Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 9.5 | ||
Character | \(\chi\) | \(=\) | 76.9 |
Dual form | 76.6.i.a.17.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 6.23353 | − | 5.23055i | 0.399881 | − | 0.335540i | −0.420567 | − | 0.907262i | \(-0.638169\pi\) |
0.820448 | + | 0.571722i | \(0.193724\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −51.5730 | − | 18.7710i | −0.922565 | − | 0.335786i | −0.163307 | − | 0.986575i | \(-0.552216\pi\) |
−0.759259 | + | 0.650789i | \(0.774438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.9937 | + | 50.2186i | −0.223645 | + | 0.387364i | −0.955912 | − | 0.293653i | \(-0.905129\pi\) |
0.732267 | + | 0.681017i | \(0.238462\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −30.6983 | + | 174.099i | −0.126330 | + | 0.716455i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 274.013 | + | 474.604i | 0.682793 | + | 1.18263i | 0.974125 | + | 0.226010i | \(0.0725683\pi\) |
−0.291332 | + | 0.956622i | \(0.594098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.6757 | − | 35.8092i | −0.0700362 | − | 0.0587674i | 0.607098 | − | 0.794627i | \(-0.292334\pi\) |
−0.677134 | + | 0.735860i | \(0.736778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −419.664 | + | 152.745i | −0.481586 | + | 0.175283i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 38.5884 | + | 218.846i | 0.0323843 | + | 0.183661i | 0.996709 | − | 0.0810613i | \(-0.0258309\pi\) |
−0.964325 | + | 0.264722i | \(0.914720\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1008.29 | + | 1208.08i | 0.640770 | + | 0.767733i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 81.9378 | + | 464.692i | 0.0405449 | + | 0.229941i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1368.59 | + | 498.127i | −0.539454 | + | 0.196345i | −0.597355 | − | 0.801977i | \(-0.703782\pi\) |
0.0579007 | + | 0.998322i | \(0.481559\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −86.4698 | − | 72.5568i | −0.0276703 | − | 0.0232182i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1707.96 | + | 2958.27i | 0.450886 | + | 0.780958i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −879.600 | + | 4988.46i | −0.194218 | + | 1.10147i | 0.719309 | + | 0.694690i | \(0.244459\pi\) |
−0.913527 | + | 0.406777i | \(0.866653\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2849.24 | + | 4935.03i | −0.532507 | + | 0.922329i | 0.466773 | + | 0.884377i | \(0.345417\pi\) |
−0.999280 | + | 0.0379518i | \(0.987917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4190.51 | + | 1525.22i | 0.669857 | + | 0.243808i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2437.95 | − | 2045.68i | 0.336398 | − | 0.282272i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7901.20 | −0.948831 | −0.474415 | − | 0.880301i | \(-0.657340\pi\) | ||||
−0.474415 | + | 0.880301i | \(0.657340\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −453.322 | −0.0477250 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6030.90 | − | 5060.53i | 0.560302 | − | 0.470150i | −0.318109 | − | 0.948054i | \(-0.603048\pi\) |
0.878412 | + | 0.477904i | \(0.158603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13086.3 | − | 4763.04i | −1.07931 | − | 0.392838i | −0.259661 | − | 0.965700i | \(-0.583611\pi\) |
−0.819652 | + | 0.572862i | \(0.805833\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4851.21 | − | 8402.54i | 0.357124 | − | 0.618557i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3726.61 | − | 21134.6i | 0.246076 | − | 1.39556i | −0.571905 | − | 0.820320i | \(-0.693796\pi\) |
0.817981 | − | 0.575245i | \(-0.195093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6722.23 | + | 11643.2i | 0.399966 | + | 0.692762i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1385.23 | + | 1162.34i | 0.0745754 | + | 0.0625762i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7952.22 | − | 2894.37i | 0.388865 | − | 0.141535i | −0.140186 | − | 0.990125i | \(-0.544770\pi\) |
0.529051 | + | 0.848590i | \(0.322548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5222.85 | − | 29620.2i | −0.232809 | − | 1.32033i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12604.1 | + | 2256.65i | 0.513837 | + | 0.0919978i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1789.95 | − | 10151.3i | −0.0669437 | − | 0.379657i | −0.999811 | − | 0.0194366i | \(-0.993813\pi\) |
0.932867 | − | 0.360220i | \(-0.117298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17924.4 | + | 6523.94i | −0.616764 | + | 0.224484i | −0.631460 | − | 0.775408i | \(-0.717544\pi\) |
0.0146961 | + | 0.999892i | \(0.495322\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7852.93 | − | 6589.39i | −0.249276 | − | 0.209167i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1528.74 | + | 2647.85i | 0.0448797 | + | 0.0777339i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7697.37 | − | 43653.9i | 0.209486 | − | 1.18805i | −0.680736 | − | 0.732528i | \(-0.738340\pi\) |
0.890222 | − | 0.455526i | \(-0.150549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5925.68 | + | 10263.6i | −0.149836 | + | 0.259523i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6445.09 | + | 2345.82i | 0.151734 | + | 0.0552267i | 0.416771 | − | 0.909012i | \(-0.363162\pi\) |
−0.265037 | + | 0.964238i | \(0.585384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16171.8 | + | 13569.8i | −0.355183 | + | 0.298034i | −0.802867 | − | 0.596158i | \(-0.796693\pi\) |
0.447684 | + | 0.894192i | \(0.352249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −918.525 | −0.0188555 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −31778.6 | −0.610812 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42246.1 | − | 35448.7i | 0.761586 | − | 0.639047i | −0.176953 | − | 0.984219i | \(-0.556624\pi\) |
0.938539 | + | 0.345173i | \(0.112180\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14247.9 | − | 5185.82i | −0.241290 | − | 0.0878224i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −35556.3 | + | 61585.3i | −0.566528 | + | 0.981255i | 0.430378 | + | 0.902649i | \(0.358380\pi\) |
−0.996906 | + | 0.0786064i | \(0.974953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2117.84 | − | 12010.9i | 0.0317941 | − | 0.180313i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20609.4 | + | 35696.5i | 0.291922 | + | 0.505624i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 98367.6 | + | 82540.2i | 1.31637 | + | 1.10456i | 0.987062 | + | 0.160339i | \(0.0512589\pi\) |
0.329305 | + | 0.944224i | \(0.393186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3035.62 | − | 1104.87i | 0.0384276 | − | 0.0139865i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8052.11 | + | 45665.8i | 0.0965390 | + | 0.547500i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −29323.8 | − | 81230.7i | −0.333358 | − | 0.923445i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31642.3 | + | 179452.i | 0.341459 | + | 1.93651i | 0.350529 | + | 0.936552i | \(0.386002\pi\) |
−0.00906989 | + | 0.999959i | \(0.502887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −91039.7 | + | 33135.7i | −0.933561 | + | 0.339788i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 37866.4 | + | 31773.7i | 0.369361 | + | 0.309931i | 0.808509 | − | 0.588484i | \(-0.200275\pi\) |
−0.439148 | + | 0.898415i | \(0.644720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35793.4 | − | 61996.0i | −0.332437 | − | 0.575799i | 0.650552 | − | 0.759462i | \(-0.274538\pi\) |
−0.982989 | + | 0.183663i | \(0.941204\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4496.97 | − | 25503.6i | 0.0398059 | − | 0.225750i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2218.09 | − | 3841.84i | 0.0187292 | − | 0.0324399i | −0.856509 | − | 0.516132i | \(-0.827371\pi\) |
0.875238 | + | 0.483692i | \(0.160705\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −39598.8 | − | 14412.8i | −0.319239 | − | 0.116193i | 0.177430 | − | 0.984133i | \(-0.443222\pi\) |
−0.496669 | + | 0.867940i | \(0.665444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −49252.4 | + | 41327.6i | −0.379419 | + | 0.318371i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 40076.5 | 0.295252 | 0.147626 | − | 0.989043i | \(-0.452837\pi\) | ||||
