.229836\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 917153. | − | 917153.i | 1.95461 | − | 1.95461i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 311303.i | − | 0.659583i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −534662. | −1.12627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 473605. | + | 473605.i | 0.991882 | + | 0.991882i | 0.999967 | − | 0.00808568i | \(-0.00257378\pi\) |
−0.00808568 | + | 0.999967i | \(0.502574\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 114410. | + | 114410.i | 0.238231 | + | 0.238231i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −639811. | −1.32459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 668623.i | − | 1.37631i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −197198. | + | 197198.i | −0.403598 | + | 0.403598i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 139642. | − | 139642.i | 0.284170 | − | 0.284170i | −0.550599 | − | 0.834770i | \(-0.685601\pi\) |
0.834770 | + | 0.550599i | \(0.185601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 230737.i | − | 0.466880i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −451687. | −0.908782 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −376728. | − | 376728.i | −0.753684 | − | 0.753684i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 161047. | + | 161047.i | 0.320377 | + | 0.320377i | 0.848912 | − | 0.528535i | \(-0.177258\pi\) |
−0.528535 | + | 0.848912i | \(0.677258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 191668. | 0.379150 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20945.4i | − | 0.0412011i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 361893. | − | 361893.i | 0.707894 | − | 0.707894i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −732090. | + | 732090.i | −1.42405 | + | 1.42405i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 132212.i | 0.255749i | 0.991790 | + | 0.127874i | \(0.0408154\pi\) | ||||
−0.991790 | + | 0.127874i | \(0.959185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 359273. | 0.691122 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 637198. | + | 637198.i | 1.21898 | + | 1.21898i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −295059. | − | 295059.i | −0.561349 | − | 0.561349i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −98417.4 | −0.186210 | −0.0931050 | − | 0.995656i | \(-0.529679\pi\) | ||||
−0.0931050 | + | 0.995656i | \(0.529679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 31927.4i | − | 0.0600770i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −595275. | + | 595275.i | −1.11399 | + | 1.11399i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 369797. | − | 369797.i | 0.688265 | − | 0.688265i | −0.273584 | − | 0.961848i | \(-0.588209\pi\) |
0.961848 | + | 0.273584i | \(0.0882090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 55738.2i | 0.103176i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34955.2 | 0.0643542 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 117481. | + | 117481.i | 0.215120 | + | 0.215120i | 0.806438 | − | 0.591318i | \(-0.201392\pi\) |
−0.591318 | + | 0.806438i | \(0.701392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 195929. | + | 195929.i | 0.356831 | + | 0.356831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 273733. | 0.495849 | 0.247925 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247925 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 810267.i | − | 1.45988i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62423.0 | + | 62423.0i | −0.111867 | + | 0.111867i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −90268.8 | + | 90268.8i | −0.160907 | + | 0.160907i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 875863.i | 1.55295i | 0.630150 | + | 0.776473i | \(0.282993\pi\) | ||||
−0.630150 | + | 0.776473i | \(0.717007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −407741. | −0.719108 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −218004. | − | 218004.i | −0.382446 | − | 0.382446i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −66071.4 | − | 66071.4i | −0.115298 | − | 0.115298i | 0.647104 | − | 0.762402i | \(-0.275980\pi\) |
−0.762402 | + | 0.647104i | \(0.775980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 83992.1 | 0.145799 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 333176.i | 0.575314i | 0.957734 | + | 0.287657i | \(0.0928763\pi\) | ||||
−0.957734 | + | 0.287657i | \(0.907124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 269790. | − | 269790.i | 0.463422 | − | 0.463422i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 333826. | − | 333826.i | 0.570423 | − | 0.570423i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 931313.i | − | 1.58309i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −110911. | −0.187552 | −0.0937762 | − | 0.995593i | \(-0.529894\pi\) | ||||
