Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(47,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.z (of order \(12\), degree \(4\), 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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 47.12 | ||
Character | \(\chi\) | \(=\) | 448.47 |
Dual form | 448.2.z.a.143.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.665801 | − | 2.48480i | 0.384400 | − | 1.43460i | −0.454710 | − | 0.890640i | \(-0.650257\pi\) |
0.839110 | − | 0.543962i | \(-0.183076\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.12401 | + | 0.837076i | −1.39710 | + | 0.374352i | −0.877302 | − | 0.479938i | \(-0.840659\pi\) |
−0.519797 | + | 0.854290i | \(0.673992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56215 | − | 2.13534i | −0.590436 | − | 0.807084i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.13287 | − | 1.80877i | −1.04429 | − | 0.602922i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.376195 | + | 1.40398i | −0.113427 | + | 0.423315i | −0.999164 | − | 0.0408713i | \(-0.986987\pi\) |
0.885737 | + | 0.464187i | \(0.153653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.11315 | + | 3.11315i | −0.863433 | + | 0.863433i | −0.991735 | − | 0.128303i | \(-0.959047\pi\) |
0.128303 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.31987i | 2.14818i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.02443 | − | 1.16881i | 0.490997 | − | 0.283477i | −0.233991 | − | 0.972239i | \(-0.575179\pi\) |
0.724988 | + | 0.688761i | \(0.241845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.40643 | + | 1.18070i | −1.01090 | + | 0.270871i | −0.726007 | − | 0.687687i | \(-0.758626\pi\) |
−0.284897 | + | 0.958558i | \(0.591959\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.34599 | + | 2.45991i | −1.38481 | + | 0.536797i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.15450 | − | 1.99965i | 0.240729 | − | 0.416955i | −0.720193 | − | 0.693774i | \(-0.755947\pi\) |
0.960922 | + | 0.276819i | \(0.0892802\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.72861 | − | 2.73006i | 0.945722 | − | 0.546013i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.12329 | + | 1.12329i | −0.216177 | + | 0.216177i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.55163 | − | 1.55163i | −0.288130 | − | 0.288130i | 0.548210 | − | 0.836341i | \(-0.315309\pi\) |
−0.836341 | + | 0.548210i | \(0.815309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.88952 | − | 6.73685i | −0.698579 | − | 1.20997i | −0.968959 | − | 0.247221i | \(-0.920483\pi\) |
0.270380 | − | 0.962754i | \(-0.412851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23814 | + | 1.86954i | 0.563687 | + | 0.325445i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.66761 | + | 5.36320i | 1.12703 | + | 0.906546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.272421 | + | 1.01669i | 0.0447857 | + | 0.167142i | 0.984697 | − | 0.174277i | \(-0.0557589\pi\) |
−0.939911 | + | 0.341420i | \(0.889092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.66282 | + | 9.80830i | 0.906778 | + | 1.57058i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.77210 | −0.432929 | −0.216464 | − | 0.976290i | \(-0.569453\pi\) | ||||
−0.216464 | + | 0.976290i | \(0.569453\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.12142 | − | 7.12142i | −1.08601 | − | 1.08601i | −0.995935 | − | 0.0900717i | \(-0.971290\pi\) |
−0.0900717 | − | 0.995935i | \(-0.528710\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.3012 | + | 3.02815i | 1.68468 | + | 0.451410i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.42516 | + | 2.46844i | −0.207880 | + | 0.360059i | −0.951047 | − | 0.309047i | \(-0.899990\pi\) |
0.743166 | + | 0.669107i | \(0.233323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.11939 | + | 6.67144i | −0.302770 | + | 0.953064i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.55638 | − | 5.80851i | −0.217937 | − | 0.813354i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0925 | + | 2.97221i | 1.52367 | + | 0.408265i | 0.920947 | − | 0.389689i | \(-0.127417\pi\) |
0.602719 | + | 0.797954i | \(0.294084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.70094i | − | 0.633875i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.7352i | 1.55437i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.77383 | − | 1.01120i | −0.491311 | − | 0.131646i | 0.00465348 | − | 0.999989i | \(-0.498519\pi\) |
−0.495965 | + | 0.868343i | \(0.665185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.72571 | − | 13.9045i | −0.477028 | − | 1.78029i | −0.613551 | − | 0.789655i | \(-0.710259\pi\) |
0.136523 | − | 0.990637i | \(-0.456407\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03167 | + | 9.51532i | 0.129978 | + | 1.19882i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.11957 | − | 12.3315i | 0.883074 | − | 1.52953i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59612 | − | 0.695627i | −0.317166 | − | 0.0849844i | 0.0967240 | − | 0.995311i | \(-0.469164\pi\) |
−0.413890 | + | 0.910327i | \(0.635830\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.20006 | − | 4.20006i | −0.505628 | − | 0.505628i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.48345 | 0.888122 | 0.444061 | − | 0.895997i | \(-0.353537\pi\) | ||||
0.444061 | + | 0.895997i | \(0.353537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.65210 | − | 9.78973i | −0.661529 | − | 1.14580i | −0.980214 | − | 0.197941i | \(-0.936575\pi\) |
0.318685 | − | 0.947861i | \(-0.396759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.63536 | − | 13.5673i | −0.419775 | − | 1.56662i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.58565 | − | 1.38991i | 0.408623 | − | 0.158395i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.706717 | + | 0.408024i | 0.0795119 | + | 0.0459062i | 0.539229 | − | 0.842159i | \(-0.318716\pi\) |
−0.459717 | + | 0.888066i | \(0.652049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.38303 | − | 5.85958i | −0.375892 | − | 0.651065i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.65285 | − | 2.65285i | −0.291188 | − | 0.291188i | 0.546361 | − | 0.837550i | \(-0.316013\pi\) |
−0.837550 | + | 0.546361i | \(0.816013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.34597 | + | 5.34597i | −0.579852 | + | 0.579852i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.88857 | + | 2.82241i | −0.524109 | + | 0.302595i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.40944 | + | 4.17328i | −0.255400 | + | 0.442367i | −0.965004 | − | 0.262234i | \(-0.915541\pi\) |
0.709604 | + | 0.704601i | \(0.248874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.5108 | + | 1.78445i | 1.20666 | + | 0.187061i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −19.3294 | + | 5.17929i | −2.00436 | + | 0.537068i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7774 | − | 7.37703i | 1.31093 | − | 0.756867i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.86541i | 0.595542i | 0.954637 | + | 0.297771i | \(0.0962432\pi\) | ||||
−0.954637 | + | 0.297771i | \(0.903757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.71804 | − | 3.71804i | 0.373677 | − | 0.373677i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.373632 | − | 1.39442i | 0.0371778 | − | 0.138749i | −0.944842 | − | 0.327525i | \(-0.893785\pi\) |
0.982020 | + | 0.188776i | \(0.0604520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.10134 | + | 1.21321i | 0.207051 | + | 0.119541i | 0.599940 | − | 0.800045i | \(-0.295191\pi\) |
−0.392889 | + | 0.919586i | \(0.628524\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.7658 | − | 12.9969i | 1.73376 | − | 1.26836i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.34758 | − | 1.16493i | 0.420297 | − | 0.112618i | −0.0424712 | − | 0.999098i | \(-0.513523\pi\) |
0.462768 | + | 0.886480i | \(0.346856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.842750 | − | 3.14518i | 0.0807208 | − | 0.301254i | −0.913749 | − | 0.406280i | \(-0.866826\pi\) |
0.994470 | + | 0.105026i | \(0.0334925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.70765 | 0.256998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.5397 | 1.08556 | 0.542781 | − | 0.839875i | \(-0.317372\pi\) | ||||