0.147626 | + | 0.989043i | \(0.452837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 79932.7 | 0.563612 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7544.41 | − | 6330.51i | 0.0509519 | − | 0.0427537i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12109.0 | − | 4407.30i | −0.0783861 | − | 0.0285302i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −69640.6 | + | 120621.i | −0.432413 | + | 0.748962i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11124.5 | − | 63089.9i | 0.0663004 | − | 0.376008i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 88851.9 | + | 153896.i | 0.508618 | + | 0.880952i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15593.3 | + | 13084.3i | 0.0857884 | + | 0.0719850i | 0.684673 | − | 0.728850i | \(-0.259945\pi\) |
−0.598885 | + | 0.800835i | \(0.704389\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −106487. | + | 38758.3i | −0.563410 | + | 0.205064i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9012.64 | − | 51113.2i | −0.0458853 | − | 0.260229i | 0.953232 | − | 0.302240i | \(-0.0977345\pi\) |
−0.999117 | + | 0.0420116i | \(0.986623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −89902.0 | + | 15608.4i | −0.440697 | + | 0.0765119i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −32554.6 | − | 184627.i | −0.153737 | − | 0.871886i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 97870.4 | − | 35621.9i | 0.445502 | − | 0.162150i | −0.109521 | − | 0.993985i | \(-0.534932\pi\) |
0.555023 | + | 0.831835i | \(0.312709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −76180.7 | − | 63923.2i | −0.334432 | − | 0.280622i | 0.460071 | − | 0.887882i | \(-0.347824\pi\) |
−0.794503 | + | 0.607261i | \(0.792268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −87315.9 | − | 151236.i | −0.369867 | − | 0.640628i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5301.49 | − | 30066.3i | 0.0216799 | − | 0.122953i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 139002. | − | 240759.i | 0.549037 | − | 0.950959i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 102804. | + | 37417.5i | 0.392388 | + | 0.142818i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 402329. | − | 337594.i | 1.48462 | − | 1.24574i | 0.583547 | − | 0.812079i | \(-0.301664\pi\) |
0.901074 | − | 0.433666i | \(-0.142780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −166773. | −0.595227 | −0.297614 | − | 0.954686i | \(-0.596191\pi\) | ||||
−0.297614 | + | 0.954686i | \(0.596191\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −39285.4 | −0.135676 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 239580. | − | 201031.i | 0.800978 | − | 0.672100i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −209840. | − | 76375.5i | −0.679421 | − | 0.247289i | −0.0208219 | − | 0.999783i | \(-0.506628\pi\) |
−0.658599 | + | 0.752494i | \(0.728851\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34431.2 | − | 59636.7i | 0.108009 | − | 0.187077i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14665.3 | − | 83171.3i | 0.0445890 | − | 0.252877i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −42579.0 | − | 73749.0i | −0.125524 | − | 0.217414i | 0.796414 | − | 0.604752i | \(-0.206728\pi\) |
−0.921938 | + | 0.387338i | \(0.873395\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −187487. | − | 157320.i | −0.536119 | − | 0.449857i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −196481. | + | 71513.2i | −0.545166 | + | 0.198424i | −0.599898 | − | 0.800077i | \(-0.704792\pi\) |
0.0547312 | + | 0.998501i | \(0.482570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −63935.4 | − | 362596.i | −0.172197 | − | 0.976576i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −241277. | + | 138456.i | −0.630995 | + | 0.362095i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 59197.6 | + | 335726.i | 0.150380 | + | 0.852845i | 0.962889 | + | 0.269897i | \(0.0869897\pi\) |
−0.812510 | + | 0.582948i | \(0.801899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6150.78 | − | 2238.70i | 0.0151822 | − | 0.00552587i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −64254.5 | − | 53915.9i | −0.154160 | − | 0.129355i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 383209. | + | 663737.i | 0.893928 | + | 1.54833i | 0.835126 | + | 0.550059i | \(0.185395\pi\) |
0.0588023 | + | 0.998270i | \(0.481272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19109.4 | + | 108375.i | −0.0433562 | + | 0.245885i | −0.998782 | − | 0.0493472i | \(-0.984286\pi\) |
0.955426 | + | 0.295232i | \(0.0953970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −77608.3 | + | 134422.i | −0.171309 | + | 0.296716i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 407488. | + | 148314.i | 0.875358 | + | 0.318604i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −93291.4 | + | 78280.8i | −0.195091 | + | 0.163701i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −198080. | −0.403353 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 764355. | 1.51604 | 0.758022 | − | 0.652229i | \(-0.226166\pi\) | ||||
0.758022 | + | 0.652229i | \(0.226166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −471126. | + | 395322.i | −0.910425 | + | 0.763937i | −0.972200 | − | 0.234153i | \(-0.924768\pi\) |
0.0617751 | + | 0.998090i | \(0.480324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23379.2 | + | 8509.33i | 0.0440294 | + | 0.0160254i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 114320. | − | 198008.i | 0.209873 | − | 0.363511i | −0.741801 | − | 0.670620i | \(-0.766028\pi\) |
0.951674 | + | 0.307109i | \(0.0993616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −55113.9 | + | 312566.i | −0.0986571 | + | 0.559512i | 0.894908 | + | 0.446250i | \(0.147241\pi\) |
−0.993565 | + | 0.113262i | \(0.963870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −180352. | − | 312380.i | −0.314870 | − | 0.545372i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −225011. | − | 188806.i | −0.383233 | − | 0.321571i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −406023. | + | 147780.i | −0.674785 | + | 0.245602i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −44709.8 | − | 253562.i | −0.0725231 | − | 0.411299i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −297073. | + | 809568.i | −0.470432 | + | 1.28200i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21986.2 | + | 124690.i | 0.0339972 | + | 0.192808i | 0.997076 | − | 0.0764102i | \(-0.0243459\pi\) |
−0.963079 | + | 0.269218i | \(0.913235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 52445.6 | − | 19088.7i | 0.0792064 | − | 0.0288288i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 585494. | + | 491288.i | 0.863827 | + | 0.724837i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −165220. | − | 286170.i | −0.238185 | − | 0.412548i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29830.2 | + | 169175.i | −0.0420287 | + | 0.238356i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6189.91 | − | 10721.2i | 0.00852518 | − | 0.0147660i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 83606.6 | + | 30430.3i | 0.112584 | + | 0.0409774i | 0.397698 | − | 0.917516i | \(-0.369809\pi\) |
−0.285114 | + | 0.958494i | \(0.592031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15286.5 | − | 12826.9i | 0.0201304 | − | 0.0168914i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 489797. | 0.630887 | 0.315443 | − | 0.948944i | \(-0.397847\pi\) | ||||
0.315443 | + | 0.948944i | \(0.397847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 228119. | 0.287456 | 0.143728 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143728 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −198093. | + | 166220.i | −0.244252 | + | 0.204952i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.40400e6 | + | 511014.i | 1.69425 | + | 0.616656i | 0.995150 | − | 0.0983701i | \(-0.0313629\pi\) |
0.699098 | + | 0.715026i | \(0.253585\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −588911. | + | 1.02002e6i | −0.695632 | + | 1.20487i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 77926.2 | − | 441941.i | 0.0901182 | − | 0.511086i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −45481.2 | − | 78775.7i | −0.0515035 | − | 0.0892067i | 0.839124 | − | 0.543940i | \(-0.183068\pi\) |