−0.0937762 | + | 0.995593i | \(0.529894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −124325. | − | 124325.i | −0.209146 | − | 0.209146i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 800998. | + | 800998.i | 1.34052 | + | 1.34052i | 0.895544 | + | 0.444972i | \(0.146787\pi\) |
0.444972 | + | 0.895544i | \(0.353213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 178818. | 0.297719 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 917967.i | 1.52050i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −232397. | + | 232397.i | −0.382962 | + | 0.382962i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55266.6 | + | 55266.6i | −0.0906068 | + | 0.0906068i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 206591.i | − | 0.336968i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 661762. | 1.07390 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −528761. | − | 528761.i | −0.853709 | − | 0.853709i | 0.136879 | − | 0.990588i | \(-0.456293\pi\) |
−0.990588 | + | 0.136879i | \(0.956293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −645552. | − | 645552.i | −1.03700 | − | 1.03700i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 259870. | 0.415340 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 624756.i | 0.993491i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 915532. | − | 915532.i | 1.44857 | − | 1.44857i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −771661. | + | 771661.i | −1.21481 | + | 1.21481i | −0.245390 | + | 0.969424i | \(0.578916\pi\) |
−0.969424 | + | 0.245390i | \(0.921084\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 301742.i | 0.472653i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49116.8 | 0.0765536 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −141961. | − | 141961.i | −0.220160 | − | 0.220160i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 137691. | + | 137691.i | 0.212477 | + | 0.212477i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −485011. | −0.744740 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 100893.i | 0.154157i | 0.997025 | + | 0.0770783i | \(0.0245592\pi\) | ||||
−0.997025 | + | 0.0770783i | \(0.975441\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51769.7 | + | 51769.7i | −0.0787107 | + | 0.0787107i | −0.745366 | − | 0.666655i | \(-0.767725\pi\) |
0.666655 | + | 0.745366i | \(0.267725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 871882. | − | 871882.i | 1.31910 | − | 1.31910i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.28783e6i | 1.93885i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 413807. | 0.619946 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −269580. | − | 269580.i | −0.401901 | − | 0.401901i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48584.3 | − | 48584.3i | −0.0720791 | − | 0.0720791i | 0.670148 | − | 0.742227i | \(-0.266231\pi\) |
−0.742227 | + | 0.670148i | \(0.766231\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 338093. | 0.499157 | 0.249578 | − | 0.968355i | \(-0.419708\pi\) | ||||
0.249578 | + | 0.968355i | \(0.419708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 717068.i | 1.05354i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −458054. | + | 458054.i | −0.669740 | + | 0.669740i | −0.957656 | − | 0.287916i | \(-0.907038\pi\) |
0.287916 | + | 0.957656i | \(0.407038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −495530. | + | 495530.i | −0.721042 | + | 0.721042i | −0.968818 | − | 0.247775i | \(-0.920301\pi\) |
0.247775 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 403396.i | 0.584157i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37235.0 | 0.0536613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.15714e6 | + | 1.15714e6i | 1.65964 | + | 1.65964i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 62601.3 | + | 62601.3i | 0.0893578 | + | 0.0893578i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −696514. | −0.989477 | −0.494739 | − | 0.869042i | \(-0.664736\pi\) | ||||
−0.494739 | + | 0.869042i | \(0.664736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 470785.i | 0.665626i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −383982. | + | 383982.i | −0.540326 | + | 0.540326i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −74970.5 | + | 74970.5i | −0.104997 | + | 0.104997i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 452827.i | − | 0.631198i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.75412e6 | 2.43357 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 116533. | + | 116533.i | 0.160912 | + | 0.160912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −78365.1 | − | 78365.1i | −0.107702 | − | 0.107702i | 0.651202 | − | 0.758904i | \(-0.274265\pi\) |
