Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.8 | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.l.3781.8 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.637931 | − | 1.10493i | 0.241115 | − | 0.417624i | −0.719917 | − | 0.694060i | \(-0.755820\pi\) |
0.961032 | + | 0.276436i | \(0.0891535\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.198096 | + | 0.343112i | −0.0597282 | + | 0.103452i | −0.894343 | − | 0.447381i | \(-0.852357\pi\) |
0.834615 | + | 0.550833i | \(0.185690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57788 | + | 2.73297i | 0.437625 | + | 0.757990i | 0.997506 | − | 0.0705839i | \(-0.0224863\pi\) |
−0.559880 | + | 0.828573i | \(0.689153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.405163 | − | 0.701763i | −0.0982665 | − | 0.170203i | 0.812701 | − | 0.582681i | \(-0.197996\pi\) |
−0.910967 | + | 0.412479i | \(0.864663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.24701 | + | 3.89194i | 0.515500 | + | 0.892871i | 0.999838 | + | 0.0179908i | \(0.00572696\pi\) |
−0.484339 | + | 0.874881i | \(0.660940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.637931 | + | 1.10493i | −0.139208 | + | 0.241115i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.399310 | − | 0.691625i | −0.0832619 | − | 0.144214i | 0.821387 | − | 0.570371i | \(-0.193200\pi\) |
−0.904649 | + | 0.426157i | \(0.859867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44753 | − | 4.23925i | 0.454496 | − | 0.787209i | −0.544163 | − | 0.838979i | \(-0.683153\pi\) |
0.998659 | + | 0.0517698i | \(0.0164862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.134765 | + | 0.233420i | −0.0242045 | + | 0.0419235i | −0.877874 | − | 0.478892i | \(-0.841039\pi\) |
0.853669 | + | 0.520815i | \(0.174372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.198096 | − | 0.343112i | 0.0344841 | − | 0.0597282i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.637931 | + | 1.10493i | −0.107830 | + | 0.186767i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.34684 | − | 4.06485i | −0.385819 | − | 0.668258i | 0.606064 | − | 0.795416i | \(-0.292748\pi\) |
−0.991882 | + | 0.127159i | \(0.959414\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.57788 | − | 2.73297i | −0.252663 | − | 0.437625i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.47144 | + | 6.01270i | −0.542147 | + | 0.939026i | 0.456633 | + | 0.889655i | \(0.349055\pi\) |
−0.998780 | + | 0.0493714i | \(0.984278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23162 | −0.340320 | −0.170160 | − | 0.985416i | \(-0.554428\pi\) | ||||
−0.170160 | + | 0.985416i | \(0.554428\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.85168 | − | 3.20720i | 0.270095 | − | 0.467818i | −0.698791 | − | 0.715326i | \(-0.746278\pi\) |
0.968886 | + | 0.247508i | \(0.0796117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.68609 | + | 4.65244i | 0.383727 | + | 0.664635i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.405163 | + | 0.701763i | 0.0567342 | + | 0.0982665i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.4945 | −1.85362 | −0.926809 | − | 0.375532i | \(-0.877460\pi\) | ||||
−0.926809 | + | 0.375532i | \(0.877460\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.198096 | − | 0.343112i | 0.0267113 | − | 0.0462653i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.24701 | − | 3.89194i | −0.297624 | − | 0.515500i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24630 | 0.552822 | 0.276411 | − | 0.961040i | \(-0.410855\pi\) | ||||
0.276411 | + | 0.961040i | \(0.410855\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.93403 | − | 3.34985i | −0.247628 | − | 0.428904i | 0.715239 | − | 0.698880i | \(-0.246318\pi\) |
−0.962867 | + | 0.269976i | \(0.912984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.637931 | − | 1.10493i | 0.0803717 | − | 0.139208i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.57788 | − | 2.73297i | −0.195712 | − | 0.338983i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.366493 | + | 8.17714i | −0.0447743 | + | 0.998997i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.399310 | + | 0.691625i | 0.0480713 | + | 0.0832619i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.11699 | − | 3.66673i | 0.251240 | − | 0.435161i | −0.712627 | − | 0.701543i | \(-0.752495\pi\) |
0.963868 | + | 0.266382i | \(0.0858283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.97631 | + | 10.3513i | 0.699475 | + | 1.21153i | 0.968649 | + | 0.248434i | \(0.0799159\pi\) |
−0.269174 | + | 0.963091i | \(0.586751\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.252743 | + | 0.437764i | 0.0288027 | + | 0.0498878i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.255601 | + | 0.442715i | −0.0287574 | + | 0.0498093i | −0.880046 | − | 0.474889i | \(-0.842488\pi\) |
0.851289 | + | 0.524698i | \(0.175822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.92890 | + | 3.34095i | 0.211724 | + | 0.366717i | 0.952254 | − | 0.305306i | \(-0.0987589\pi\) |
−0.740530 | + | 0.672023i | \(0.765426\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.405163 | + | 0.701763i | 0.0439461 | + | 0.0761169i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.44753 | + | 4.23925i | −0.262403 | + | 0.454496i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.151145 | −0.0160214 | −0.00801068 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00801068 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.02632 | 0.422073 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.134765 | − | 0.233420i | 0.0139745 | − | 0.0242045i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.24701 | − | 3.89194i | −0.230538 | − | 0.399304i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.70238 | + | 6.41271i | 0.375920 | + | 0.651112i | 0.990464 | − | 0.137770i | \(-0.0439934\pi\) |
−0.614544 | + | 0.788882i | \(0.710660\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.198096 | + | 0.343112i | −0.0199094 | + | 0.0344841i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.40349 | + | 4.16297i | −0.239156 | + | 0.414231i | −0.960472 | − | 0.278375i | \(-0.910204\pi\) |
0.721316 | + | 0.692606i | \(0.243537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.28897 | − | 9.16076i | 0.521138 | − | 0.902637i | −0.478560 | − | 0.878055i | \(-0.658841\pi\) |
0.999698 | − | 0.0245820i | \(-0.00782549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.637931 | − | 1.10493i | 0.0622557 | − | 0.107830i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.9381 | 1.05743 | 0.528713 | − | 0.848800i | \(-0.322675\pi\) | ||||
0.528713 | + | 0.848800i | \(0.322675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5903 | −1.11015 | −0.555075 | − | 0.831800i | \(-0.687311\pi\) | ||||
−0.555075 | + | 0.831800i | \(0.687311\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.34684 | + | 4.06485i | 0.222753 | + | 0.385819i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.17900 | − | 8.97029i | 0.487199 | − | 0.843854i | −0.512693 | − | 0.858572i | \(-0.671352\pi\) |
0.999892 | + | 0.0147186i | \(0.00468525\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.399310 | + | 0.691625i | 0.0372358 | + | 0.0644944i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.57788 | + | 2.73297i | 0.145875 | + | 0.252663i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.03386 | −0.0947742 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.42152 | + | 9.39034i | 0.492865 | + | 0.853667i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.47144 | − | 6.01270i | 0.313009 | − | 0.542147i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.69595 | + | 11.5977i | −0.594169 | + | 1.02913i | 0.399494 | + | 0.916736i | \(0.369186\pi\) |