−0.890628 | + | 0.454733i | \(0.849735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 116320. | + | 97603.7i | 0.129006 | + | 0.108249i | 0.705008 | − | 0.709199i | \(-0.250943\pi\) |
−0.576002 | + | 0.817448i | \(0.695388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −895947. | + | 326098.i | −0.973344 | + | 0.354268i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −128130. | − | 726660.i | −0.136375 | − | 0.773421i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 230.624 | − | 87661.6i | 0.000240526 | − | 0.0914255i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 100484. | + | 569873.i | 0.102707 | + | 0.582478i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −446089. | + | 162363.i | −0.446927 | + | 0.162668i | −0.555672 | − | 0.831401i | \(-0.687539\pi\) |
0.108745 | + | 0.994070i | \(0.465317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −611425. | − | 513046.i | −0.600540 | − | 0.503913i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −49621.9 | − | 85947.6i | −0.0477884 | − | 0.0827720i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 235146. | − | 1.33358e6i | 0.222078 | − | 1.25947i | −0.646116 | − | 0.763239i | \(-0.723608\pi\) |
0.868193 | − | 0.496226i | \(-0.165281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 229085. | − | 396787.i | 0.212201 | − | 0.367543i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −841482. | − | 306274.i | −0.764616 | − | 0.278298i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −542040. | + | 454825.i | −0.483216 | + | 0.405467i | −0.851588 | − | 0.524212i | \(-0.824360\pi\) |
0.368371 | + | 0.929679i | \(0.379915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −464450. | −0.406279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.04491e6 | 0.897016 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 796656. | − | 668474.i | 0.671259 | − | 0.563253i | −0.242179 | − | 0.970232i | \(-0.577862\pi\) |
0.913438 | + | 0.406978i | \(0.133418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.62320e6 | + | 590795.i | 1.34260 | + | 0.488668i | 0.910631 | − | 0.413220i | \(-0.135596\pi\) |
0.431972 | + | 0.901887i | \(0.357818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13143.5 | − | 22765.2i | 0.0106734 | − | 0.0184869i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10741.9 | − | 60920.4i | 0.00856545 | − | 0.0485771i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.06622e6 | − | 1.84675e6i | −0.834928 | − | 1.44614i | −0.894089 | − | 0.447889i | \(-0.852176\pi\) |
0.0591610 | − | 0.998248i | \(-0.481157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −771716. | − | 647547.i | −0.593536 | − | 0.498036i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −114867. | + | 41808.2i | −0.0867821 | + | 0.0315861i | −0.385046 | − | 0.922897i | \(-0.625815\pi\) |
0.298264 | + | 0.954483i | \(0.403592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −353629. | − | 2.00553e6i | −0.262471 | − | 1.48855i | −0.776141 | − | 0.630559i | \(-0.782826\pi\) |
0.513670 | − | 0.857988i | \(-0.328285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −607672. | − | 352975.i | −0.443157 | − | 0.257413i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 79274.3 | + | 449587.i | 0.0568104 | + | 0.322188i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.28782e6 | − | 468730.i | 0.907010 | − | 0.330125i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.13588e6 | + | 953115.i | 0.786320 | + | 0.659801i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.14587e6 | − | 1.98471e6i | −0.779770 | − | 1.35060i | −0.932074 | − | 0.362267i | \(-0.882003\pi\) |
0.152305 | − | 0.988334i | \(-0.451331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −98237.2 | + | 557131.i | −0.0657235 | + | 0.372737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −936003. | + | 1.62121e6i | −0.615724 | + | 1.06647i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 76243.2 | + | 27750.3i | 0.0493200 | + | 0.0179510i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 618615. | − | 519079.i | 0.393554 | − | 0.330231i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 402236. | 0.251695 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.04687e6 | 0.644384 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.86619e6 | − | 1.56592e6i | 1.13008 | − | 0.948254i | 0.131015 | − | 0.991380i | \(-0.458176\pi\) |
0.999070 | + | 0.0431267i | \(0.0137319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −547393. | − | 199235.i | −0.326139 | − | 0.118705i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 349201. | − | 604834.i | 0.204727 | − | 0.354597i | −0.745319 | − | 0.666708i | \(-0.767703\pi\) |
0.950046 | + | 0.312111i | \(0.101036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −249321. | + | 1.41397e6i | −0.143846 | + | 0.815792i | 0.824440 | + | 0.565949i | \(0.191490\pi\) |
−0.968286 | + | 0.249843i | \(0.919621\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 281309. | + | 487242.i | 0.159738 | + | 0.276674i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 694313. | + | 582598.i | 0.388067 | + | 0.325627i | 0.815860 | − | 0.578250i | \(-0.196264\pi\) |
−0.427792 | + | 0.903877i | \(0.640709\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.60857e6 | + | 949440.i | −1.43524 | + | 0.522385i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6268.43 | − | 35550.0i | −0.00339544 | − | 0.0192565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −225474. | + | 267278.i | −0.120251 | + | 0.142547i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1091.96 | + | 6192.83i | 0.000573455 | + | 0.00325223i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −322227. | + | 117281.i | −0.166645 | + | 0.0606539i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 953303. | + | 799916.i | 0.485558 | + | 0.407432i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.76318e6 | − | 3.05392e6i | −0.884560 | − | 1.53210i | −0.846217 | − | 0.532838i | \(-0.821125\pi\) |
−0.0383427 | − | 0.999265i | \(-0.512208\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 242553. | − | 1.37559e6i | 0.119866 | − | 0.679795i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.21640e6 | + | 2.10687e6i | −0.592197 | + | 1.02572i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.49626e6 | + | 1.27253e6i | 1.67698 | + | 0.610372i | 0.992892 | − | 0.119022i | \(-0.0379760\pi\) |
0.684093 | + | 0.729395i | \(0.260198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 249818. | − | 209622.i | 0.118066 | − | 0.0990690i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.12292e6 | −1.45437 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.75420e6 | −0.805091 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 498263. | − | 418092.i | 0.225378 | − | 0.189114i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.20176e6 | + | 437406.i | 0.535790 | + | 0.195012i | 0.595722 | − | 0.803191i | \(-0.296866\pi\) |
−0.0599317 | + | 0.998202i | \(0.519088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.95602e6 | + | 3.38792e6i | −0.859625 | + | 1.48891i | 0.0126622 | + | 0.999920i | \(0.495969\pi\) |
−0.872287 | + | 0.488994i | \(0.837364\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33044.8 | − | 187407.i | 0.0143165 | − | 0.0811927i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.03793e6 | + | 3.52980e6i | 0.870468 | + | 1.50769i | 0.861513 | + | 0.507735i | \(0.169517\pi\) |
0.00895472 | + | 0.999960i | \(0.497150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −288359. | − | 241962.i | −0.121440 | − | 0.101901i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −98534.1 | + | 35863.5i | −0.0409182 | + | 0.0148930i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −424380. | − | 2.40678e6i | −0.173788 | − | 0.985599i | −0.939534 | − | 0.342456i | \(-0.888741\pi\) |
0.765746 | − | 0.643143i | \(-0.222370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −442795. | + | 2.43619e6i | −0.178827 | + | 0.983880i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 196808. | + | 1.11615e6i | 0.0783928 | + | 0.444588i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.08875e6 | − | 396272.i | 0.427755 | − | 0.155690i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.40089e6 | + | 2.01459e6i | 0.930481 | + | 0.780767i | 0.975904 | − | 0.218201i | \(-0.0700189\pi\) |