−0.758904 | + | 0.651202i | \(0.774265\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −232060. | −0.317444 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 576243.i | 0.784593i | 0.919839 | + | 0.392296i | \(0.128319\pi\) | ||||
−0.919839 | + | 0.392296i | \(0.871681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 74196.4 | − | 74196.4i | 0.100553 | − | 0.100553i | −0.655040 | − | 0.755594i | \(-0.727348\pi\) |
0.755594 | + | 0.655040i | \(0.227348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 924574. | − | 924574.i | 1.24720 | − | 1.24720i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 299840.i | 0.402594i | 0.979530 | + | 0.201297i | \(0.0645157\pi\) | ||||
−0.979530 | + | 0.201297i | \(0.935484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −879131. | −1.17495 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12352.5 | + | 12352.5i | 0.0164329 | + | 0.0164329i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 237686. | + | 237686.i | 0.314749 | + | 0.314749i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −82363.5 | −0.108567 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 561050.i | − | 0.736161i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −319272. | + | 319272.i | −0.417009 | + | 0.417009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 438353. | − | 438353.i | 0.569934 | − | 0.569934i | −0.362176 | − | 0.932110i | \(-0.617966\pi\) |
0.932110 | + | 0.362176i | \(0.117966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 206044.i | 0.266675i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1526.15 | −0.00196628 | −0.000983142 | − | 1.00000i | \(-0.500313\pi\) | ||||
−0.000983142 | 1.00000i | \(0.500313\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 114980. | + | 114980.i | 0.147469 | + | 0.147469i | 0.776986 | − | 0.629517i | \(-0.216747\pi\) |
−0.629517 | + | 0.776986i | \(0.716747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.59474e6 | + | 1.59474e6i | 2.03612 | + | 2.03612i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 833028. | 1.05880 | 0.529398 | − | 0.848373i | \(-0.322418\pi\) | ||||
0.529398 | + | 0.848373i | \(0.322418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.15143e6i | − | 1.45692i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −435238. | + | 435238.i | −0.548241 | + | 0.548241i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 104878. | − | 104878.i | 0.131517 | − | 0.131517i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.22223e6i | 1.52584i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −197907. | −0.245967 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 71663.1 | + | 71663.1i | 0.0886699 | + | 0.0886699i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −611606. | − | 611606.i | −0.753394 | − | 0.753394i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.64630e6 | −2.01898 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 538686.i | − | 0.657716i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.13198e6 | + | 1.13198e6i | −1.37602 | + | 1.37602i | −0.524787 | + | 0.851234i | \(0.675855\pi\) |
−0.851234 | + | 0.524787i | \(0.824145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −320668. | + | 320668.i | −0.388086 | + | 0.388086i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 369952.i | − | 0.445768i | −0.974845 | − | 0.222884i | \(-0.928453\pi\) | ||
0.974845 | − | 0.222884i | \(-0.0715471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −154820. | −0.185732 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.06980e6 | − | 1.06980e6i | −1.27780 | − | 1.27780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −966058. | − | 966058.i | −1.14885 | − | 1.14885i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −815703. | −0.965831 | −0.482915 | − | 0.875667i | \(-0.660422\pi\) | ||||
−0.482915 | + | 0.875667i | \(0.660422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 397746.i | − | 0.468906i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 130222. | − | 130222.i | 0.152856 | − | 0.152856i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −994881. | + | 994881.i | −1.16275 | + | 1.16275i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 305811.i | − | 0.355872i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 329861. | 0.382208 | 0.191104 | − | 0.981570i | \(-0.438793\pi\) | ||||
0.191104 | + | 0.981570i | \(0.438793\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12942.0 | − | 12942.0i | −0.0149314 | − | 0.0149314i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 423383. | + | 423383.i | 0.486374 | + | 0.486374i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 827947. | 0.947064 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 884572.i | − | 1.00752i | −0.863844 | − | 0.503760i | \(-0.831949\pi\) | ||