−0.993664 | + | 0.112395i | \(0.964148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.23162 | 0.196484 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.97325 | −0.347145 | −0.173572 | − | 0.984821i | \(-0.555531\pi\) | ||||
−0.173572 | + | 0.984821i | \(0.555531\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.73375 | 0.497179 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9590 | 0.936293 | 0.468146 | − | 0.883651i | \(-0.344922\pi\) | ||||
0.468146 | + | 0.883651i | \(0.344922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.91210 | 0.586276 | 0.293138 | − | 0.956070i | \(-0.405300\pi\) | ||||
0.293138 | + | 0.956070i | \(0.405300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.85168 | + | 3.20720i | −0.155939 | + | 0.270095i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.25029 | −0.104554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.44753 | + | 4.23925i | −0.203257 | + | 0.352051i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.68609 | − | 4.65244i | −0.221545 | − | 0.383727i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.4625 | 1.26674 | 0.633370 | − | 0.773849i | \(-0.281671\pi\) | ||||
0.633370 | + | 0.773849i | \(0.281671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.39067 | + | 11.0690i | 0.520065 | + | 0.900779i | 0.999728 | + | 0.0233265i | \(0.00742572\pi\) |
−0.479663 | + | 0.877453i | \(0.659241\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.405163 | − | 0.701763i | −0.0327555 | − | 0.0567342i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.134765 | − | 0.233420i | 0.0108246 | − | 0.0187488i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24885 | − | 3.89513i | −0.179478 | − | 0.310865i | 0.762224 | − | 0.647314i | \(-0.224108\pi\) |
−0.941702 | + | 0.336448i | \(0.890774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4945 | 1.07019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.01893 | −0.0803028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.839614 | + | 1.45425i | −0.0657636 | + | 0.113906i | −0.897032 | − | 0.441965i | \(-0.854282\pi\) |
0.831269 | + | 0.555871i | \(0.187615\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.198096 | + | 0.343112i | −0.0154218 | + | 0.0267113i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.61904 | − | 11.4645i | 0.512197 | − | 0.887151i | −0.487703 | − | 0.873010i | \(-0.662165\pi\) |
0.999900 | − | 0.0141416i | \(-0.00450156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.52058 | − | 2.63373i | 0.116968 | − | 0.202594i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.24701 | + | 3.89194i | 0.171833 | + | 0.297624i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.85480 | + | 17.0690i | 0.749246 | + | 1.29773i | 0.948184 | + | 0.317721i | \(0.102917\pi\) |
−0.198938 | + | 0.980012i | \(0.563749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.637931 | − | 1.10493i | 0.0482230 | − | 0.0835247i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.24630 | −0.319172 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8857 | −1.18735 | −0.593676 | − | 0.804704i | \(-0.702324\pi\) | ||||
−0.593676 | + | 0.804704i | \(0.702324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4536 | + | 21.5702i | −0.925666 | + | 1.60330i | −0.135179 | + | 0.990821i | \(0.543161\pi\) |
−0.790487 | + | 0.612479i | \(0.790172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.93403 | + | 3.34985i | 0.142968 | + | 0.247628i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.34684 | + | 4.06485i | 0.172543 | + | 0.298854i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.321045 | 0.0234771 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.637931 | + | 1.10493i | −0.0464026 | + | 0.0803717i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7379 | + | 20.3306i | 0.849324 | + | 1.47107i | 0.881812 | + | 0.471601i | \(0.156324\pi\) |
−0.0324880 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.6977 | −1.63382 | −0.816909 | − | 0.576767i | \(-0.804314\pi\) | ||||
−0.816909 | + | 0.576767i | \(0.804314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.57788 | + | 2.73297i | 0.112994 | + | 0.195712i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.66683 | + | 11.5473i | −0.474992 | + | 0.822710i | −0.999590 | − | 0.0286400i | \(-0.990882\pi\) |
0.524598 | + | 0.851350i | \(0.324216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.65718 | + | 16.7267i | 0.684579 | + | 1.18573i | 0.973569 | + | 0.228394i | \(0.0733473\pi\) |
−0.288990 | + | 0.957332i | \(0.593319\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.366493 | − | 8.17714i | 0.0258504 | − | 0.576771i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.12271 | − | 5.40870i | −0.219172 | − | 0.379616i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.47144 | − | 6.01270i | 0.242456 | − | 0.419945i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.399310 | − | 0.691625i | −0.0277540 | − | 0.0480713i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.78050 | −0.123159 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.90244 | + | 13.6874i | 0.544027 | + | 0.942282i | 0.998667 | + | 0.0516068i | \(0.0164342\pi\) |
−0.454641 | + | 0.890675i | \(0.650232\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.11699 | + | 3.66673i | −0.145054 | + | 0.251240i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.23162 | 0.152196 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.171942 | + | 0.297812i | 0.0116722 | + | 0.0202168i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.97631 | − | 10.3513i | −0.403842 | − | 0.699475i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.27860 | − | 2.21460i | 0.0860078 | − | 0.148970i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.134772 | 0.00902497 | 0.00451248 | − | 0.999990i | \(-0.498564\pi\) | ||||
0.00451248 | + | 0.999990i | \(0.498564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.05133 | − | 13.9453i | 0.534386 | − | 0.925583i | −0.464807 | − | 0.885412i | \(-0.653876\pi\) |
0.999193 | − | 0.0401711i | \(-0.0127903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.14349 | + | 10.6408i | 0.405973 | + | 0.703167i | 0.994434 | − | 0.105359i | \(-0.0335992\pi\) |
−0.588461 | + | 0.808526i | \(0.700266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.252743 | − | 0.437764i | −0.0166293 | − | 0.0288027i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.41572 | + | 4.18416i | −0.158259 | + | 0.274113i | −0.934241 | − | 0.356642i | \(-0.883922\pi\) |
0.775982 | + | 0.630755i | \(0.217255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.85168 | + | 3.20720i | −0.120790 | + | 0.209214i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.255601 | − | 0.442715i | 0.0166031 | − | 0.0287574i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.22293 | + | 2.11817i | −0.0791045 | + | 0.137013i | −0.902864 | − | 0.429927i | \(-0.858539\pi\) |
0.823759 | + | 0.566940i | \(0.191873\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1372 | 1.16832 | 0.584159 | − | 0.811639i | \(-0.301425\pi\) | ||||