−0.0454224 | + | 0.998968i | \(0.514463\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 695893. | + | 1.20532e6i | 0.266058 | + | 0.460826i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −85213.1 | + | 483268.i | −0.0321419 | + | 0.182286i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.32324e6 | + | 4.02398e6i | −0.864615 | + | 1.49756i | 0.00281439 | + | 0.999996i | \(0.499104\pi\) |
−0.867429 | + | 0.497561i | \(0.834229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.35882e6 | + | 494571.i | 0.498982 | + | 0.181614i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 216170. | − | 181388.i | 0.0783326 | − | 0.0657289i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.39435e6 | −1.57144 | −0.785718 | − | 0.618585i | \(-0.787706\pi\) | ||||
−0.785718 | + | 0.618585i | \(0.787706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 165640. | 0.0584590 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.16232e6 | − | 2.65350e6i | 1.10156 | − | 0.924319i | 0.104032 | − | 0.994574i | \(-0.466826\pi\) |
0.997529 | + | 0.0702547i | \(0.0223812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.63892e6 | + | 596517.i | 0.563514 | + | 0.205102i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.23097e6 | − | 2.13210e6i | 0.417801 | − | 0.723652i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −120666. | + | 684333.i | −0.0404308 | + | 0.229295i | −0.998327 | − | 0.0578202i | \(-0.981585\pi\) |
0.957896 | + | 0.287115i | \(0.0926961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −161825. | − | 280289.i | −0.0535307 | − | 0.0927180i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −323531. | − | 271475.i | −0.105666 | − | 0.0886641i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.84417e6 | + | 1.03519e6i | −0.917196 | + | 0.333832i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −700660. | − | 3.97364e6i | −0.223116 | − | 1.26535i | −0.866254 | − | 0.499604i | \(-0.833479\pi\) |
0.643138 | − | 0.765750i | \(-0.277632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −478766. | + | 567532.i | −0.150554 | + | 0.178467i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 601652. | + | 3.41214e6i | 0.186846 | + | 1.05966i | 0.923560 | + | 0.383453i | \(0.125265\pi\) |
−0.736714 | + | 0.676204i | \(0.763624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 298313. | − | 108577.i | 0.0914976 | − | 0.0333024i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 637465. | + | 534897.i | 0.193116 | + | 0.162044i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.16503e6 | − | 3.74994e6i | −0.647855 | − | 1.12212i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 165554. | − | 938903.i | 0.0489363 | − | 0.277532i | −0.950514 | − | 0.310682i | \(-0.899443\pi\) |
0.999450 | + | 0.0331498i | \(0.0105539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 423756. | − | 733967.i | 0.123740 | − | 0.214325i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 561680. | + | 204435.i | 0.162037 | + | 0.0589766i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.98976e6 | − | 2.50871e6i | 0.852151 | − | 0.715040i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −809228. | −0.227893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.67305e6 | −0.465559 | −0.232780 | − | 0.972530i | \(-0.574782\pi\) | ||||
−0.232780 | + | 0.972530i | \(0.574782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.44937e6 | − | 2.05526e6i | 0.673517 | − | 0.565148i | −0.240587 | − | 0.970628i | \(-0.577340\pi\) |
0.914104 | + | 0.405479i | \(0.132895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.56511e6 | + | 1.29759e6i | 0.968773 | + | 0.352605i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12542.0 | − | 21723.4i | 0.00336818 | − | 0.00583386i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 192071. | − | 1.08929e6i | 0.0509791 | − | 0.289117i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −124216. | − | 215149.i | −0.0325863 | − | 0.0564411i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.98412e6 | − | 4.18217e6i | −1.29239 | − | 1.08445i | −0.991406 | − | 0.130820i | \(-0.958239\pi\) |
−0.300989 | − | 0.953628i | \(-0.597317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 631885. | − | 229987.i | 0.161964 | − | 0.0589501i | −0.259766 | − | 0.965672i | \(-0.583645\pi\) |
0.421730 | + | 0.906722i | \(0.361423\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −392827. | − | 2.22783e6i | −0.0995356 | − | 0.564495i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.98172e6 | − | 1.15111e6i | −0.496407 | − | 0.288344i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 584926. | + | 3.31728e6i | 0.144857 | + | 0.821525i | 0.967482 | + | 0.252941i | \(0.0813978\pi\) |
−0.822625 | + | 0.568585i | \(0.807491\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23343e6 | + | 812903.i | −0.546861 | + | 0.199041i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 875761. | + | 734851.i | 0.212020 | + | 0.177906i | 0.742613 | − | 0.669721i | \(-0.233586\pi\) |
−0.530593 | + | 0.847627i | \(0.678031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.52374e6 | − | 6.10330e6i | −0.843537 | − | 1.46105i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 742126. | − | 4.20881e6i | 0.175675 | − | 0.996300i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.32175e6 | + | 5.75344e6i | −0.777591 | + | 1.34683i | 0.155736 | + | 0.987799i | \(0.450225\pi\) |
−0.933327 | + | 0.359028i | \(0.883108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.05429e6 | + | 1.47564e6i | 0.938585 | + | 0.341617i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.03958e6 | + | 872314.i | −0.238020 | + | 0.199723i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −177295. | −0.0401484 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.19460e6 | 1.61145 | 0.805723 | − | 0.592292i | \(-0.201777\pi\) | ||||
0.805723 | + | 0.592292i | \(0.201777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −581497. | + | 487934.i | −0.128830 | + | 0.108101i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.84545e6 | + | 1.39963e6i | 0.842742 | + | 0.306733i | 0.727078 | − | 0.686555i | \(-0.240878\pi\) |
0.115664 | + | 0.993288i | \(0.463100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.24350e6 | + | 3.88586e6i | −0.486378 | + | 0.842431i | −0.999877 | − | 0.0156588i | \(-0.995015\pi\) |
0.513500 | + | 0.858090i | \(0.328349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 441923. | − | 2.50627e6i | 0.0947794 | − | 0.537521i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.95647e6 | − | 3.38870e6i | −0.415126 | − | 0.719020i | 0.580315 | − | 0.814392i | \(-0.302929\pi\) |
−0.995442 | + | 0.0953718i | \(0.969596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.96906e6 | + | 1.65224e6i | 0.413359 | + | 0.346849i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.70753e6 | + | 621490.i | −0.354663 | + | 0.129087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.32527e6 | − | 7.51597e6i | −0.272365 | − | 1.54466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 467.291 | − | 177621.i | 9.50284e−5 | − | 0.0361209i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 259787. | + | 1.47332e6i | 0.0522782 | + | 0.296484i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.70914e6 | + | 2.80590e6i | −1.53521 | + | 0.558770i | −0.964890 | − | 0.262654i | \(-0.915402\pi\) |
−0.570318 | + | 0.821424i | \(0.693180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 337189. | + | 282936.i | 0.0664525 | + | 0.0557603i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −343615. | − | 595159.i | −0.0670200 | − | 0.116082i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.73662e6 | − | 9.84885e6i | 0.335235 | − | 1.90121i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.05649e6 | − | 5.29399e6i | 0.583983 | − | 1.01149i | −0.411019 | − | 0.911627i | \(-0.634827\pi\) |
0.995001 | − | 0.0998607i | \(-0.0318397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −651166. | − | 237005.i | −0.123146 | − | 0.0448214i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 574415. | − | 481992.i | 0.107528 | − | 0.0902268i | −0.587438 | − | 0.809269i | \(-0.699864\pi\) |