0.863844 | − | 0.503760i | \(-0.168051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.08068e6 | − | 1.08068e6i | 1.22565 | − | 1.22565i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 441727. | − | 441727.i | 0.498856 | − | 0.498856i | −0.412226 | − | 0.911082i | \(-0.635249\pi\) |
0.911082 | + | 0.412226i | \(0.135249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 234743.i | − | 0.263979i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −823056. | −0.921650 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −98614.4 | − | 98614.4i | −0.109961 | − | 0.109961i | 0.649985 | − | 0.759947i | \(-0.274775\pi\) |
−0.759947 | + | 0.649985i | \(0.774775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 334497. | + | 334497.i | 0.371416 | + | 0.371416i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.81832e6 | 2.01053 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 327664.i | 0.360780i | 0.983595 | + | 0.180390i | \(0.0577360\pi\) | ||||
−0.983595 | + | 0.180390i | \(0.942264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55377.0 | + | 55377.0i | −0.0607187 | + | 0.0607187i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −287373. | + | 287373.i | −0.313778 | + | 0.313778i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.69446e6i | − | 1.84244i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 880090. | 0.952973 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 76836.2 | + | 76836.2i | 0.0828539 | + | 0.0828539i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −796705. | − | 796705.i | −0.855545 | − | 0.855545i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −386677. | −0.413519 | −0.206760 | − | 0.978392i | \(-0.566292\pi\) | ||||
−0.206760 | + | 0.978392i | \(0.566292\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 448251.i | 0.477390i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 718740. | − | 718740.i | 0.762313 | − | 0.762313i | −0.214427 | − | 0.976740i | \(-0.568788\pi\) |
0.976740 | + | 0.214427i | \(0.0687884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −591032. | + | 591032.i | −0.624288 | + | 0.624288i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.68960e6i | − | 1.77735i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.27845e6 | −1.33935 | −0.669675 | − | 0.742654i | \(-0.733567\pi\) | ||||
−0.669675 | + | 0.742654i | \(0.733567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60909.2 | + | 60909.2i | 0.0635503 | + | 0.0635503i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −229643. | − | 229643.i | −0.238625 | − | 0.238625i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 414529. | 0.428991 | 0.214495 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214495 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.53555e6i | 1.58267i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −417251. | + | 417251.i | −0.428314 | + | 0.428314i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −208992. | + | 208992.i | −0.213667 | + | 0.213667i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 176697.i | 0.179921i | 0.995945 | + | 0.0899605i | \(0.0286741\pi\) | ||||
−0.995945 | + | 0.0899605i | \(0.971326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.07025e6 | −1.08539 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.47322e6 | + | 1.47322e6i | 1.48806 | + | 1.48806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.20434e6 | + | 1.20434e6i | 1.21160 | + | 1.21160i | 0.970500 | + | 0.241102i | \(0.0775089\pi\) |
0.241102 | + | 0.970500i | \(0.422491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −696585. | −0.697980 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 128.5.f.a.31.2 | 14 | ||
4.3 | odd | 2 | 128.5.f.b.31.6 | 14 | |||
8.3 | odd | 2 | 16.5.f.a.11.6 | yes | 14 | ||
8.5 | even | 2 | 64.5.f.a.15.6 | 14 | |||
16.3 | odd | 4 | inner | 128.5.f.a.95.2 | 14 | ||
16.5 | even | 4 | 16.5.f.a.3.6 | ✓ | 14 | ||
16.11 | odd | 4 | 64.5.f.a.47.6 | 14 | |||
16.13 | even | 4 | 128.5.f.b.95.6 | 14 | |||
24.5 | odd | 2 | 576.5.m.a.271.1 | 14 | |||
24.11 | even | 2 | 144.5.m.a.91.2 | 14 | |||
48.5 | odd | 4 | 144.5.m.a.19.2 | 14 | |||
48.11 | even | 4 | 576.5.m.a.559.1 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.6 | ✓ | 14 | 16.5 | even | 4 | ||
16.5.f.a.11.6 | yes | 14 | 8.3 | odd | 2 | ||
64.5.f.a.15.6 | 14 | 8.5 | even | 2 | |||
64.5.f.a.47.6 | 14 | 16.11 | odd | 4 | |||
128.5.f.a.31.2 | 14 | 1.1 | even | 1 | trivial | ||
128.5.f.a.95.2 | 14 | 16.3 | odd | 4 | inner | ||
128.5.f.b.31.6 | 14 | 4.3 | odd | 2 | |||
128.5.f.b.95.6 | 14 | 16.13 | even | 4 | |||
144.5.m.a.19.2 | 14 | 48.5 | odd | 4 | |||
144.5.m.a.91.2 | 14 | 24.11 | even | 2 | |||
576.5.m.a.271.1 | 14 | 24.5 | odd | 2 | |||
576.5.m.a.559.1 | 14 | 48.11 | even | 4 |