0.584159 | + | 0.811639i | \(0.301425\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.68609 | − | 4.65244i | −0.171608 | − | 0.297234i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.09103 | + | 12.2820i | −0.451191 | + | 0.781487i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.92890 | − | 3.34095i | −0.122239 | − | 0.211724i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.8009 | + | 18.7078i | 0.681748 | + | 1.18082i | 0.974447 | + | 0.224618i | \(0.0721135\pi\) |
−0.292698 | + | 0.956205i | \(0.594553\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.316407 | 0.0198923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.405163 | − | 0.701763i | −0.0253723 | − | 0.0439461i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2554 | + | 22.9591i | −0.826851 | + | 1.43215i | 0.0736456 | + | 0.997284i | \(0.476537\pi\) |
−0.900497 | + | 0.434863i | \(0.856797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.98849 | −0.372107 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.44753 | − | 4.23925i | 0.151499 | − | 0.262403i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.98177 | −0.122201 | −0.0611005 | − | 0.998132i | \(-0.519461\pi\) | ||||
−0.0611005 | + | 0.998132i | \(0.519461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.4945 | 0.828963 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.151145 | 0.00924993 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.6325 | −1.19701 | −0.598507 | − | 0.801117i | \(-0.704239\pi\) | ||||
−0.598507 | + | 0.801117i | \(0.704239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1989 | 0.984012 | 0.492006 | − | 0.870592i | \(-0.336264\pi\) | ||||
0.492006 | + | 0.870592i | \(0.336264\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.02632 | −0.243684 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.198096 | + | 0.343112i | −0.0119456 | + | 0.0206905i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.6486 | 1.24066 | 0.620328 | − | 0.784343i | \(-0.287000\pi\) | ||||
0.620328 | + | 0.784343i | \(0.287000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.134765 | + | 0.233420i | −0.00806818 | + | 0.0139745i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.36886 | + | 5.83504i | 0.200969 | + | 0.348089i | 0.948841 | − | 0.315754i | \(-0.102257\pi\) |
−0.747872 | + | 0.663843i | \(0.768924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5873 | 0.986015 | 0.493007 | − | 0.870025i | \(-0.335898\pi\) | ||||
0.493007 | + | 0.870025i | \(0.335898\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.24701 | + | 3.89194i | 0.133101 | + | 0.230538i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.42907 | + | 7.67138i | 0.261440 | + | 0.452827i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17169 | − | 14.1538i | 0.480687 | − | 0.832575i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.70238 | − | 6.41271i | −0.217037 | − | 0.375920i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.5791 | −1.78645 | −0.893225 | − | 0.449611i | \(-0.851563\pi\) | ||||
−0.893225 | + | 0.449611i | \(0.851563\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.24630 | −0.247229 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.198096 | − | 0.343112i | 0.0114947 | − | 0.0199094i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.26013 | − | 2.18260i | 0.0728750 | − | 0.126223i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.42362 | + | 2.46579i | −0.0820562 | + | 0.142126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.40349 | − | 4.16297i | 0.138077 | − | 0.239156i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.93403 | + | 3.34985i | 0.110743 | + | 0.191812i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.72786 | + | 16.8491i | 0.555198 | + | 0.961631i | 0.997888 | + | 0.0649567i | \(0.0206909\pi\) |
−0.442690 | + | 0.896675i | \(0.645976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.28897 | + | 9.16076i | −0.300879 | + | 0.521138i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.9314 | 1.81066 | 0.905331 | − | 0.424706i | \(-0.139623\pi\) | ||||
0.905331 | + | 0.424706i | \(0.139623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0643 | −1.36019 | −0.680097 | − | 0.733122i | \(-0.738062\pi\) | ||||
−0.680097 | + | 0.733122i | \(0.738062\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.637931 | + | 1.10493i | −0.0359433 | + | 0.0622557i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6368 | − | 27.0837i | −0.878248 | − | 1.52117i | −0.853262 | − | 0.521483i | \(-0.825379\pi\) |
−0.0249863 | − | 0.999688i | \(-0.507954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.969693 | + | 1.67956i | 0.0542924 | + | 0.0940372i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.9381 | −0.610506 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.82081 | − | 3.15374i | 0.101313 | − | 0.175479i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57788 | + | 2.73297i | 0.0875251 | + | 0.151598i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.5903 | 0.640946 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.36248 | − | 4.09194i | −0.130248 | − | 0.225596i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6369 | + | 23.6198i | −0.749551 | + | 1.29826i | 0.198487 | + | 0.980103i | \(0.436397\pi\) |
−0.948038 | + | 0.318157i | \(0.896936\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.34684 | − | 4.06485i | −0.128606 | − | 0.222753i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.366493 | − | 8.17714i | 0.0200237 | − | 0.446765i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.41117 | + | 4.17628i | 0.131345 | + | 0.227496i | 0.924195 | − | 0.381920i | \(-0.124737\pi\) |
−0.792850 | + | 0.609417i | \(0.791404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.17900 | + | 8.97029i | −0.281285 | + | 0.487199i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0533929 | − | 0.0924792i | −0.00289139 | − | 0.00500803i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7852 | 0.852320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.399310 | − | 0.691625i | −0.0214981 | − | 0.0372358i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.67706 | + | 13.2971i | −0.412126 | + | 0.713824i | −0.995122 | − | 0.0986516i | \(-0.968547\pi\) |
0.582996 | + | 0.812475i | \(0.301880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.66432 | −0.356733 | −0.178367 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178367 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.57788 | − | 2.73297i | −0.0842211 | − | 0.145875i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.15671 | − | 8.93168i | −0.274464 | − | 0.475386i | 0.695536 | − | 0.718491i | \(-0.255167\pi\) |
−0.970000 | + | 0.243106i | \(0.921834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.11699 | + | 3.66673i | −0.112358 | + | 0.194610i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03386 | 0.0547179 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.396073 | −0.0209039 | −0.0104520 | − | 0.999945i | \(-0.503327\pi\) | ||||
−0.0104520 | + | 0.999945i | \(0.503327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.598113 | + | 1.03596i | −0.0314796 | + | 0.0545243i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.42152 | − | 9.39034i | −0.284556 | − | 0.492865i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.97631 | − | 10.3513i | −0.312815 | − | 0.541811i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.40357 | − | 7.62721i | 0.229865 | − | 0.398137i | −0.727903 | − | 0.685680i | \(-0.759505\pi\) |