0.694967 | + | 0.719042i | \(0.255419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.12565e6 | −0.208586 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.31718e6 | 0.975367 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −304671. | + | 255649.i | −0.0553274 | + | 0.0464252i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.50875e6 | + | 2.36899e6i | 1.17016 | + | 0.425905i | 0.852718 | − | 0.522372i | \(-0.174953\pi\) |
0.317446 | + | 0.948276i | \(0.397175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −850716. | + | 1.47348e6i | −0.151422 | + | 0.262271i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 310961. | − | 1.76355e6i | 0.0548007 | − | 0.310790i | −0.945070 | − | 0.326868i | \(-0.894007\pi\) |
0.999871 | + | 0.0160776i | \(0.00511788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.35646e6 | − | 2.34946e6i | −0.236689 | − | 0.409958i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.29512e6 | − | 1.92583e6i | −0.396539 | − | 0.332735i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.57557e6 | + | 3.48522e6i | −1.63821 | + | 0.596260i | −0.986725 | − | 0.162400i | \(-0.948077\pi\) |
−0.651487 | + | 0.758660i | \(0.725854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −212574. | − | 1.20557e6i | −0.0360128 | − | 0.204239i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.85169e6 | + | 5.04613e6i | −0.310653 | + | 0.846575i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 682244. | + | 3.86920e6i | 0.113350 | + | 0.642840i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.10517e7 | − | 4.02250e6i | 1.81846 | − | 0.661865i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.12504e6 | + | 1.78312e6i | 0.346298 | + | 0.290578i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.39630e6 | + | 2.41846e6i | 0.225364 | + | 0.390342i | 0.956429 | − | 0.291966i | \(-0.0943095\pi\) |
−0.731065 | + | 0.682308i | \(0.760976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.49781e6 | + | 8.49448e6i | −0.239443 | + | 1.35795i | 0.593610 | + | 0.804753i | \(0.297702\pi\) |
−0.833053 | + | 0.553194i | \(0.813409\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26631.4 | − | 46127.0i | 0.00421693 | − | 0.00730394i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.18996e6 | − | 433110.i | −0.186640 | − | 0.0679316i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.30561e6 | + | 2.77374e6i | −0.513585 | + | 0.430949i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.82227e6 | 0.280464 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −438587. | −0.0668709 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −186508. | + | 156499.i | −0.0281718 | + | 0.0236389i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.86045e6 | + | 2.13303e6i | 0.876991 | + | 0.319199i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.68395e6 | + | 6.38080e6i | −0.546188 | + | 0.946026i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.51343e6 | + | 8.58309e6i | −0.222315 | + | 1.26081i | 0.645436 | + | 0.763814i | \(0.276676\pi\) |
−0.867752 | + | 0.496998i | \(0.834436\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 447741. | + | 775511.i | 0.0651670 | + | 0.112873i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.77168e6 | + | 1.48662e6i | 0.255503 | + | 0.214392i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.03856e6 | + | 2.92580e6i | −1.14871 | + | 0.418096i | −0.845051 | − | 0.534685i | \(-0.820430\pi\) |
−0.303658 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −585561. | − | 3.32088e6i | −0.0829166 | − | 0.470243i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.91333e6 | + | 3.96720e6i | −0.970082 | + | 0.556679i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 555312. | + | 3.14933e6i | 0.0772190 | + | 0.437931i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.31585e6 | − | 1.20687e6i | 0.456944 | − | 0.166314i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.60451e6 | + | 2.18544e6i | 0.355703 | + | 0.298471i | 0.803075 | − | 0.595877i | \(-0.203196\pi\) |
−0.447372 | + | 0.894348i | \(0.647640\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 387909. | + | 671878.i | 0.0525049 | + | 0.0909412i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −172083. | + | 975932.i | −0.0230851 | + | 0.130922i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.56746e6 | + | 4.44697e6i | −0.341375 | + | 0.591280i | −0.984688 | − | 0.174324i | \(-0.944226\pi\) |
0.643313 | + | 0.765603i | \(0.277559\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.06686e6 | − | 752276.i | −0.272390 | − | 0.0991417i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 673525. | − | 565155.i | 0.0879825 | − | 0.0738261i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.24402e6 | −0.679022 | −0.339511 | − | 0.940602i | \(-0.610262\pi\) | ||||
−0.339511 | + | 0.940602i | \(0.610262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24825e7 | 1.60218 | 0.801088 | − | 0.598547i | \(-0.204255\pi\) | ||||
0.801088 | + | 0.598547i | \(0.204255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.76463e6 | − | 3.99800e6i | 0.606237 | − | 0.508693i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 154484. | + | 56227.7i | 0.0194857 | + | 0.00709220i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.40693e6 | − | 2.43688e6i | 0.175928 | − | 0.304715i | −0.764554 | − | 0.644559i | \(-0.777041\pi\) |
0.940482 | + | 0.339844i | \(0.110374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −869028. | + | 4.92850e6i | −0.107730 | + | 0.610968i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.06182e6 | − | 3.57117e6i | −0.253402 | − | 0.438905i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.55269e6 | + | 2.98106e6i | 0.432898 | + | 0.363245i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −507917. | + | 184867.i | −0.0613626 | + | 0.0223341i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.40702e6 | − | 7.97961e6i | −0.168541 | − | 0.955842i | −0.945338 | − | 0.326092i | \(-0.894268\pi\) |
0.776797 | − | 0.629751i | \(-0.216843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.83476e6 | + | 1.53385e6i | −1.04932 | + | 0.182178i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −323075. | − | 1.83225e6i | −0.0380482 | − | 0.215782i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.90589e6 | + | 2.51354e6i | −0.806460 | + | 0.293528i | −0.712161 | − | 0.702016i | \(-0.752283\pi\) |
−0.0942994 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 541765. | + | 454595.i | 0.0627362 | + | 0.0526420i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.29134e6 | + | 2.23667e6i | 0.148288 | + | 0.256842i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −874115. | + | 4.95735e6i | −0.0995409 | + | 0.564524i | 0.893720 | + | 0.448625i | \(0.148086\pi\) |
−0.993261 | + | 0.115899i | \(0.963025\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.09419e6 | − | 3.62725e6i | 0.236500 | − | 0.409630i | −0.723208 | − | 0.690631i | \(-0.757333\pi\) |
0.959708 | + | 0.281001i | \(0.0906664\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.36379e6 | + | 2.68020e6i | 0.824723 | + | 0.300175i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.85575e6 | − | 4.91356e6i | 0.650420 | − | 0.545767i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.66875e6 | 0.624476 | 0.312238 | − | 0.950004i | \(-0.398921\pi\) | ||||
0.312238 | + | 0.950004i | \(0.398921\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.39017e6 | −0.261147 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −915850. | + | 768489.i | −0.0992479 | + | 0.0832789i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.42908e7 | − | 5.20142e6i | −1.53605 | − | 0.559076i | −0.570955 | − | 0.820981i | \(-0.693427\pi\) |
−0.965093 | + | 0.261906i | \(0.915649\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.75798e6 | + | 3.04492e6i | −0.187425 | + | 0.324629i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.36523e6 | − | 1.34139e7i | 0.250127 | − | 1.41854i | −0.558150 | − | 0.829740i | \(-0.688489\pi\) |