0.542781 | + | 0.839875i | \(0.317372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.93280 | + | 7.21331i | −0.180235 | + | 0.672645i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.3841 | − | 4.12215i | 1.42226 | − | 0.381093i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.65827 | − | 2.49701i | −0.518693 | − | 0.228901i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.69665 | + | 4.44366i | 0.699695 | + | 0.403969i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.84566 | + | 6.88811i | −0.166418 | + | 0.621080i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.05228 | + | 1.05228i | −0.0941192 | + | 0.0941192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.49210i | 0.398610i | 0.979938 | + | 0.199305i | \(0.0638684\pi\) | ||||
−0.979938 | + | 0.199305i | \(0.936132\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.4368 | + | 12.9539i | −1.97545 | + | 1.14053i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3612 | − | 3.58012i | 1.16737 | − | 0.312796i | 0.377465 | − | 0.926024i | \(-0.376796\pi\) |
0.789907 | + | 0.613227i | \(0.210129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.40469 | + | 7.56482i | 0.815490 | + | 0.655953i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.56889 | − | 4.44945i | 0.221095 | − | 0.382947i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.18423 | + | 1.26106i | −0.186611 | + | 0.107740i | −0.590395 | − | 0.807114i | \(-0.701028\pi\) |
0.403784 | + | 0.914854i | \(0.367695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00381 | + | 6.00381i | −0.509237 | + | 0.509237i | −0.914292 | − | 0.405055i | \(-0.867252\pi\) |
0.405055 | + | 0.914292i | \(0.367252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.18472 | + | 5.18472i | 0.436632 | + | 0.436632i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.19964 | − | 5.54195i | −0.267568 | − | 0.463441i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.14613 | + | 3.54847i | 0.510409 | + | 0.294685i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.1661 | + | 9.70812i | 1.25088 | + | 0.800713i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.19951 | − | 8.20870i | −0.180191 | − | 0.672483i | −0.995609 | − | 0.0936097i | \(-0.970159\pi\) |
0.815418 | − | 0.578873i | \(-0.196507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.11927 | − | 8.86683i | −0.416600 | − | 0.721572i | 0.578995 | − | 0.815331i | \(-0.303445\pi\) |
−0.995595 | + | 0.0937588i | \(0.970112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.45639 | −0.683659 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.7902 | + | 17.7902i | 1.42894 | + | 1.42894i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1817 | + | 3.79998i | 1.13183 | + | 0.303272i | 0.775660 | − | 0.631151i | \(-0.217417\pi\) |
0.356166 | + | 0.934423i | \(0.384084\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7707 | − | 25.5836i | 1.17139 | − | 2.02892i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.07342 | + | 0.658494i | −0.478653 | + | 0.0518966i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.94974 | + | 22.2047i | 0.466019 | + | 1.73921i | 0.653488 | + | 0.756937i | \(0.273305\pi\) |
−0.187468 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.6809 | − | 3.12989i | −0.909358 | − | 0.243662i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.82099i | 0.295677i | 0.989011 | + | 0.147839i | \(0.0472316\pi\) | ||||
−0.989011 | + | 0.147839i | \(0.952768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.38341i | − | 0.491032i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.9404 | + | 4.27121i | 1.21899 | + | 0.326628i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.15162 | + | 8.02996i | 0.163585 | + | 0.610506i | 0.998216 | + | 0.0596981i | \(0.0190138\pi\) |
−0.834632 | + | 0.550808i | \(0.814320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2164 | − | 5.83245i | −0.999067 | − | 0.440892i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.02524 | + | 8.70397i | −0.377720 | + | 0.654230i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6644 | − | 5.00112i | −1.39504 | − | 0.373801i | −0.518482 | − | 0.855089i | \(-0.673503\pi\) |
−0.876563 | + | 0.481288i | \(0.840169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.07189 | − | 6.07189i | −0.451320 | − | 0.451320i | 0.444472 | − | 0.895793i | \(-0.353391\pi\) |
−0.895793 | + | 0.444472i | \(0.853391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −37.0306 | −2.73738 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.70209 | − | 2.94810i | −0.125140 | − | 0.216749i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.879398 | + | 3.28196i | 0.0643080 | + | 0.240001i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.15336 | + | 0.643867i | 0.302112 | + | 0.0468344i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.1707 | − | 7.60410i | −0.952997 | − | 0.550213i | −0.0589865 | − | 0.998259i | \(-0.518787\pi\) |
−0.894011 | + | 0.448046i | \(0.852120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2397 | − | 19.4678i | −0.809053 | − | 1.40132i | −0.913521 | − | 0.406792i | \(-0.866647\pi\) |
0.104468 | − | 0.994528i | \(-0.466686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −25.9010 | − | 25.9010i | −1.85481 | − | 1.85481i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.31581 | + | 8.31581i | −0.592477 | + | 0.592477i | −0.938300 | − | 0.345823i | \(-0.887600\pi\) |
0.345823 | + | 0.938300i | \(0.387600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.85088 | + | 5.11006i | −0.627422 | + | 0.362242i | −0.779753 | − | 0.626087i | \(-0.784655\pi\) |
0.152331 | + | 0.988330i | \(0.451322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.45699 | + | 5.98769i | −0.243837 | + | 0.422339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.889390 | + | 5.73713i | −0.0624229 | + | 0.402668i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.66006 | − | 2.32046i | 0.604845 | − | 0.162068i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.23378 | + | 4.17642i | −0.502782 | + | 0.290282i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.63070i | − | 0.458655i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.73766 | + | 5.73766i | −0.394997 | + | 0.394997i | −0.876464 | − | 0.481467i | \(-0.840104\pi\) |
0.481467 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.98248 | − | 18.5949i | 0.341394 | − | 1.27410i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.2086 | + | 16.2862i | 1.92381 | + | 1.11071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.30949 | + | 18.8294i | −0.564085 | + | 1.27822i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.0887 | + | 7.52635i | −1.89806 | + | 0.508583i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.66369 | + | 9.94104i | −0.179179 | + | 0.668706i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4929 | −1.17141 | −0.585705 | − | 0.810524i | \(-0.699182\pi\) | ||||
−0.585705 | + | 0.810524i | \(0.699182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.7522 | −1.31681 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.53614 | − | 16.9291i | 0.301074 | − | 1.12362i | −0.635198 | − | 0.772349i | \(-0.719081\pi\) |
0.936272 | − | 0.351275i | \(-0.114252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.75227 | − | 1.80926i | 0.446202 | − | 0.119560i | −0.0287195 | − | 0.999588i | \(-0.509143\pi\) |
0.474922 | + | 0.880028i | \(0.342476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.06634 | − | 9.83503i | −0.0701597 | − | 0.647098i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.0933 | + | 14.4876i | 1.64392 | + | 0.949116i | 0.979422 | + | 0.201823i | \(0.0646866\pi\) |
0.664495 | + | 0.747293i | \(0.268647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.38593 | − | 8.90440i | 0.155641 | − | 0.580859i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.48439 | − | 1.48439i | 0.0964215 | − | 0.0964215i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3587i | 0.864105i | 0.901848 | + | 0.432053i | \(0.142211\pi\) | ||||
−0.901848 | + | 0.432053i | \(0.857789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5510 | − | 6.09164i | 0.679651 | − | 0.392397i | −0.120072 | − | 0.992765i | \(-0.538313\pi\) |