0.957768 | + | 0.287543i | \(0.0928383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.47144 | + | 6.01270i | −0.180716 | + | 0.313009i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.60859 | + | 14.9105i | −0.446936 | + | 0.774115i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.77879 | − | 8.27711i | 0.247436 | − | 0.428572i | −0.715377 | − | 0.698738i | \(-0.753745\pi\) |
0.962814 | + | 0.270166i | \(0.0870786\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.4477 | 0.795595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.9734 | + | 19.0065i | 0.563665 | + | 0.976296i | 0.997173 | + | 0.0751465i | \(0.0239424\pi\) |
−0.433507 | + | 0.901150i | \(0.642724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.69595 | − | 11.5977i | 0.343044 | − | 0.594169i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.34372 | + | 2.32738i | 0.0686606 | + | 0.118924i | 0.898312 | − | 0.439358i | \(-0.144794\pi\) |
−0.829651 | + | 0.558282i | \(0.811461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.252743 | − | 0.437764i | −0.0128810 | − | 0.0223105i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.23162 | −0.113440 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.41142 | + | 2.44465i | 0.0715617 | + | 0.123948i | 0.899586 | − | 0.436744i | \(-0.143868\pi\) |
−0.828024 | + | 0.560692i | \(0.810535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.323571 | + | 0.560442i | −0.0163637 | + | 0.0283428i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.97325 | 0.200424 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.255601 | − | 0.442715i | 0.0128607 | − | 0.0222754i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.2818 | 0.666594 | 0.333297 | − | 0.942822i | \(-0.391839\pi\) | ||||
0.333297 | + | 0.942822i | \(0.391839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.73375 | −0.287046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.5196 | −0.775014 | −0.387507 | − | 0.921867i | \(-0.626664\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.850574 | −0.0423701 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85960 | 0.0921770 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.25265 | + | 7.36581i | −0.210280 | + | 0.364216i | −0.951802 | − | 0.306713i | \(-0.900771\pi\) |
0.741522 | + | 0.670929i | \(0.234104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9590 | −0.540569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.70885 | − | 4.69186i | 0.133294 | − | 0.230871i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.92890 | − | 3.34095i | −0.0946859 | − | 0.164001i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.91210 | −0.338487 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.42591 | − | 2.46975i | −0.0696604 | − | 0.120655i | 0.829091 | − | 0.559113i | \(-0.188858\pi\) |
−0.898752 | + | 0.438458i | \(0.855525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0879 | + | 29.5972i | 0.832816 | + | 1.44248i | 0.895797 | + | 0.444464i | \(0.146606\pi\) |
−0.0629811 | + | 0.998015i | \(0.520061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.85168 | − | 3.20720i | 0.0900316 | − | 0.155939i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.405163 | − | 0.701763i | −0.0196533 | − | 0.0340405i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.93512 | −0.238827 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.25029 | 0.0603645 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.40057 | − | 4.15791i | 0.115631 | − | 0.200279i | −0.802401 | − | 0.596786i | \(-0.796444\pi\) |
0.918032 | + | 0.396506i | \(0.129778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8358 | − | 20.5002i | 0.568791 | − | 0.985175i | −0.427895 | − | 0.903828i | \(-0.640745\pi\) |
0.996686 | − | 0.0813463i | \(-0.0259220\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.44753 | − | 4.23925i | 0.117350 | − | 0.203257i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.79451 | − | 3.10818i | 0.0858429 | − | 0.148684i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.82558 | + | 15.2864i | 0.421222 | + | 0.729578i | 0.996059 | − | 0.0886896i | \(-0.0282679\pi\) |
−0.574837 | + | 0.818268i | \(0.694935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.68609 | + | 4.65244i | 0.127909 | + | 0.221545i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.1982 | − | 17.6638i | 0.484531 | − | 0.839233i | −0.515311 | − | 0.857003i | \(-0.672323\pi\) |
0.999842 | + | 0.0177704i | \(0.00565680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.151145 | 0.00716497 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.4625 | −0.731353 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.86508 | − | 10.1586i | 0.276790 | − | 0.479415i | −0.693795 | − | 0.720172i | \(-0.744063\pi\) |
0.970585 | + | 0.240758i | \(0.0773960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37535 | − | 2.38218i | −0.0647629 | − | 0.112173i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.39067 | − | 11.0690i | −0.300260 | − | 0.520065i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.02632 | −0.188757 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.21088 | + | 15.9537i | −0.430867 | + | 0.746283i | −0.996948 | − | 0.0780661i | \(-0.975125\pi\) |
0.566081 | + | 0.824349i | \(0.308459\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.405163 | + | 0.701763i | 0.0189114 | + | 0.0327555i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.69453 | 0.265221 | 0.132610 | − | 0.991168i | \(-0.457664\pi\) | ||||
0.132610 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.37110 | − | 9.30301i | −0.249616 | − | 0.432348i | 0.713803 | − | 0.700346i | \(-0.246971\pi\) |
−0.963419 | + | 0.267999i | \(0.913638\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.134765 | + | 0.233420i | −0.00624959 | + | 0.0108246i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7396 | − | 20.3336i | −0.543243 | − | 0.940925i | −0.998715 | − | 0.0506749i | \(-0.983863\pi\) |
0.455472 | − | 0.890250i | \(-0.349471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.80136 | + | 5.62140i | 0.406409 | + | 0.259572i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.24885 | + | 3.89513i | 0.103622 | + | 0.179478i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.442076 | − | 0.765698i | 0.0203267 | − | 0.0352068i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.24701 | + | 3.89194i | 0.103100 | + | 0.178574i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4945 | −0.617873 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.8767 | + | 24.0351i | 0.634041 | + | 1.09819i | 0.986718 | + | 0.162446i | \(0.0519382\pi\) |
−0.352677 | + | 0.935745i | \(0.614728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.40608 | − | 12.8277i | 0.337688 | − | 0.584893i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.01893 | 0.0463628 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.70238 | − | 6.41271i | −0.168117 | − | 0.291186i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.89159 | − | 13.6686i | −0.357602 | − | 0.619385i | 0.629958 | − | 0.776629i | \(-0.283072\pi\) |
−0.987560 | + | 0.157245i | \(0.949739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.839614 | − | 1.45425i | 0.0379686 | − | 0.0657636i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8770 | 0.897038 | 0.448519 | − | 0.893773i | \(-0.351952\pi\) | ||||
0.448519 | + | 0.893773i | \(0.351952\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.96660 | −0.178647 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.198096 | − | 0.343112i | 0.00890375 | − | 0.0154218i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.70098 | − | 4.67824i | −0.121156 | − | 0.209848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0933 | − | 38.2668i | −0.989034 | − | 1.71306i | −0.622420 | − | 0.782684i | \(-0.713850\pi\) |