0.808277 | − | 0.588802i | \(-0.200400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.22728e6 | − | 2.12572e6i | −0.128741 | − | 0.222987i | 0.794448 | − | 0.607332i | \(-0.207760\pi\) |
−0.923189 | + | 0.384346i | \(0.874427\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.81109e6 | − | 3.19788e6i | −0.396570 | − | 0.332762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.99709e6 | + | 2.54673e6i | −0.722267 | + | 0.262884i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.63232e6 | − | 9.25733e6i | −0.167149 | − | 0.947951i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.38267e6 | + | 6.60032e6i | 0.242045 | + | 0.670496i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −304895. | − | 1.72914e6i | −0.0307272 | − | 0.174263i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.33848e7 | − | 4.87167e6i | 1.33825 | − | 0.487084i | 0.428991 | − | 0.903309i | \(-0.358869\pi\) |
0.909262 | + | 0.416224i | \(0.136647\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 789248. | + | 662258.i | 0.0782896 | + | 0.0656928i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −558586. | − | 967499.i | −0.0549738 | − | 0.0952174i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 130059. | − | 737602.i | 0.0126997 | − | 0.0720233i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −606258. | + | 1.05007e6i | −0.0587361 | + | 0.101734i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.43998e6 | + | 2.70793e6i | 0.715198 | + | 0.260311i | 0.673886 | − | 0.738835i | \(-0.264624\pi\) |
0.0413124 | + | 0.999146i | \(0.486846\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.49275e6 | − | 5.44806e6i | 0.619300 | − | 0.519654i | −0.278284 | − | 0.960499i | \(-0.589765\pi\) |
0.897583 | + | 0.440845i | \(0.145321\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.21941e6 | 0.588640 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.43995e7 | 1.35234 | 0.676169 | − | 0.736746i | \(-0.263639\pi\) | ||||
0.676169 | + | 0.736746i | \(0.263639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.32737e6 | − | 3.63110e6i | 0.403286 | − | 0.338397i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.52673e6 | − | 919656.i | −0.233672 | − | 0.0850497i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.57952e6 | − | 4.46785e6i | 0.236731 | − | 0.410030i | −0.723043 | − | 0.690803i | \(-0.757257\pi\) |
0.959774 | + | 0.280772i | \(0.0905906\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −494639. | + | 2.80524e6i | −0.0450490 | + | 0.255485i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.86603e6 | − | 3.23207e6i | −0.168658 | − | 0.292124i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.93040e6 | − | 4.13709e6i | −0.442251 | − | 0.371092i | 0.394300 | − | 0.918982i | \(-0.370987\pi\) |
−0.836551 | + | 0.547889i | \(0.815431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.91519e7 | + | 6.97073e6i | −1.70494 | + | 0.620547i | −0.996373 | − | 0.0850983i | \(-0.972880\pi\) |
−0.708566 | + | 0.705645i | \(0.750657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17493.0 | − | 99207.8i | −0.00154554 | − | 0.00876520i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.92950e6 | + | 882581.i | 0.432263 | + | 0.0773928i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.28107e6 | − | 7.26532e6i | −0.111496 | − | 0.632325i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 680332. | − | 247621.i | 0.0587700 | − | 0.0213905i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00779e6 | − | 6.71934e6i | −0.686604 | − | 0.576129i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.15315e6 | − | 7.19347e6i | −0.353460 | − | 0.612211i | 0.633393 | − | 0.773830i | \(-0.281662\pi\) |
−0.986853 | + | 0.161619i | \(0.948328\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 66955.7 | − | 379724.i | 0.00565624 | − | 0.0320781i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.48034e6 | − | 9.49222e6i | 0.459553 | − | 0.795969i | −0.539384 | − | 0.842060i | \(-0.681343\pi\) |
0.998937 | + | 0.0460906i | \(0.0146763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.92927e6 | − | 3.61396e6i | −0.826500 | − | 0.300821i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.05316e6 | − | 2.56191e6i | 0.252280 | − | 0.211688i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.88927e7 | −1.54968 | −0.774838 | − | 0.632159i | \(-0.782169\pi\) | ||||
−0.774838 | + | 0.632159i | \(0.782169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.71613e6 | −0.465453 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.42198e6 | − | 1.19319e6i | 0.114948 | − | 0.0964532i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −443012. | − | 161243.i | −0.0355523 | − | 0.0129400i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.75357e6 | + | 4.76933e6i | −0.219382 | + | 0.379981i | −0.954619 | − | 0.297829i | \(-0.903737\pi\) |
0.735237 | + | 0.677810i | \(0.237071\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 975549. | − | 5.53261e6i | 0.0771642 | − | 0.437620i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.72896e6 | + | 4.72670e6i | 0.214306 | + | 0.371189i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.34020e6 | + | 1.12456e6i | 0.104493 | + | 0.0876800i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.14248e7 | − | 4.15827e6i | 0.884411 | − | 0.321899i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 228643. | + | 1.29670e6i | 0.0175736 | + | 0.0996651i | 0.992333 | − | 0.123593i | \(-0.0394418\pi\) |
−0.974759 | + | 0.223258i | \(0.928331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.96671e6 | − | 9.54525e6i | −0.607982 | − | 0.728448i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.66429e6 | + | 9.43868e6i | 0.126112 | + | 0.715218i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.69352e6 | + | 980361.i | −0.202662 | + | 0.0737628i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.11882e6 | + | 5.97340e6i | 0.531854 | + | 0.446278i | 0.868741 | − | 0.495267i | \(-0.164930\pi\) |
−0.336887 | + | 0.941545i | \(0.609374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.87469e6 | + | 8.44321e6i | 0.361637 | + | 0.626374i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.44118e6 | − | 8.17334e6i | 0.106168 | − | 0.602110i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −837788. | + | 1.45109e6i | −0.0612871 | + | 0.106152i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −695549. | − | 253159.i | −0.0505277 | − | 0.0183906i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.70837e6 | + | 5.62899e6i | −0.483944 | + | 0.406077i | −0.851850 | − | 0.523786i | \(-0.824519\pi\) |
0.367906 | + | 0.929863i | \(0.380075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.15113e6 | 0.297392 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23560e6 | 0.0879089 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 438006. | − | 367530.i | 0.0309481 | − | 0.0259686i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.75800e7 | + | 6.39860e6i | 1.23363 | + | 0.449003i | 0.874838 | − | 0.484416i | \(-0.160968\pi\) |
0.358788 | + | 0.933419i | \(0.383190\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.03702e6 | + | 3.52821e6i | −0.141963 | + | 0.245887i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 537390. | − | 3.04769e6i | 0.0371960 | − | 0.210949i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.12351e7 | + | 1.94597e7i | 0.772352 | + | 1.33775i | 0.936271 | + | 0.351280i | \(0.114253\pi\) |
−0.163918 | + | 0.986474i | \(0.552413\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.59953e6 | − | 3.85947e6i | −0.314048 | − | 0.263517i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.28275e7 | − | 8.30854e6i | 1.54807 | − | 0.563450i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.15804e6 | + | 1.22389e7i | 0.145361 | + | 0.824384i | 0.967076 | + | 0.254486i | \(0.0819062\pi\) |
−0.821715 | + | 0.569898i | \(0.806983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −457081. | − | 547648.i | −0.0305807 | − | 0.0366400i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.21380e6 | + | 1.82264e7i | 0.213573 | + | 1.21123i | 0.883365 | + | 0.468686i | \(0.155272\pi\) |