0.799724 | + | 0.600368i | \(0.204979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.4157 | + | 5.73831i | −1.37381 | + | 0.368113i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03650 | − | 22.6157i | 0.0662195 | − | 1.44487i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0422 | − | 17.3936i | 0.638969 | − | 1.10673i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.35808 | + | 4.82554i | −0.529672 | + | 0.305806i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.68926 | − | 6.68926i | 0.422223 | − | 0.422223i | −0.463746 | − | 0.885968i | \(-0.653495\pi\) |
0.885968 | + | 0.463746i | \(0.153495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.37314 | + | 2.37314i | 0.149198 | + | 0.149198i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.72432 | + | 16.8430i | 0.608961 | + | 1.05475i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.32837 | + | 1.92163i | 0.207618 | + | 0.119868i | 0.600204 | − | 0.799847i | \(-0.295086\pi\) |
−0.392586 | + | 0.919715i | \(0.628419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.74542 | − | 2.16993i | 0.108455 | − | 0.134833i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.05452 | + | 7.66759i | 0.127172 | + | 0.474612i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.15784 | − | 5.46953i | −0.194720 | − | 0.337266i | 0.752088 | − | 0.659062i | \(-0.229047\pi\) |
−0.946809 | + | 0.321797i | \(0.895713\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.1409 | −2.28155 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.76556 | + | 8.76556i | 0.536444 | + | 0.536444i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.2914 | − | 6.24090i | −1.42010 | − | 0.380514i | −0.534580 | − | 0.845118i | \(-0.679530\pi\) |
−0.885519 | + | 0.464603i | \(0.846197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.73315 | − | 8.19805i | 0.287518 | − | 0.497996i | −0.685699 | − | 0.727886i | \(-0.740503\pi\) |
0.973217 | + | 0.229890i | \(0.0738365\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0979 | − | 27.4141i | 0.732200 | − | 1.65918i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.05407 | + | 7.66590i | 0.123865 | + | 0.462271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3278 | + | 3.03526i | 0.680619 | + | 0.182371i | 0.582533 | − | 0.812807i | \(-0.302062\pi\) |
0.0980853 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.1409i | 1.68475i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.59517i | 0.333780i | 0.985976 | + | 0.166890i | \(0.0533724\pi\) | ||||
−0.985976 | + | 0.166890i | \(0.946628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.70559 | − | 0.992910i | −0.220275 | − | 0.0590224i | 0.146994 | − | 0.989137i | \(-0.453040\pi\) |
−0.367268 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.82326 | − | 36.6609i | −0.581880 | − | 2.17160i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.33042 | + | 5.91938i | 0.255617 | + | 0.349410i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.76778 | + | 9.99009i | −0.339281 | + | 0.587652i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.5744 | + | 3.90519i | 0.854365 | + | 0.228927i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.74731 | + | 9.74731i | 0.569444 | + | 0.569444i | 0.931973 | − | 0.362529i | \(-0.118087\pi\) |
−0.362529 | + | 0.931973i | \(0.618087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.6359 | 0.735692 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.15450 | − | 1.99965i | −0.0669908 | − | 0.116031i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.63108 | + | 9.81932i | 0.152159 | + | 0.567866i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.08198 | + | 26.3314i | −0.235282 | + | 1.51772i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.21608 | − | 1.85681i | −0.184759 | − | 0.106671i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.2783 | + | 40.3192i | 1.33291 | + | 2.30867i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.5735 | + | 20.5735i | 1.17419 | + | 1.17419i | 0.981201 | + | 0.192988i | \(0.0618178\pi\) |
0.192988 | + | 0.981201i | \(0.438182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.41365 | − | 4.41365i | 0.251084 | − | 0.251084i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.495271 | + | 0.285945i | −0.0280843 | + | 0.0162145i | −0.513976 | − | 0.857804i | \(-0.671828\pi\) |
0.485892 | + | 0.874019i | \(0.338495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.707287 | − | 1.22506i | 0.0399782 | − | 0.0692443i | −0.845344 | − | 0.534222i | \(-0.820604\pi\) |
0.885322 | + | 0.464978i | \(0.153938\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.1880 | − | 28.8624i | −0.630372 | − | 1.62621i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.2914 | + | 6.77681i | −1.42051 | + | 0.380624i | −0.885663 | − | 0.464328i | \(-0.846296\pi\) |
−0.534843 | + | 0.844951i | \(0.679629\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.76217 | − | 1.59474i | 0.154652 | − | 0.0892882i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 11.5785i | − | 0.646248i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.54051 | + | 7.54051i | −0.419565 | + | 0.419565i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.22177 | + | 23.2200i | −0.345122 | + | 1.28801i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.25406 | − | 4.18813i | −0.401150 | − | 0.231604i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.49728 | − | 0.812871i | 0.413338 | − | 0.0448150i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.71378 | + | 0.727156i | −0.149163 | + | 0.0399681i | −0.332628 | − | 0.943058i | \(-0.607935\pi\) |
0.183465 | + | 0.983026i | \(0.441269\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.985490 | − | 3.67790i | 0.0540045 | − | 0.201548i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.69259 | 0.474927 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.9205 | −1.30303 | −0.651517 | − | 0.758634i | \(-0.725867\pi\) | ||||
−0.651517 | + | 0.758634i | \(0.725867\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.68312 | − | 28.6738i | 0.417290 | − | 1.55735i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.9216 | − | 2.92644i | 0.591438 | − | 0.158475i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5566 | − | 5.89614i | 0.947969 | − | 0.318362i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.6368 | + | 9.60525i | 0.895695 | + | 0.517130i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.23720 | − | 12.0814i | 0.173782 | − | 0.648563i | −0.822974 | − | 0.568079i | \(-0.807687\pi\) |
0.996756 | − | 0.0804837i | \(-0.0256465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9157 | − | 21.9157i | 1.17312 | − | 1.17312i | 0.191662 | − | 0.981461i | \(-0.438612\pi\) |
0.981461 | − | 0.191662i | \(-0.0613878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6.99394i | − | 0.373309i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.1984 | + | 10.5069i | −0.968604 | + | 0.559224i | −0.898810 | − | 0.438337i | \(-0.855567\pi\) |
−0.0697939 | + | 0.997561i | \(0.522234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.3784 | + | 6.26421i | −1.24079 | + | 0.332470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.97186 | + | 12.3972i | −0.527767 | + | 0.656127i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.78310 | + | 8.28458i | −0.252443 | + | 0.437243i | −0.964198 | − | 0.265184i | \(-0.914567\pi\) |
0.711755 | + | 0.702428i | \(0.247901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.56807 | − | 0.905328i | 0.0825302 | − | 0.0476488i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.1661 | − | 16.1661i | 0.848498 | − | 0.848498i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.8520 | + | 25.8520i | 1.35315 | + | 1.35315i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.06305 | + | 5.30536i | 0.159890 | + | 0.276938i | 0.934829 | − | 0.355099i | \(-0.115553\pi\) |
−0.774939 | + | 0.632036i | \(0.782219\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.68463 | + | 5.01408i | 0.452104 | + | 0.261022i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.9813 | − | 28.3292i | −0.570123 | − | 1.47078i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.25162 | − | 15.8673i | −0.220140 | − | 0.821575i | −0.984293 | − | 0.176540i | \(-0.943509\pi\) |