−0.366614 | − | 0.930373i | \(-0.619483\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.61904 | + | 11.4645i | −0.295717 | + | 0.512197i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.32110 | − | 16.1446i | 0.415607 | − | 0.719853i | −0.579885 | − | 0.814699i | \(-0.696902\pi\) |
0.995492 | + | 0.0948457i | \(0.0302358\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.40349 | − | 4.16297i | 0.106954 | − | 0.185250i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.52058 | + | 2.63373i | −0.0675314 | + | 0.116968i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.9221 | −1.76952 | −0.884759 | − | 0.466050i | \(-0.845677\pi\) | ||||
−0.884759 | + | 0.466050i | \(0.845677\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.2499 | 0.674616 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.24701 | − | 3.89194i | −0.0992079 | − | 0.171833i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.28897 | + | 9.16076i | −0.233060 | + | 0.403671i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.733619 | + | 1.27067i | 0.0322645 | + | 0.0558838i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.85480 | − | 17.0690i | −0.432578 | − | 0.749246i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.778849 | 0.0341220 | 0.0170610 | − | 0.999854i | \(-0.494569\pi\) | ||||
0.0170610 | + | 0.999854i | \(0.494569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.69671 | − | 6.40289i | −0.161646 | − | 0.279979i | 0.773813 | − | 0.633414i | \(-0.218347\pi\) |
−0.935459 | + | 0.353435i | \(0.885014\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.637931 | + | 1.10493i | −0.0278416 | + | 0.0482230i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.218408 | 0.00951398 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1811 | − | 19.3662i | 0.486135 | − | 0.842010i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.24630 | 0.184274 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.9100 | −0.949030 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.9381 | −0.472896 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.8857 | 0.685519 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.12841 | −0.0916773 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.57101 | −0.282510 | −0.141255 | − | 0.989973i | \(-0.545114\pi\) | ||||
−0.141255 | + | 0.989973i | \(0.545114\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.4536 | − | 21.5702i | 0.534433 | − | 0.925666i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.5903 | 0.496474 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.930680 | + | 1.61199i | −0.0397930 | + | 0.0689235i | −0.885236 | − | 0.465142i | \(-0.846003\pi\) |
0.845443 | + | 0.534066i | \(0.179337\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.93403 | − | 3.34985i | −0.0825426 | − | 0.142968i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.9985 | 0.937169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.326112 | + | 0.564842i | 0.0138677 | + | 0.0240195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.34684 | − | 4.06485i | −0.0996180 | − | 0.172543i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.8596 | + | 29.2017i | −0.714364 | + | 1.23731i | 0.248841 | + | 0.968544i | \(0.419950\pi\) |
−0.963204 | + | 0.268770i | \(0.913383\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.52124 | − | 6.09896i | −0.148933 | − | 0.257959i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.321045 | −0.0135545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.40249 | 0.185543 | 0.0927714 | − | 0.995687i | \(-0.470427\pi\) | ||||
0.0927714 | + | 0.995687i | \(0.470427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.17900 | + | 8.97029i | −0.217882 | + | 0.377383i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.637931 | − | 1.10493i | 0.0267906 | − | 0.0464026i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.3850 | − | 19.7194i | 0.477285 | − | 0.826681i | −0.522377 | − | 0.852715i | \(-0.674954\pi\) |
0.999661 | + | 0.0260339i | \(0.00828778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.29626 | + | 10.9054i | −0.263490 | + | 0.456378i | −0.967167 | − | 0.254142i | \(-0.918207\pi\) |
0.703677 | + | 0.710520i | \(0.251540\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.7379 | − | 20.3306i | −0.490358 | − | 0.849324i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.399310 | − | 0.691625i | −0.0166524 | − | 0.0288428i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.85892 | + | 3.21974i | −0.0773878 | + | 0.134040i | −0.902122 | − | 0.431481i | \(-0.857991\pi\) |
0.824734 | + | 0.565520i | \(0.191325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.6977 | 0.943285 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.92201 | 0.204199 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.67322 | − | 4.63015i | 0.110713 | − | 0.191761i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.57788 | − | 2.73297i | −0.0652374 | − | 0.112994i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.32677 | − | 2.29803i | −0.0547616 | − | 0.0948499i | 0.837345 | − | 0.546675i | \(-0.184107\pi\) |
−0.892107 | + | 0.451825i | \(0.850773\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.21128 | −0.0499097 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.66683 | − | 11.5473i | 0.274237 | − | 0.474992i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.3424 | − | 24.8418i | −0.588972 | − | 1.02013i | −0.994367 | − | 0.105988i | \(-0.966200\pi\) |
0.405396 | − | 0.914141i | \(-0.367134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.03386 | 0.0423843 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.65718 | − | 16.7267i | −0.395242 | − | 0.684579i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.9479 | − | 27.6226i | 0.651614 | − | 1.12863i | −0.331117 | − | 0.943590i | \(-0.607425\pi\) |
0.982731 | − | 0.185039i | \(-0.0592413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.43018 | − | 11.1374i | −0.262293 | − | 0.454304i | 0.704558 | − | 0.709646i | \(-0.251145\pi\) |
−0.966851 | + | 0.255342i | \(0.917812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.366493 | + | 8.17714i | −0.0149248 | + | 0.332999i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.42152 | − | 9.39034i | −0.220416 | − | 0.381772i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2787 | − | 24.7314i | 0.579553 | − | 1.00381i | −0.415978 | − | 0.909375i | \(-0.636561\pi\) |
0.995531 | − | 0.0944402i | \(-0.0301061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.12271 | + | 5.40870i | 0.126539 | + | 0.219172i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.6869 | 0.472801 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.60763 | + | 11.4447i | 0.266880 | + | 0.462249i | 0.968054 | − | 0.250740i | \(-0.0806741\pi\) |
−0.701175 | + | 0.712989i | \(0.747341\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.47144 | + | 6.01270i | −0.139982 | + | 0.242456i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2276 | −0.653300 | −0.326650 | − | 0.945145i | \(-0.605920\pi\) | ||||
−0.326650 | + | 0.945145i | \(0.605920\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7548 | + | 34.2164i | 0.794014 | + | 1.37527i | 0.923463 | + | 0.383687i | \(0.125346\pi\) |