−0.669792 | + | 0.742549i | \(0.733617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.70863e7 | + | 9.85860e6i | −1.78796 | + | 0.650766i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.63040e6 | − | 8.08087e6i | −0.631456 | − | 0.529854i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 128621. | + | 222778.i | 0.00837737 | + | 0.0145100i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.82373e6 | − | 1.03429e7i | 0.117995 | − | 0.669180i | −0.867229 | − | 0.497909i | \(-0.834101\pi\) |
0.985224 | − | 0.171271i | \(-0.0547875\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.93146e6 | + | 3.34539e6i | −0.124136 | + | 0.215010i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.60096e6 | + | 3.13049e6i | 0.549136 | + | 0.199869i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.07683e6 | + | 3.42087e6i | −0.258573 | + | 0.216968i | −0.762853 | − | 0.646572i | \(-0.776202\pi\) |
0.504281 | + | 0.863540i | \(0.331758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.49485e6 | −0.409228 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.04886e7 | −1.28248 | −0.641241 | − | 0.767340i | \(-0.721580\pi\) | ||||
−0.641241 | + | 0.767340i | \(0.721580\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.87191e6 | − | 1.57072e6i | 0.116405 | − | 0.0976756i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.02606e6 | + | 737427.i | 0.125170 | + | 0.0455581i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −287122. | + | 497310.i | −0.0176229 | + | 0.0305238i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −609711. | + | 3.45784e6i | −0.0371799 | + | 0.210858i | −0.997738 | − | 0.0672214i | \(-0.978587\pi\) |
0.960558 | + | 0.278079i | \(0.0896977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.50957e6 | − | 9.54286e6i | −0.333797 | − | 0.578153i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.02804e7 | + | 1.70173e7i | 1.22075 | + | 1.02433i | 0.998785 | + | 0.0492803i | \(0.0156928\pi\) |
0.221969 | + | 0.975054i | \(0.428752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 604444. | − | 220000.i | 0.0361495 | − | 0.0131573i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −647407. | − | 3.67163e6i | −0.0384702 | − | 0.218175i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.21944e7 | + | 2.18330e6i | 0.719974 | + | 0.128905i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 652702. | + | 3.70165e6i | 0.0382901 | + | 0.217154i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.62595e7 | + | 5.91798e6i | −0.947770 | + | 0.344960i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.38842e6 | + | 7.87782e6i | 0.543774 | + | 0.456280i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.75399e6 | − | 4.77005e6i | −0.158499 | − | 0.274528i | 0.775829 | − | 0.630943i | \(-0.217332\pi\) |
−0.934327 | + | 0.356416i | \(0.883999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −999833. | + | 5.67033e6i | −0.0571788 | + | 0.324277i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.16197e6 | + | 2.01258e6i | −0.0660316 | + | 0.114370i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 998553. | + | 363443.i | 0.0563882 | + | 0.0205236i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.89516e6 | + | 2.42933e6i | −0.162463 | + | 0.136323i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.43780e7 | 0.801776 | 0.400888 | − | 0.916127i | \(-0.368702\pi\) | ||||
0.400888 | + | 0.916127i | \(0.368702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.76903e6 | 0.264279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.73899e7 | + | 1.45918e7i | −0.957667 | + | 0.803578i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.08716e7 | − | 3.95693e6i | −0.594981 | − | 0.216556i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.31755e6 | + | 4.01411e6i | −0.126049 | + | 0.218323i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.46949e6 | − | 8.33391e6i | 0.0794298 | − | 0.450469i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.85184e6 | + | 1.70639e7i | 0.529232 | + | 0.916656i | 0.999419 | + | 0.0340896i | \(0.0108532\pi\) |
−0.470187 | + | 0.882567i | \(0.655814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.67971e6 | + | 3.92674e6i | 0.249843 | + | 0.209643i | 0.759105 | − | 0.650969i | \(-0.225637\pi\) |
−0.509262 | + | 0.860612i | \(0.670082\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.32084e7 | − | 4.80747e6i | 0.700849 | − | 0.255088i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 811581. | + | 4.60271e6i | 0.0427994 | + | 0.242728i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.44074e6 | − | 2.06118e7i | −0.389997 | − | 1.08034i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 99168.8 | + | 562414.i | 0.00516613 | + | 0.0292986i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.87272e6 | − | 1.40955e6i | 0.200520 | − | 0.0729833i | −0.239808 | − | 0.970820i | \(-0.577084\pi\) |
0.440328 | + | 0.897837i | \(0.354862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −285331. | − | 239421.i | −0.0146842 | − | 0.0123215i | 0.635416 | − | 0.772170i | \(-0.280829\pi\) |
−0.650100 | + | 0.759849i | \(0.725273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −251688. | − | 435936.i | −0.0128744 | − | 0.0222991i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 271216. | − | 1.53814e6i | 0.0137896 | − | 0.0782047i | −0.977136 | − | 0.212614i | \(-0.931802\pi\) |
0.990926 | + | 0.134409i | \(0.0429136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.34675e6 | + | 1.09929e7i | −0.320749 | + | 0.555554i | −0.980643 | − | 0.195805i | \(-0.937268\pi\) |
0.659894 | + | 0.751359i | \(0.270601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.63059e7 | − | 5.93486e6i | −0.819109 | − | 0.298131i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.28868e6 | + | 1.92043e6i | −0.114280 | + | 0.0958926i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.14755e7 | 0.569580 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.94655e7 | −0.960401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.14530e7 | + | 9.61020e6i | −0.561713 | + | 0.471333i | −0.878884 | − | 0.477035i | \(-0.841711\pi\) |
0.317171 | + | 0.948368i | \(0.397267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.83687e6 | − | 1.76048e6i | −0.235817 | − | 0.0858303i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −497348. | + | 861431.i | −0.0241041 | + | 0.0417495i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.50896e6 | + | 1.99003e7i | −0.169058 | + | 0.958776i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.03828e6 | − | 6.99450e6i | −0.193414 | − | 0.335003i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.26944e7 | − | 1.06518e7i | −0.604424 | − | 0.507172i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.08135e7 | − | 3.93580e6i | 0.511851 | − | 0.186298i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.03106e6 | + | 3.42039e7i | 0.283806 | + | 1.60954i | 0.709520 | + | 0.704685i | \(0.248912\pi\) |
−0.425714 | + | 0.904858i | \(0.639977\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.50423e7 | − | 2.61159e6i | 0.703721 | − | 0.122177i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.31012e6 | − | 7.43004e6i | −0.0609337 | − | 0.345572i | −0.999998 | − | 0.00183155i | \(-0.999417\pi\) |
0.939065 | − | 0.343741i | \(-0.111694\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.55252e7 | − | 9.29041e6i | 1.18028 | − | 0.429588i | 0.323981 | − | 0.946064i | \(-0.394979\pi\) |
0.856302 | + | 0.516476i | \(0.172756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.84575e6 | + | 2.38786e6i | 0.130824 | + | 0.109775i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.16468e6 | − | 5.48138e6i | −0.144645 | − | 0.250532i | 0.784596 | − | 0.620008i | \(-0.212871\pi\) |
−0.929240 | + | 0.369476i | \(0.879537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.24893e6 | − | 1.84256e7i | 0.147639 | − | 0.837301i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.57598e6 | − | 9.65788e6i | 0.251926 | − | 0.436349i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.84001e7 | + | 1.03368e7i | 1.27576 | + | 0.464340i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.89170e6 | + | 1.58733e6i | −0.0844904 | + | 0.0708959i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.22138e7 | −1.43056 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.03046e7 | −0.454999 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.06978e7 | − | 1.73675e7i | 0.908712 | − | 0.762500i | −0.0631619 | − | 0.998003i | \(-0.520118\pi\) |