0.764153 | − | 0.645035i | \(-0.223157\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.91411 | + | 3.31533i | 0.0988440 | + | 0.171203i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.66091 | 0.497562 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.05253 | − | 6.05253i | −0.310897 | − | 0.310897i | 0.534360 | − | 0.845257i | \(-0.320553\pi\) |
−0.845257 | + | 0.534360i | \(0.820553\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.1620 | + | 2.99085i | 0.571846 | + | 0.153226i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.64030 | + | 16.6975i | −0.492596 | + | 0.853202i | −0.999964 | − | 0.00852805i | \(-0.997285\pi\) |
0.507367 | + | 0.861730i | \(0.330619\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0381 | + | 7.34357i | −0.511591 | + | 0.374263i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.42954 | + | 35.1915i | 0.479330 | + | 1.78889i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.6476 | − | 7.40814i | −1.40179 | − | 0.375608i | −0.522801 | − | 0.852455i | \(-0.675113\pi\) |
−0.878986 | + | 0.476847i | \(0.841779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.39753i | − | 0.272965i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 35.5835i | − | 1.79495i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.54934 | − | 0.683093i | −0.128271 | − | 0.0343701i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.40028 | − | 8.95799i | −0.120467 | − | 0.449588i | 0.879171 | − | 0.476507i | \(-0.158097\pi\) |
−0.999638 | + | 0.0269184i | \(0.991431\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.0587 | − | 18.3321i | 1.25451 | − | 0.917754i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5281 | − | 30.3596i | 0.875312 | − | 1.51609i | 0.0188827 | − | 0.999822i | \(-0.493989\pi\) |
0.856430 | − | 0.516264i | \(-0.172678\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.0815 | + | 8.86416i | 1.64791 | + | 0.441555i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.4735 | + | 15.4735i | 0.768886 | + | 0.768886i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.52989 | −0.0758338 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4392 | − | 30.2056i | −0.862314 | − | 1.49357i | −0.869690 | − | 0.493598i | \(-0.835681\pi\) |
0.00737621 | − | 0.999973i | \(-0.497652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.67923 | + | 6.26699i | 0.0828306 | + | 0.309128i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.73603 | + | 9.63807i | 0.183838 | + | 0.474258i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5082 | + | 6.06689i | 0.515826 | + | 0.297812i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9209 | + | 18.9156i | 0.534801 | + | 0.926302i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.57828 | − | 8.57828i | −0.419076 | − | 0.419076i | 0.465809 | − | 0.884885i | \(-0.345763\pi\) |
−0.884885 | + | 0.465809i | \(0.845763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.41183 | + | 7.41183i | −0.361230 | + | 0.361230i | −0.864266 | − | 0.503035i | \(-0.832217\pi\) |
0.503035 | + | 0.864266i | \(0.332217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.92967 | − | 5.15555i | 0.434175 | − | 0.250671i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.38184 | − | 11.0537i | 0.309565 | − | 0.536182i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.8709 | + | 29.6766i | −1.15519 | + | 1.43615i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.9010 | + | 4.26065i | −0.767706 | + | 0.205706i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.39637 | − | 0.806195i | 0.0672608 | − | 0.0388331i | −0.465992 | − | 0.884789i | \(-0.654303\pi\) |
0.533253 | + | 0.845956i | \(0.320969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.0869i | 0.628917i | 0.949271 | + | 0.314458i | \(0.101823\pi\) | ||||
−0.949271 | + | 0.314458i | \(0.898177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.9093 | − | 12.9093i | 0.618956 | − | 0.618956i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.72622 | + | 10.1744i | −0.130413 | + | 0.486708i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.71358 | − | 0.989334i | −0.0817846 | − | 0.0472184i | 0.458550 | − | 0.888669i | \(-0.348369\pi\) |
−0.540335 | + | 0.841450i | \(0.681702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.7069 | − | 17.0673i | 0.890803 | − | 0.812729i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.5156 | − | 8.98048i | 1.59237 | − | 0.426675i | 0.649646 | − | 0.760237i | \(-0.274917\pi\) |
0.942728 | + | 0.333562i | \(0.108251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.03377 | − | 15.0542i | 0.191219 | − | 0.713640i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.8614 | −1.03401 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0460 | 0.946031 | 0.473015 | − | 0.881054i | \(-0.343166\pi\) | ||||
0.473015 | + | 0.881054i | \(0.343166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04285 | − | 3.89196i | 0.0491058 | − | 0.183265i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.4407 | + | 6.81682i | −1.19531 | + | 0.320282i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −37.4537 | + | 4.06081i | −1.75586 | + | 0.190374i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9859 | − | 15.0030i | −1.21557 | − | 0.701810i | −0.251603 | − | 0.967830i | \(-0.580958\pi\) |
−0.963967 | + | 0.266020i | \(0.914291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.961116 | + | 3.58693i | −0.0448611 | + | 0.167424i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2334 | − | 18.2334i | 0.849213 | − | 0.849213i | −0.140822 | − | 0.990035i | \(-0.544974\pi\) |
0.990035 | + | 0.140822i | \(0.0449744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 31.3804i | − | 1.45837i | −0.684316 | − | 0.729186i | \(-0.739899\pi\) | ||
0.684316 | − | 0.729186i | \(-0.260101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 56.0497 | − | 32.3603i | 2.59924 | − | 1.50067i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.0310 | − | 6.17115i | 1.06575 | − | 0.285567i | 0.317004 | − | 0.948424i | \(-0.397323\pi\) |
0.748745 | + | 0.662858i | \(0.230657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.57011 | + | 6.63028i | 0.118677 | + | 0.306158i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.8844 | − | 32.7088i | 0.870148 | − | 1.50714i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.6774 | − | 7.31928i | 0.582906 | − | 0.336541i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.6129 | + | 17.6129i | −0.808135 | + | 0.808135i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.3752 | − | 29.3752i | −1.34500 | − | 1.34500i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.6784 | + | 30.6199i | 0.807747 | + | 1.39906i | 0.914421 | + | 0.404764i | \(0.132646\pi\) |
−0.106674 | + | 0.994294i | \(0.534020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.01319 | − | 2.31701i | −0.182986 | − | 0.105647i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.40746 | + | 15.5297i | −0.109543 | + | 0.706625i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.90979 | − | 18.3236i | −0.222942 | − | 0.832032i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.31153 | − | 9.19984i | −0.240688 | − | 0.416884i | 0.720222 | − | 0.693743i | \(-0.244040\pi\) |
−0.960911 | + | 0.276859i | \(0.910706\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 59.1357 | 2.67421 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9088 | − | 26.9088i | −1.21438 | − | 1.21438i | −0.969572 | − | 0.244806i | \(-0.921276\pi\) |
−0.244806 | − | 0.969572i | \(-0.578724\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.95472 | − | 1.32761i | −0.223149 | − | 0.0597927i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.50291 | + | 14.7275i | −0.382177 | + | 0.661950i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.6902 | − | 15.9797i | −0.524379 | − | 0.716789i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.28081 | − | 12.2441i | −0.146869 | − | 0.548123i | −0.999665 | − | 0.0258790i | \(-0.991762\pi\) |
0.852796 | − | 0.522244i | \(-0.174905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.49441 | + | 2.54402i | 0.424179 | + | 0.113658i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.7074i | 0.611183i | 0.952163 | + | 0.305591i | \(0.0988542\pi\) | ||||