−0.129449 | + | 0.991586i | \(0.541321\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.399310 | + | 0.691625i | 0.0160238 | + | 0.0277540i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0964201 | + | 0.167005i | −0.00386299 | + | 0.00669090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.78050 | 0.0711061 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.90171 | + | 3.29386i | −0.0758261 | + | 0.131335i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9545 | + | 18.9738i | 0.436092 | + | 0.755334i | 0.997384 | − | 0.0722841i | \(-0.0230288\pi\) |
−0.561292 | + | 0.827618i | \(0.689695\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.90244 | − | 13.6874i | −0.314094 | − | 0.544027i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.69595 | − | 11.5977i | 0.265721 | − | 0.460241i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.47666 | + | 14.6820i | −0.335857 | + | 0.581722i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.11699 | − | 3.66673i | 0.0837467 | − | 0.145054i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.05891 | + | 8.76229i | −0.199815 | + | 0.346090i | −0.948468 | − | 0.316872i | \(-0.897367\pi\) |
0.748653 | + | 0.662962i | \(0.230701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0113 | −0.789167 | −0.394584 | − | 0.918860i | \(-0.629111\pi\) | ||||
−0.394584 | + | 0.918860i | \(0.629111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.23162 | −0.0878701 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.21176 | − | 3.83089i | −0.0869534 | − | 0.150608i | 0.819269 | − | 0.573410i | \(-0.194380\pi\) |
−0.906222 | + | 0.422802i | \(0.861046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.841176 | + | 1.45696i | −0.0330190 | + | 0.0571907i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.171942 | − | 0.297812i | −0.00673893 | − | 0.0116722i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.209793 | − | 0.363372i | −0.00820984 | − | 0.0142199i | 0.861891 | − | 0.507093i | \(-0.169280\pi\) |
−0.870101 | + | 0.492873i | \(0.835947\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.97325 | 0.155248 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.97631 | + | 10.3513i | 0.233158 | + | 0.403842i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.936555 | + | 1.62216i | −0.0364830 | + | 0.0631904i | −0.883690 | − | 0.468072i | \(-0.844949\pi\) |
0.847207 | + | 0.531262i | \(0.178282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6664 | −0.570457 | −0.285228 | − | 0.958460i | \(-0.592069\pi\) | ||||
−0.285228 | + | 0.958460i | \(0.592069\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.27860 | + | 2.21460i | −0.0496567 | + | 0.0860078i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.73375 | −0.222345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.90930 | −0.151369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.134772 | −0.00521057 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.53250 | 0.0591614 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.6890 | −1.02878 | −0.514392 | − | 0.857555i | \(-0.671982\pi\) | ||||
−0.514392 | + | 0.857555i | \(0.671982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.99612 | − | 13.8497i | 0.307316 | − | 0.532287i | −0.670458 | − | 0.741947i | \(-0.733903\pi\) |
0.977774 | + | 0.209661i | \(0.0672359\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.44745 | 0.362560 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.05133 | + | 13.9453i | −0.308528 | + | 0.534386i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.17371 | + | 12.4252i | 0.274495 | + | 0.475438i | 0.970007 | − | 0.243075i | \(-0.0781562\pi\) |
−0.695513 | + | 0.718514i | \(0.744823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9590 | −0.418723 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.14349 | − | 10.6408i | −0.234389 | − | 0.405973i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.2928 | − | 36.8802i | −0.811191 | − | 1.40502i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.996519 | − | 1.72602i | 0.0379094 | − | 0.0656609i | −0.846448 | − | 0.532471i | \(-0.821264\pi\) |
0.884358 | + | 0.466810i | \(0.154597\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.252743 | + | 0.437764i | 0.00960091 | + | 0.0166293i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.91210 | −0.262191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.62599 | 0.213100 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.41572 | − | 4.18416i | 0.0913711 | − | 0.158259i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.6284 | + | 39.1935i | −0.854662 | + | 1.48032i | 0.0222959 | + | 0.999751i | \(0.492902\pi\) |
−0.876958 | + | 0.480567i | \(0.840431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5468 | − | 18.2675i | 0.397779 | − | 0.688973i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.85168 | − | 3.20720i | 0.0697381 | − | 0.120790i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.06652 | + | 5.31137i | 0.115328 | + | 0.199755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.66494 | + | 11.5440i | 0.250307 | + | 0.433544i | 0.963610 | − | 0.267311i | \(-0.0861351\pi\) |
−0.713303 | + | 0.700855i | \(0.752802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.255601 | + | 0.442715i | −0.00958580 | + | 0.0166031i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.215252 | 0.00806126 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.25029 | 0.0467581 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.22293 | − | 2.11817i | 0.0456710 | − | 0.0791045i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.7027 | − | 23.7338i | −0.511025 | − | 0.885121i | −0.999918 | − | 0.0127778i | \(-0.995933\pi\) |
0.488893 | − | 0.872344i | \(-0.337401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.74799 | − | 11.6879i | −0.251308 | − | 0.435279i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.1372 | −0.674529 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44753 | − | 4.23925i | 0.0908991 | − | 0.157442i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.3913 | − | 17.9982i | −0.385391 | − | 0.667517i | 0.606432 | − | 0.795135i | \(-0.292600\pi\) |
−0.991823 | + | 0.127618i | \(0.959267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.904172 | + | 1.56607i | 0.0334420 | + | 0.0579233i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7811 | − | 34.2619i | 0.730631 | − | 1.26549i | −0.225983 | − | 0.974131i | \(-0.572559\pi\) |
0.956614 | − | 0.291359i | \(-0.0941074\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.68609 | + | 4.65244i | 0.0990779 | + | 0.171608i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.73308 | − | 1.74561i | −0.100674 | − | 0.0643003i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.4427 | + | 38.8719i | 0.825567 | + | 1.42992i | 0.901485 | + | 0.432810i | \(0.142478\pi\) |
−0.0759177 | + | 0.997114i | \(0.524189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.09103 | − | 12.2820i | 0.260496 | − | 0.451191i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.9220 | − | 24.1137i | −0.510750 | − | 0.884644i | −0.999922 | − | 0.0124575i | \(-0.996035\pi\) |
0.489173 | − | 0.872187i | \(-0.337299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.4625 | −0.566504 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.92890 | + | 3.34095i | 0.0705747 | + | 0.122239i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.97776 | − | 12.0858i | 0.254962 | − | 0.441607i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.8633 | −0.651840 | −0.325920 | − | 0.945397i | \(-0.605674\pi\) | ||||