0.971873 | + | 0.235504i | \(0.0756740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.75239e7 | − | 6.37819e6i | −0.764996 | − | 0.278436i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.17187e7 | − | 2.02974e7i | 0.508675 | − | 0.881052i | −0.491274 | − | 0.871005i | \(-0.663469\pi\) |
0.999950 | − | 0.0100467i | \(-0.00319801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.38716e6 | − | 7.86699e6i | 0.0598722 | − | 0.339552i | −0.940127 | − | 0.340824i | \(-0.889294\pi\) |
0.999999 | + | 0.00127210i | \(0.000404923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.30174e6 | + | 3.98673e6i | 0.0987865 | + | 0.171103i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.42289e6 | + | 4.55035e6i | 0.231431 | + | 0.194194i | 0.751127 | − | 0.660157i | \(-0.229510\pi\) |
−0.519696 | + | 0.854351i | \(0.673955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.10918e6 | + | 403710.i | −0.0470705 | + | 0.0171323i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.44290e6 | − | 8.18311e6i | −0.0608896 | − | 0.345322i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.92897e7 | − | 1.68079e7i | 1.22910 | − | 0.705316i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.30418e6 | − | 4.14241e7i | −0.304799 | − | 1.72860i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 620414. | − | 225812.i | 0.0257454 | − | 0.00937057i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.21120e7 | − | 1.85542e7i | −0.912493 | − | 0.765672i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 940285. | + | 1.62862e6i | 0.0385876 | + | 0.0668356i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.14108e6 | − | 6.47139e6i | 0.0465690 | − | 0.264106i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.01984e6 | − | 5.23051e6i | 0.122564 | − | 0.212287i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.22883e7 | − | 1.53917e7i | −1.70687 | − | 0.621251i | −0.710296 | − | 0.703903i | \(-0.751439\pi\) |
−0.996578 | + | 0.0826519i | \(0.973661\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.69420e6 | + | 5.61710e6i | −0.268713 | + | 0.225477i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.75563e7 | 1.10008 | 0.550040 | − | 0.835138i | \(-0.314612\pi\) | ||||
0.550040 | + | 0.835138i | \(0.314612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.89715e7 | −1.54729 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.52572e6 | − | 5.47573e6i | 0.257677 | − | 0.216217i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.82814e6 | + | 1.02936e6i | 0.111065 | + | 0.0404244i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34089e7 | − | 4.05453e7i | 0.914306 | − | 1.58362i | 0.106391 | − | 0.994324i | \(-0.466070\pi\) |
0.807915 | − | 0.589300i | \(-0.200596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.44234e6 | − | 1.95225e7i | 0.133722 | − | 0.758378i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −191047. | − | 330903.i | −0.00738136 | − | 0.0127849i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 683215. | + | 573286.i | 0.0262545 | + | 0.0220301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.18922e7 | − | 4.32841e6i | 0.454531 | − | 0.165436i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 407827. | + | 2.31290e6i | 0.0155037 | + | 0.0879261i | 0.991578 | − | 0.129512i | \(-0.0413411\pi\) |
−0.976074 | + | 0.217438i | \(0.930230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.28795e6 | + | 1.98607e7i | −0.275570 | + | 0.750968i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −986862. | − | 5.59677e6i | −0.0371152 | − | 0.210491i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.28073e6 | − | 2.28600e6i | 0.234953 | − | 0.0855159i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.23241e6 | − | 3.55141e6i | −0.157485 | − | 0.132145i | 0.560640 | − | 0.828059i | \(-0.310555\pi\) |
−0.718125 | + | 0.695914i | \(0.754999\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.84169e6 | + | 1.01181e7i | 0.216210 | + | 0.374486i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.57824e6 | + | 4.86496e7i | −0.315809 | + | 1.79104i | 0.251839 | + | 0.967769i | \(0.418965\pi\) |
−0.567648 | + | 0.823272i | \(0.692146\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.73306e6 | + | 9.92995e6i | −0.209946 | + | 0.363637i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.02156e7 | + | 3.71816e6i | 0.372120 | + | 0.135441i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.82651e7 | − | 1.53262e7i | 0.661830 | − | 0.555341i | −0.248805 | − | 0.968554i | \(-0.580038\pi\) |
0.910635 | + | 0.413212i | \(0.135593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.17607e6 | 0.0423904 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.37533e6 | 0.264442 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.47639e7 | − | 1.23884e7i | 0.526585 | − | 0.441858i | −0.340335 | − | 0.940304i | \(-0.610540\pi\) |
0.866920 | + | 0.498447i | \(0.166096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.94200e7 | − | 1.43477e7i | −1.39865 | − | 0.509067i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.12945e7 | + | 1.95626e7i | −0.398645 | + | 0.690473i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.04874e6 | + | 5.94773e6i | −0.0368233 | + | 0.208836i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.92180e6 | − | 3.32866e6i | −0.0671275 | − | 0.116268i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 600767. | + | 504103.i | 0.0208757 | + | 0.0175168i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.17180e7 | − | 1.15444e7i | 1.09645 | − | 0.399074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.07102e6 | + | 4.57730e7i | 0.277563 | + | 1.57414i | 0.730700 | + | 0.682699i | \(0.239194\pi\) |
−0.453136 | + | 0.891441i | \(0.649695\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7485.90 | + | 2.84544e6i | −0.000256115 | + | 0.0973509i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.76725e6 | − | 3.27077e7i | −0.196300 | − | 1.11327i | −0.910555 | − | 0.413388i | \(-0.864345\pi\) |
0.714255 | − | 0.699885i | \(-0.246766\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.41889e6 | − | 1.97231e6i | 0.183497 | − | 0.0667873i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39198.7 | + | 32891.6i | 0.00132057 | + | 0.00110809i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.02870e7 | + | 1.78177e7i | 0.344789 | + | 0.597192i | 0.985315 | − | 0.170744i | \(-0.0546171\pi\) |
−0.640526 | + | 0.767936i | \(0.721284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.22199e7 | + | 6.93027e7i | −0.407486 | + | 2.31097i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.72486e6 | − | 6.45165e6i | 0.123577 | − | 0.214042i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.02333e7 | − | 1.10040e7i | −0.997933 | − | 0.363218i | −0.209146 | − | 0.977884i | \(-0.567068\pi\) |
−0.788787 | + | 0.614666i | \(0.789291\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.61264e6 | + | 8.06596e6i | −0.315684 | + | 0.264890i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.01264e7 | 0.330875 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.02825e7 | 0.659371 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.72919e7 | + | 3.12916e7i | −1.20623 | + | 1.01215i | −0.206801 | + | 0.978383i | \(0.566305\pi\) |
−0.999430 | + | 0.0337652i | \(0.989250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.69646e7 | − | 9.81429e6i | −0.867801 | − | 0.315854i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.70957e6 | − | 1.50854e7i | 0.278894 | − | 0.483059i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.67241e6 | + | 5.48549e7i | −0.308174 | + | 1.74774i | 0.299998 | + | 0.953940i | \(0.403014\pi\) |
−0.608173 | + | 0.793805i | \(0.708097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.34949e7 | − | 2.33738e7i | −0.427815 | − | 0.740997i |
(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 | 76.6.i.a.9.5 | ✓ | 48 | |
19.17 | even | 9 | inner | 76.6.i.a.17.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.i.a.9.5 | ✓ | 48 | 1.1 | even | 1 | trivial | |
76.6.i.a.17.5 | yes | 48 | 19.17 | even | 9 | inner |