−0.952163 | + | 0.305591i | \(0.901146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.66892i | 0.207764i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.8615 | − | 4.25008i | −0.704434 | − | 0.188753i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.16734 | + | 23.0168i | 0.273363 | + | 1.02020i | 0.956931 | + | 0.290317i | \(0.0937606\pi\) |
−0.683568 | + | 0.729887i | \(0.739573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0750 | + | 27.3622i | −0.534168 | + | 1.21043i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.62343 | − | 6.27596i | 0.159978 | − | 0.277091i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.58014 | − | 2.03109i | −0.334021 | − | 0.0895007i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.92950 | − | 2.92950i | −0.128839 | − | 0.128839i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.3854 | 0.938715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8589 | + | 20.5402i | 0.519548 | + | 0.899884i | 0.999742 | + | 0.0227214i | \(0.00723308\pi\) |
−0.480194 | + | 0.877163i | \(0.659434\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.85978 | − | 18.1369i | −0.212503 | − | 0.793073i | −0.987031 | − | 0.160532i | \(-0.948679\pi\) |
0.774527 | − | 0.632540i | \(-0.217988\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.2920 | + | 28.9569i | −1.01655 | + | 1.26378i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.7482 | − | 9.09220i | −0.686000 | − | 0.396063i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.83428 | + | 15.3014i | 0.384099 | + | 0.665279i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.99392 | + | 9.99392i | 0.433699 | + | 0.433699i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.62996 | − | 8.62996i | 0.373805 | − | 0.373805i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.6067 | + | 7.27851i | −0.545037 | + | 0.314677i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.8536 | + | 43.0476i | −1.07251 | + | 1.85764i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.56926 | − | 5.48534i | −0.369104 | − | 0.236271i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.2496 | − | 6.76561i | 1.08556 | − | 0.290876i | 0.328691 | − | 0.944437i | \(-0.393392\pi\) |
0.756874 | + | 0.653561i | \(0.226726\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.1301 | + | 11.0448i | −0.820952 | + | 0.473977i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5310i | 0.451100i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.8532 | − | 23.8532i | 1.01989 | − | 1.01989i | 0.0200929 | − | 0.999798i | \(-0.493604\pi\) |
0.999798 | − | 0.0200929i | \(-0.00639620\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.4779 | + | 50.3001i | −0.575221 | + | 2.14675i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.66915 | + | 5.00513i | 0.369318 | + | 0.213226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.232726 | − | 2.14648i | −0.00989651 | − | 0.0912775i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.45871 | + | 2.26650i | −0.359052 | + | 0.0962077i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1522 | − | 41.6206i | 0.472534 | − | 1.76352i | −0.158083 | − | 0.987426i | \(-0.550532\pi\) |
0.630617 | − | 0.776094i | \(-0.282802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.3401 | 1.87539 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.74052 | 0.369025 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.30901 | − | 8.61735i | 0.0973133 | − | 0.363178i | −0.900047 | − | 0.435793i | \(-0.856468\pi\) |
0.997360 | + | 0.0726153i | \(0.0231345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.0500 | + | 9.65958i | −1.51664 | + | 0.406382i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.22743 | + | 16.3775i | −0.303524 | + | 0.687789i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.49552 | − | 3.17284i | −0.230384 | − | 0.133012i | 0.380365 | − | 0.924836i | \(-0.375798\pi\) |
−0.610749 | + | 0.791824i | \(0.709132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.71490 | − | 36.2565i | 0.406556 | − | 1.51729i | −0.394612 | − | 0.918848i | \(-0.629121\pi\) |
0.801168 | − | 0.598439i | \(-0.204212\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.6637 | + | 27.6637i | −1.15567 | + | 1.15567i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 12.6074i | − | 0.525765i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.63907 | + | 0.946316i | −0.0682353 | + | 0.0393957i | −0.533729 | − | 0.845655i | \(-0.679210\pi\) |
0.465494 | + | 0.885051i | \(0.345877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −55.8569 | + | 14.9668i | −2.32134 | + | 0.622000i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.52061 | + | 9.80889i | −0.0630854 | + | 0.406941i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.34585 | + | 14.4554i | −0.345650 | + | 0.598683i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −44.6094 | + | 25.7553i | −1.84437 | + | 1.06485i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.8519 | + | 26.8519i | −1.10830 | + | 1.10830i | −0.114923 | + | 0.993374i | \(0.536662\pi\) |
−0.993374 | + | 0.114923i | \(0.963338\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.0931 | + | 25.0931i | 1.03394 | + | 1.03394i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.1265 | + | 26.1998i | 0.622220 | + | 1.07772i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.8885 | − | 13.7920i | −0.980984 | − | 0.566372i | −0.0784171 | − | 0.996921i | \(-0.524987\pi\) |
−0.902567 | + | 0.430549i | \(0.858320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.7667 | + | 3.06430i | 0.810354 | + | 0.125624i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.80456 | + | 25.3950i | 0.278492 | + | 1.03935i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.8101 | + | 20.4557i | 0.482548 | + | 0.835797i | 0.999799 | − | 0.0200365i | \(-0.00637824\pi\) |
−0.517252 | + | 0.855833i | \(0.673045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.61717 | 0.229129 | 0.114565 | − | 0.993416i | \(-0.463453\pi\) | ||||
0.114565 | + | 0.993416i | \(0.463453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.87508 | + | 6.87508i | 0.279975 | + | 0.279975i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.7641 | − | 7.43936i | −1.12877 | − | 0.302453i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.43281 | − | 4.21375i | 0.0987446 | − | 0.171031i | −0.812421 | − | 0.583072i | \(-0.801851\pi\) |
0.911165 | + | 0.412041i | \(0.135184\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.6635 | + | 6.02975i | 0.553672 | + | 0.244338i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.24791 | − | 12.1214i | −0.131396 | − | 0.490378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.99109 | + | 1.06941i | 0.161199 | + | 0.0431931i | 0.338516 | − | 0.940961i | \(-0.390075\pi\) |
−0.177317 | + | 0.984154i | \(0.556742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 23.0635i | − | 0.930010i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.3025i | − | 1.01864i | −0.860578 | − | 0.509319i | \(-0.829897\pi\) | ||
0.860578 | − | 0.509319i | \(-0.170103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.7405 | + | 4.75356i | 0.713051 | + | 0.191062i | 0.597069 | − | 0.802190i | \(-0.296332\pi\) |
0.115982 | + | 0.993251i | \(0.462998\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.949348 | + | 3.54302i | 0.0380960 | + | 0.142176i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.6753 | − | 1.37428i | 0.507825 | − | 0.0550595i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.2438 | + | 19.4749i | −0.449753 | + | 0.778995i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.4760 | − | 4.41472i | −0.657987 | − | 0.176307i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.73981 | + | 1.73981i | 0.0693707 | + | 0.0693707i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.4293 | 1.64928 | 0.824638 | − | 0.565661i | \(-0.191379\pi\) | ||||