−0.325920 | + | 0.945397i | \(0.605674\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.8009 | − | 18.7078i | −0.393608 | − | 0.681748i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.39067 | − | 11.0690i | −0.232580 | − | 0.402841i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.36267 | + | 12.7525i | −0.267601 | + | 0.463498i | −0.968242 | − | 0.250016i | \(-0.919564\pi\) |
0.700641 | + | 0.713514i | \(0.252898\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.316407 | −0.0114848 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.1522 | −0.984265 | −0.492132 | − | 0.870520i | \(-0.663782\pi\) | ||||
−0.492132 | + | 0.870520i | \(0.663782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.39381 | + | 12.8065i | −0.267674 | + | 0.463625i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.405163 | + | 0.701763i | 0.0146487 | + | 0.0253723i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.70016 | + | 11.6050i | 0.241929 | + | 0.419033i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9693 | + | 25.9275i | −0.539806 | + | 0.934971i | 0.459108 | + | 0.888380i | \(0.348169\pi\) |
−0.998914 | + | 0.0465909i | \(0.985164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.2554 | − | 22.9591i | 0.477383 | − | 0.826851i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.92267 | − | 3.33017i | 0.0691537 | − | 0.119778i | −0.829375 | − | 0.558692i | \(-0.811303\pi\) |
0.898529 | + | 0.438914i | \(0.144637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.134765 | + | 0.233420i | −0.00484091 | + | 0.00838470i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.98849 | 0.214836 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.2014 | −1.11791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.838733 | + | 1.45273i | 0.0300122 | + | 0.0519827i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.44753 | + | 4.23925i | −0.0874677 | + | 0.151499i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.24885 | + | 3.89513i | 0.0802650 | + | 0.139023i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3853 | + | 31.8442i | 0.655364 | + | 1.13512i | 0.981802 | + | 0.189905i | \(0.0608181\pi\) |
−0.326438 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.98177 | 0.0705527 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.60768 | − | 11.4448i | −0.234942 | − | 0.406932i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.10335 | − | 10.5713i | 0.216736 | − | 0.375399i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.4945 | −0.478602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.6157 | − | 25.3152i | 0.517716 | − | 0.896711i | −0.482072 | − | 0.876132i | \(-0.660116\pi\) |
0.999788 | − | 0.0205793i | \(-0.00655105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00092 | −0.106165 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.151145 | −0.00534045 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.73553 | −0.167113 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.01893 | 0.0359125 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.6325 | 0.691097 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.9794 | −0.737596 | −0.368798 | − | 0.929510i | \(-0.620231\pi\) | ||||
−0.368798 | + | 0.929510i | \(0.620231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5242 | − | 35.5490i | 0.720703 | − | 1.24829i | −0.240015 | − | 0.970769i | \(-0.577152\pi\) |
0.960718 | − | 0.277525i | \(-0.0895142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.1989 | −0.568120 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.839614 | − | 1.45425i | 0.0294104 | − | 0.0509403i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.01448 | − | 8.68534i | −0.175435 | − | 0.303862i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.02632 | 0.140691 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.81163 | − | 15.2622i | −0.307528 | − | 0.532654i | 0.670293 | − | 0.742096i | \(-0.266168\pi\) |
−0.977821 | + | 0.209443i | \(0.932835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.7257 | − | 32.4338i | −0.652736 | − | 1.13057i | −0.982456 | − | 0.186493i | \(-0.940288\pi\) |
0.329720 | − | 0.944079i | \(-0.393046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.198096 | − | 0.343112i | 0.00689682 | − | 0.0119456i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.9726 | + | 46.7180i | 0.937930 | + | 1.62454i | 0.769323 | + | 0.638859i | \(0.220593\pi\) |
0.168607 | + | 0.985683i | \(0.446073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.4348 | −0.640268 | −0.320134 | − | 0.947372i | \(-0.603728\pi\) | ||||
−0.320134 | + | 0.947372i | \(0.603728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.6486 | −0.716293 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.17661 | − | 3.77000i | 0.0754150 | − | 0.130623i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.61904 | + | 11.4645i | −0.229061 | + | 0.396746i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.134765 | − | 0.233420i | 0.00465817 | − | 0.00806818i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.01582 | − | 5.22355i | 0.104118 | − | 0.180337i | −0.809260 | − | 0.587451i | \(-0.800131\pi\) |
0.913377 | + | 0.407114i | \(0.133465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.51916 | + | 4.36331i | 0.0868675 | + | 0.150459i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.36886 | − | 5.83504i | −0.116030 | − | 0.200969i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.52058 | + | 2.63373i | −0.0523096 | + | 0.0906029i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8342 | 0.475349 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.5873 | −0.569276 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.87424 | + | 3.24627i | −0.0642480 | + | 0.111281i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.8343 | − | 46.4784i | −0.918789 | − | 1.59139i | −0.801257 | − | 0.598320i | \(-0.795835\pi\) |
−0.117531 | − | 0.993069i | \(-0.537498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.24701 | − | 3.89194i | −0.0768461 | − | 0.133101i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.1692 | 1.30383 | 0.651917 | − | 0.758290i | \(-0.273965\pi\) | ||||
0.651917 | + | 0.758290i | \(0.273965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.85685 | − | 8.41231i | 0.165714 | − | 0.287024i | −0.771195 | − | 0.636599i | \(-0.780341\pi\) |
0.936908 | + | 0.349575i | \(0.113674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.42907 | − | 7.67138i | −0.150942 | − | 0.261440i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.1358 | 0.447148 | 0.223574 | − | 0.974687i | \(-0.428228\pi\) | ||||
0.223574 | + | 0.974687i | \(0.428228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.85480 | − | 17.0690i | −0.335073 | − | 0.580364i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.17169 | + | 14.1538i | −0.277525 | + | 0.480687i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.101267 | − | 0.175400i | −0.00343526 | − | 0.00595004i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.9262 | + | 11.9009i | −0.776824 | + | 0.403248i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.70238 | + | 6.41271i | 0.125307 | + | 0.217037i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.637931 | + | 1.10493i | −0.0215660 | + | 0.0373534i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.6683 | + | 42.7268i | 0.832990 | + | 1.44278i | 0.895657 | + | 0.444746i | \(0.146706\pi\) |
−0.0626674 | + | 0.998034i | \(0.519961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.5791 | 1.03141 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.81030 | − | 8.33168i | −0.162063 | − | 0.280701i | 0.773545 | − | 0.633741i | \(-0.218481\pi\) |
−0.935608 | + | 0.353039i | \(0.885148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5403 | + | 28.6487i | −0.556627 | + | 0.964106i | 0.441148 | + | 0.897434i | \(0.354571\pi\) |
−0.997775 | + | 0.0666719i | \(0.978762\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.24630 | 0.142738 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.4481 | − | 28.4890i | −0.552274 | − | 0.956567i | −0.998110 | − | 0.0614522i | \(-0.980427\pi\) |
0.445836 | − | 0.895115i | \(-0.352907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.54310 | + | 14.7971i | 0.286526 | + | 0.496278i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.198096 | + | 0.343112i | −0.00663647 | + | 0.0114947i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6429 | 0.556935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.8857 | 0.531000 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.26013 | + | 2.18260i | −0.0420744 | + | 0.0728750i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.659685 | + | 1.14261i | 0.0220017 | + | 0.0381081i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.46749 | + | 9.46998i | 0.182149 | + | 0.315491i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.42362 | − | 2.46579i | 0.0473752 | − | 0.0820562i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.4536 | − | 21.5702i | 0.413970 | − | 0.717018i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.23573 | − | 14.2647i | 0.273463 | − | 0.473651i | −0.696283 | − | 0.717767i | \(-0.745164\pi\) |
0.969746 | + | 0.244116i | \(0.0784976\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.40349 | + | 4.16297i | −0.0797187 | + | 0.138077i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.94871 | 0.230221 | 0.115110 | − | 0.993353i | \(-0.463278\pi\) | ||||
0.115110 | + | 0.993353i | \(0.463278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.52843 | −0.0505836 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.93403 | − | 3.34985i | −0.0639372 | − | 0.110743i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.53466 | + | 4.39016i | −0.0837018 | + | 0.144976i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.7034 | − | 28.9311i | −0.550994 | − | 0.954349i | −0.998203 | − | 0.0599197i | \(-0.980916\pi\) |
0.447210 | − | 0.894429i | \(-0.352418\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.72786 | − | 16.8491i | −0.320544 | − | 0.555198i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.3614 | 0.439796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.34684 | − | 4.06485i | −0.0771637 | − | 0.133652i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.28897 | − | 9.16076i | 0.173713 | − | 0.300879i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.16111 | −0.136522 | −0.0682609 | − | 0.997668i | \(-0.521745\pi\) | ||||
−0.0682609 | + | 0.997668i | \(0.521745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0713 | + | 20.9082i | −0.395622 | + | 0.685238i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.9314 | −1.04539 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.321045 | −0.0104993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.23307 | 0.105620 | 0.0528099 | − | 0.998605i | \(-0.483182\pi\) | ||||
0.0528099 | + | 0.998605i | \(0.483182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0643 | 0.785308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.5570 | −0.996131 | −0.498065 | − | 0.867139i | \(-0.665956\pi\) | ||||
−0.498065 | + | 0.867139i | \(0.665956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.54471 | 0.180561 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.637931 | − | 1.10493i | 0.0207519 | − | 0.0359433i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.08738 | −0.0353350 | −0.0176675 | − | 0.999844i | \(-0.505624\pi\) | ||||
−0.0176675 | + | 0.999844i | \(0.505624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.8598 | + | 32.6662i | −0.612216 | + | 1.06039i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6368 | + | 27.0837i | 0.507057 | + | 0.878248i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.4069 | −1.17933 | −0.589667 | − | 0.807646i | \(-0.700741\pi\) | ||||
−0.589667 | + | 0.807646i | \(0.700741\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.7379 | − | 20.3306i | −0.379829 | − | 0.657884i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.969693 | − | 1.67956i | −0.0313457 | − | 0.0542924i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.99110 | − | 12.1089i | 0.225754 | − | 0.391018i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4637 | + | 26.7839i | 0.498828 | + | 0.863996i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.9381 | 0.352476 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.6977 | 0.730665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.18753 | + | 3.78891i | −0.0703463 | + | 0.121843i | −0.899053 | − | 0.437840i | \(-0.855744\pi\) |
0.828707 | + | 0.559683i | \(0.189077\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.82081 | + | 3.15374i | −0.0584929 | + | 0.101313i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.7527 | − | 22.0883i | 0.409253 | − | 0.708847i | −0.585553 | − | 0.810634i | \(-0.699123\pi\) |
0.994806 | + | 0.101787i | \(0.0324560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.40944 | − | 7.63737i | 0.141360 | − | 0.244843i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.57788 | − | 2.73297i | −0.0505326 | − | 0.0875251i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.37763 | − | 11.0464i | −0.204038 | − | 0.353405i | 0.745788 | − | 0.666184i | \(-0.232073\pi\) |
−0.949826 | + | 0.312779i | \(0.898740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0299412 | − | 0.0518598i | 0.000956926 | − | 0.00165745i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.5903 | −0.370050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.9035 | 1.65546 | 0.827732 | − | 0.561123i | \(-0.189631\pi\) | ||||
0.827732 | + | 0.561123i | \(0.189631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.66683 | − | 11.5473i | 0.212423 | − | 0.367927i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.36248 | + | 4.09194i | 0.0751986 | + | 0.130248i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.891110 | + | 1.54345i | 0.0283356 | + | 0.0490788i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.9247 | 0.569397 | 0.284699 | − | 0.958617i | \(-0.408106\pi\) | ||||
0.284699 | + | 0.958617i | \(0.408106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6369 | − | 23.6198i | 0.432753 | − | 0.749551i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.65718 | − | 16.7267i | −0.306153 | − | 0.530273i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.78152 | −0.214773 | −0.107386 | − | 0.994217i | \(-0.534248\pi\) | ||||
−0.107386 | + | 0.994217i | \(0.534248\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.34684 | + | 4.06485i | 0.0742508 | + | 0.128606i |
(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 | 4020.2.q.l.841.8 | ✓ | 22 | |
67.29 | even | 3 | inner | 4020.2.q.l.3781.8 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.l.841.8 | ✓ | 22 | 1.1 | even | 1 | trivial | |
4020.2.q.l.3781.8 | yes | 22 | 67.29 | even | 3 | inner |