0.824638 | + | 0.565661i | \(0.191379\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.4368 | + | 18.0771i | 0.414826 | + | 0.718500i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.76023 | − | 14.0334i | −0.149220 | − | 0.556897i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1712 | − | 27.3672i | −0.561484 | − | 1.08433i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.4447 | − | 13.5358i | −0.927458 | − | 0.535468i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0933 | − | 29.6065i | −0.675146 | − | 1.16939i | −0.976426 | − | 0.215852i | \(-0.930747\pi\) |
0.301280 | − | 0.953536i | \(-0.402586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.46526 | + | 3.46526i | 0.136657 | + | 0.136657i | 0.772126 | − | 0.635469i | \(-0.219193\pi\) |
−0.635469 | + | 0.772126i | \(0.719193\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 59.2493 | − | 59.2493i | 2.33294 | − | 2.33294i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.2890 | + | 15.7553i | −1.07284 | + | 0.619406i | −0.928957 | − | 0.370188i | \(-0.879293\pi\) |
−0.143886 | + | 0.989594i | \(0.545960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.83939 | − | 4.91797i | 0.111456 | − | 0.193047i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.2549 | + | 33.1841i | 1.61691 | + | 1.30059i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.3649 | − | 5.18880i | 0.757805 | − | 0.203053i | 0.140828 | − | 0.990034i | \(-0.455024\pi\) |
0.616977 | + | 0.786981i | \(0.288357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.7436 | + | 22.3686i | −1.51384 | + | 0.874015i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.8933i | 1.59540i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.3969 | + | 29.3969i | −1.14514 | + | 1.14514i | −0.157643 | + | 0.987496i | \(0.550390\pi\) |
−0.987496 | + | 0.157643i | \(0.949610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5518 | − | 46.8440i | 0.488208 | − | 1.82202i | −0.0769483 | − | 0.997035i | \(-0.524518\pi\) |
0.565157 | − | 0.824984i | \(-0.308816\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.9280 | + | 13.2375i | 0.890450 | + | 0.514102i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −35.7127 | − | 15.7601i | −1.38488 | − | 0.611151i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.89406 | + | 1.31136i | −0.189499 | + | 0.0507760i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.6468 | + | 43.4664i | −0.450290 | + | 1.68051i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.9232 | 0.807733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6457 | 0.448909 | 0.224454 | − | 0.974485i | \(-0.427940\pi\) | ||||
0.224454 | + | 0.974485i | \(0.427940\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.24495 | + | 8.37826i | −0.0864080 | + | 0.322479i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6233 | − | 8.74138i | 1.25381 | − | 0.335959i | 0.430006 | − | 0.902826i | \(-0.358512\pi\) |
0.823809 | + | 0.566868i | \(0.191845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5247 | − | 9.16263i | 0.480653 | − | 0.351630i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.0453 | − | 22.5428i | −1.49622 | − | 0.863843i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.76166 | + | 6.57460i | −0.0674080 | + | 0.251570i | −0.991405 | − | 0.130830i | \(-0.958236\pi\) |
0.923997 | + | 0.382400i | \(0.124902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.76794 | − | 5.76794i | 0.220382 | − | 0.220382i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 17.9827i | − | 0.686081i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.7854 | + | 25.2795i | −1.66809 | + | 0.963073i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.7544 | + | 7.97267i | −1.13191 | + | 0.303295i | −0.775695 | − | 0.631108i | \(-0.782600\pi\) |
−0.356217 | + | 0.934403i | \(0.615934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.7474 | − | 2.13117i | −0.522221 | − | 0.0809565i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.7303 | − | 23.7816i | 0.520821 | − | 0.902088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.61193 | + | 3.24005i | −0.212567 | + | 0.122726i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 52.7060 | − | 52.7060i | 1.99352 | − | 1.99352i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.2191 | − | 28.2191i | −1.06582 | − | 1.06582i | −0.997675 | − | 0.0681440i | \(-0.978292\pi\) |
−0.0681440 | − | 0.997675i | \(-0.521708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.40080 | − | 4.15831i | −0.0905480 | − | 0.156834i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.5371 | − | 11.8571i | −0.773473 | − | 0.446565i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.56123 | + | 1.38045i | −0.133934 | + | 0.0519171i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.97862 | − | 18.5805i | −0.186976 | − | 0.697804i | −0.994199 | − | 0.107557i | \(-0.965697\pi\) |
0.807223 | − | 0.590247i | \(-0.200970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.47604 | − | 2.55657i | −0.0553557 | − | 0.0958790i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.9618 | −0.672673 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.6347 | + | 14.6347i | 0.547308 | + | 0.547308i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.1938 | + | 8.89426i | 1.23965 | + | 0.332162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.9289 | + | 20.6615i | −0.444873 | + | 0.770543i | −0.998043 | − | 0.0625253i | \(-0.980085\pi\) |
0.553170 | + | 0.833068i | \(0.313418\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.691981 | − | 6.38229i | −0.0257707 | − | 0.237689i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.11163 | − | 30.2730i | −0.301675 | − | 1.12587i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.5731 | − | 3.10100i | −0.429814 | − | 0.115168i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.5645i | − | 1.05940i | −0.848185 | − | 0.529700i | \(-0.822305\pi\) | ||
0.848185 | − | 0.529700i | \(-0.177695\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.7360i | 1.36059i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.7404 | − | 6.09328i | −0.841085 | − | 0.225368i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.04445 | + | 22.5582i | 0.223257 | + | 0.833206i | 0.983095 | + | 0.183094i | \(0.0586113\pi\) |
−0.759839 | + | 0.650112i | \(0.774722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −55.5055 | − | 17.6331i | −2.04735 | − | 0.650406i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.95329 | − | 3.38320i | 0.0719504 | − | 0.124622i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.72028 | − | 0.460947i | −0.0632814 | − | 0.0169562i | 0.227039 | − | 0.973886i | \(-0.427095\pi\) |
−0.290321 | + | 0.956929i | \(0.593762\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.5335 | − | 36.5335i | −1.34209 | − | 1.34209i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.7041 | −0.612815 | −0.306407 | − | 0.951900i | \(-0.599127\pi\) | ||||
−0.306407 | + | 0.951900i | \(0.599127\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.7426 | + | 23.8029i | 0.503490 | + | 0.872070i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.51266 | + | 13.1094i | 0.128522 | + | 0.479649i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.27909 | − | 7.46379i | −0.339051 | − | 0.272721i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51512 | − | 0.874754i | −0.0552874 | − | 0.0319202i | 0.472101 | − | 0.881544i | \(-0.343496\pi\) |
−0.527389 | + | 0.849624i | \(0.676829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.1678 | − | 21.0752i | −0.443419 | − | 0.768024i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.4148 | + | 23.4148i | 0.852153 | + | 0.852153i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6771 | + | 15.6771i | −0.569792 | + | 0.569792i | −0.932070 | − | 0.362278i | \(-0.881999\pi\) |
0.362278 | + | 0.932070i | \(0.381999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.47683 | − | 4.31675i | 0.271392 | − | 0.156688i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.9814 | + | 45.0012i | −0.941826 | + | 1.63129i | −0.179842 | + | 0.983695i | \(0.557559\pi\) |
−0.761984 | + | 0.647596i | \(0.775775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.03255 | + | 3.11368i | −0.290798 | + | 0.112723i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.4178 | − | 7.07864i | 0.955139 | − | 0.255929i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8965 | − | 8.60050i | 0.537882 | − | 0.310546i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.9699i | − | 1.26105i | −0.776170 | − | 0.630524i | \(-0.782840\pi\) | ||
0.776170 | − | 0.630524i | \(-0.217160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.99090 | − | 6.99090i | 0.251771 | − | 0.251771i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.55817 | + | 13.2793i | −0.127978 | + | 0.477622i | −0.999928 | − | 0.0119731i | \(-0.996189\pi\) |
0.871950 | + | 0.489595i | \(0.162855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.7841 | − | 21.2373i | −1.32132 | − | 0.762866i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.22974 | − | 5.78176i | −0.151741 | − | 0.207419i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.2150 | − | 3.27301i | 0.437650 | − | 0.117268i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.81523 | + | 10.5066i | −0.100737 | + | 0.375956i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.48586 | 0.124574 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −47.4847 | −1.69480 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.42575 | + | 23.9812i | −0.229053 | + | 0.854838i | 0.751687 | + | 0.659520i | \(0.229240\pi\) |
−0.980740 | + | 0.195318i | \(0.937426\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.6932 | + | 4.20498i | −0.558692 | + | 0.149701i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0267 | − | 24.6412i | −0.640954 | − | 0.876139i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.8856 | + | 31.6882i | 1.94904 | + | 1.12528i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.7284 | + | 92.2878i | −0.877027 | + | 3.27311i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.3302 | + | 13.3302i | −0.472179 | + | 0.472179i | −0.902619 | − | 0.430440i | \(-0.858358\pi\) |
0.430440 | + | 0.902619i | \(0.358358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.66293i | 0.235717i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0970 | − | 8.71624i | 0.533425 | − | 0.307973i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.8709 | − | 4.25258i | 0.560070 | − | 0.150070i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4222 | − | 7.14106i | 0.649298 | − | 0.251689i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.0148 | + | 53.7192i | −1.09177 | + | 1.89101i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.7601 | − | 10.8311i | 0.659569 | − | 0.380803i | −0.132544 | − | 0.991177i | \(-0.542314\pi\) |
0.792113 | + | 0.610375i | \(0.208981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.51326 | − | 1.51326i | 0.0531379 | − | 0.0531379i | −0.680039 | − | 0.733176i | \(-0.738037\pi\) |
0.733176 | + | 0.680039i | \(0.238037\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.2192 | − | 17.2192i | −0.603904 | − | 0.603904i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.1741 | − | 64.3874i | −1.30215 | − | 2.25539i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.7883 | + | 22.9718i | 1.39202 | + | 0.803681i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −32.8344 | − | 26.4109i | −1.14733 | − | 0.922871i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4214 | + | 46.3574i | 0.433511 | + | 1.61788i | 0.744605 | + | 0.667506i | \(0.232638\pi\) |
−0.311094 | + | 0.950379i | \(0.600695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0408 | + | 26.0514i | 0.524290 | + | 0.908096i | 0.999600 | + | 0.0282782i | \(0.00900244\pi\) |
−0.475310 | + | 0.879818i | \(0.657664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.4158 | 0.710789 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.5866 | − | 22.5866i | −0.785414 | − | 0.785414i | 0.195325 | − | 0.980739i | \(-0.437424\pi\) |
−0.980739 | + | 0.195325i | \(0.937424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.9742 | + | 8.56747i | 1.11051 | + | 0.297561i | 0.767038 | − | 0.641602i | \(-0.221730\pi\) |
0.343473 | + | 0.939162i | \(0.388397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.0840 | − | 26.1263i | 0.523260 | − | 0.906313i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.50706 | + | 15.9831i | 0.121512 | + | 0.553780i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.19846 | − | 11.9368i | −0.110687 | − | 0.413091i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.9365 | + | 3.19838i | 0.412586 | + | 0.110552i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 35.7894i | − | 1.23559i | −0.786340 | − | 0.617794i | \(-0.788027\pi\) | ||
0.786340 | − | 0.617794i | \(-0.211973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 24.1849i | − | 0.833962i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.9029 | + | 3.72527i | 0.478841 | + | 0.128305i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.34340 | + | 19.9418i | 0.183818 | + | 0.686020i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.53455 | − | 23.3766i | −0.0870880 | − | 0.803231i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.93437 | + | 8.54658i | −0.169347 | + | 0.293318i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.34752 | + | 0.629017i | 0.0804721 | + | 0.0215624i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.27195 | + | 1.27195i | 0.0435507 | + | 0.0435507i | 0.728547 | − | 0.684996i | \(-0.240196\pi\) |
−0.684996 | + | 0.728547i | \(0.740196\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −53.3733 | −1.82533 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.1377 | − | 29.6834i | −0.585412 | − | 1.01396i | −0.994824 | − | 0.101614i | \(-0.967599\pi\) |
0.409411 | − | 0.912350i | \(-0.365734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5677 | + | 43.1714i | 0.394686 | + | 1.47299i | 0.822314 | + | 0.569034i | \(0.192683\pi\) |
−0.427628 | + | 0.903955i | \(0.640651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.5917 | − | 6.81912i | 0.599523 | − | 0.232395i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.5858 | + | 18.8134i | 1.10923 | + | 0.640416i | 0.938631 | − | 0.344924i | \(-0.112095\pi\) |
0.170602 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4434 | − | 23.2846i | −0.457088 | − | 0.791700i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.9832 | + | 20.9832i | 0.712627 | + | 0.712627i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.838719 | + | 0.838719i | −0.0284516 | + | 0.0284516i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2477 | − | 5.91651i | 0.347230 | − | 0.200473i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.6092 | − | 18.3756i | 0.359065 | − | 0.621920i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.89081 | + | 0.603167i | 0.131533 | + | 0.0203908i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5119 | + | 5.49616i | −0.692639 | + | 0.185592i | −0.587931 | − | 0.808911i | \(-0.700057\pi\) |
−0.104708 | + | 0.994503i | \(0.533391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.7099 | − | 17.7304i | 1.03582 | − | 0.598031i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.13017i | − | 0.105458i | −0.998609 | − | 0.0527291i | \(-0.983208\pi\) | ||
0.998609 | − | 0.0527291i | \(-0.0167920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.90657 | + | 5.90657i | −0.198772 | + | 0.198772i | −0.799473 | − | 0.600702i | \(-0.794888\pi\) |
0.600702 | + | 0.799473i | \(0.294888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.41301 | − | 31.3978i | 0.282800 | − | 1.05543i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.9702 | − | 24.2315i | −1.40922 | − | 0.813615i | −0.413908 | − | 0.910318i | \(-0.635837\pi\) |
−0.995313 | + | 0.0967040i | \(0.969170\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.59219 | − | 7.01733i | 0.321712 | − | 0.235354i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.49940 | − | 2.54536i | 0.318242 | − | 0.0852727i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.36536 | − | 12.5597i | 0.112617 | − | 0.420294i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.4941 | 2.08895 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.1508 | 0.873151 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.41800 | + | 16.4882i | −0.147348 | + | 0.549912i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.9299 | − | 6.94789i | 0.863849 | − | 0.231468i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 62.7105 | + | 27.6744i | 2.08688 | + | 0.920946i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0513 | + | 13.8860i | 0.799491 | + | 0.461587i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.69974 | − | 36.1999i | 0.322075 | − | 1.20200i | −0.595146 | − | 0.803618i | \(-0.702906\pi\) |
0.917220 | − | 0.398381i | \(-0.130428\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.69271 | + | 3.69271i | −0.122480 | + | 0.122480i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0871i | 0.400463i | 0.979749 | + | 0.200231i | \(0.0641694\pi\) | ||||
−0.979749 | + | 0.200231i | \(0.935831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.72253 | − | 2.72656i | 0.156293 | − | 0.0902358i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 115.684 | − | 30.9974i | 3.82439 | − | 1.02474i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.5169 | − | 22.9381i | −0.941712 | − | 0.757481i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.6308 | + | 47.8579i | −0.911455 | + | 1.57869i | −0.0994447 | + | 0.995043i | \(0.531707\pi\) |
−0.812010 | + | 0.583643i | \(0.801627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 64.8188 | − | 37.4231i | 2.13585 | − | 1.23313i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.2971 | + | 23.2971i | −0.766833 | + | 0.766833i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.06379 | + | 4.06379i | 0.133617 | + | 0.133617i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.38882 | − | 7.60165i | −0.144148 | − | 0.249671i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.64695 | + | 4.99232i | 0.283697 | + | 0.163793i | 0.635096 | − | 0.772433i | \(-0.280961\pi\) |
−0.351399 | + | 0.936226i | \(0.614294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.46199 | − | 31.8996i | 0.0479147 | − | 1.04547i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.380765 | + | 1.42103i | 0.0124657 | + | 0.0465226i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.49450 | − | 9.51675i | −0.179689 | − | 0.311231i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.92416 | −0.258871 | −0.129436 | − | 0.991588i | \(-0.541317\pi\) | ||||
−0.129436 | + | 0.991588i | \(0.541317\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.57311 | − | 2.57311i | −0.0839703 | − | 0.0839703i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.10702 | + | 1.63637i | 0.199083 | + | 0.0533441i | 0.356983 | − | 0.934111i | \(-0.383806\pi\) |
−0.157900 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.20038 | + | 5.54321i | −0.104219 | + | 0.180512i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.5141 | + | 1.46523i | −0.439613 | + | 0.0476638i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.94453 | + | 10.9891i | 0.0956843 | + | 0.357098i | 0.997122 | − | 0.0758096i | \(-0.0241541\pi\) |
−0.901438 | + | 0.432908i | \(0.857487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.0727 | + | 12.8811i | 1.56051 | + | 0.418137i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 67.3561i | 2.18417i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.7329i | − | 0.412460i | −0.978504 | − | 0.206230i | \(-0.933880\pi\) | ||
0.978504 | − | 0.206230i | \(-0.0661195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.5105 | + | 12.7304i | 1.53741 | + | 0.411946i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.12356 | − | 7.92522i | −0.0686448 | − | 0.256186i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.10489 | + | 2.69411i | 0.197137 | + | 0.0869974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.7568 | + | 25.5595i | −0.476025 | + | 0.824500i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7275 | − | 4.21417i | −0.506812 | − | 0.135800i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51.4090 | + | 51.4090i | 1.65491 | + | 1.65491i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6644 | 0.342944 | 0.171472 | − | 0.985189i | \(-0.445148\pi\) | ||||
0.171472 | + | 0.985189i | \(0.445148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.7162 | + | 23.7571i | 0.440628 | + | 0.763190i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.596517 | − | 2.22623i | −0.0191431 | − | 0.0714431i | 0.955694 | − | 0.294364i | \(-0.0951077\pi\) |
−0.974837 | + | 0.222920i | \(0.928441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.1990 | + | 3.44137i | 0.711669 | + | 0.110325i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 53.5546 | + | 30.9198i | 1.71512 | + | 0.990225i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.66274 | + | 13.2723i | 0.245153 | + | 0.424617i | 0.962175 | − | 0.272434i | \(-0.0878286\pi\) |
−0.717022 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.95277 | − | 4.95277i | −0.158291 | − | 0.158291i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.32913 | + | 8.32913i | −0.265929 | + | 0.265929i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.1184 | + | 9.30595i | −0.514097 | + | 0.296814i | −0.734516 | − | 0.678591i | \(-0.762591\pi\) |
0.220419 | + | 0.975405i | \(0.429257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.0177 | − | 32.9396i | 0.605954 | − | 1.04954i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.97187 | − | 19.1705i | 0.0945956 | − | 0.610202i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.4620 | + | 6.01867i | −0.714249 | + | 0.191383i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7555 | + | 13.7153i | −0.754619 | + | 0.435680i | −0.827361 | − | 0.561671i | \(-0.810159\pi\) |
0.0727413 | + | 0.997351i | \(0.476825\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.22736i | 0.229353i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.3727 | − | 23.3727i | 0.740965 | − | 0.740965i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.02660 | − | 18.7595i | 0.159194 | − | 0.594120i | −0.839516 | − | 0.543335i | \(-0.817161\pi\) |
0.998710 | − | 0.0507843i | \(-0.0161721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.44804 | − | 0.836028i | −0.0458140 | − | 0.0264507i |
(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 | 448.2.z.a.47.12 | 56 | ||
4.3 | odd | 2 | 112.2.v.a.19.7 | yes | 56 | ||
7.3 | odd | 6 | inner | 448.2.z.a.367.12 | 56 | ||
8.3 | odd | 2 | 896.2.z.b.607.12 | 56 | |||
8.5 | even | 2 | 896.2.z.a.607.3 | 56 | |||
16.3 | odd | 4 | 896.2.z.a.159.3 | 56 | |||
16.5 | even | 4 | 112.2.v.a.75.13 | yes | 56 | ||
16.11 | odd | 4 | inner | 448.2.z.a.271.12 | 56 | ||
16.13 | even | 4 | 896.2.z.b.159.12 | 56 | |||
28.3 | even | 6 | 112.2.v.a.3.13 | ✓ | 56 | ||
28.11 | odd | 6 | 784.2.w.f.227.13 | 56 | |||
28.19 | even | 6 | 784.2.j.a.195.6 | 56 | |||
28.23 | odd | 6 | 784.2.j.a.195.5 | 56 | |||
28.27 | even | 2 | 784.2.w.f.19.7 | 56 | |||
56.3 | even | 6 | 896.2.z.b.479.12 | 56 | |||
56.45 | odd | 6 | 896.2.z.a.479.3 | 56 | |||
112.3 | even | 12 | 896.2.z.a.31.3 | 56 | |||
112.5 | odd | 12 | 784.2.j.a.587.5 | 56 | |||
112.37 | even | 12 | 784.2.j.a.587.6 | 56 | |||
112.45 | odd | 12 | 896.2.z.b.31.12 | 56 | |||
112.53 | even | 12 | 784.2.w.f.619.7 | 56 | |||
112.59 | even | 12 | inner | 448.2.z.a.143.12 | 56 | ||
112.69 | odd | 4 | 784.2.w.f.411.13 | 56 | |||
112.101 | odd | 12 | 112.2.v.a.59.7 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.v.a.3.13 | ✓ | 56 | 28.3 | even | 6 | ||
112.2.v.a.19.7 | yes | 56 | 4.3 | odd | 2 | ||
112.2.v.a.59.7 | yes | 56 | 112.101 | odd | 12 | ||
112.2.v.a.75.13 | yes | 56 | 16.5 | even | 4 | ||
448.2.z.a.47.12 | 56 | 1.1 | even | 1 | trivial | ||
448.2.z.a.143.12 | 56 | 112.59 | even | 12 | inner | ||
448.2.z.a.271.12 | 56 | 16.11 | odd | 4 | inner | ||
448.2.z.a.367.12 | 56 | 7.3 | odd | 6 | inner | ||
784.2.j.a.195.5 | 56 | 28.23 | odd | 6 | |||
784.2.j.a.195.6 | 56 | 28.19 | even | 6 | |||
784.2.j.a.587.5 | 56 | 112.5 | odd | 12 | |||
784.2.j.a.587.6 | 56 | 112.37 | even | 12 | |||
784.2.w.f.19.7 | 56 | 28.27 | even | 2 | |||
784.2.w.f.227.13 | 56 | 28.11 | odd | 6 | |||
784.2.w.f.411.13 | 56 | 112.69 | odd | 4 | |||
784.2.w.f.619.7 | 56 | 112.53 | even | 12 | |||
896.2.z.a.31.3 | 56 | 112.3 | even | 12 | |||
896.2.z.a.159.3 | 56 | 16.3 | odd | 4 | |||
896.2.z.a.479.3 | 56 | 56.45 | odd | 6 | |||
896.2.z.a.607.3 | 56 | 8.5 | even | 2 | |||
896.2.z.b.31.12 | 56 | 112.45 | odd | 12 | |||
896.2.z.b.159.12 | 56 | 16.13 | even | 4 | |||
896.2.z.b.479.12 | 56 | 56.3 | even | 6 | |||
896.2.z.b.607.12 | 56 | 8.3 | odd | 2 |