Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(35,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.l (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 179.8 | ||
Root | \(0.608741 + 1.27649i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.179 |
Dual form | 216.2.l.b.35.8 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40985 | + | 0.111062i | 0.996912 | + | 0.0785324i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.97533 | + | 0.313160i | 0.987665 | + | 0.156580i | ||||
\(5\) | −1.74322 | + | 3.01934i | −0.779591 | + | 1.35029i | 0.152587 | + | 0.988290i | \(0.451240\pi\) |
−0.932178 | + | 0.362001i | \(0.882094\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80802 | − | 1.04386i | 0.683367 | − | 0.394542i | −0.117756 | − | 0.993043i | \(-0.537570\pi\) |
0.801122 | + | 0.598501i | \(0.204237\pi\) | |||||||
\(8\) | 2.75013 | + | 0.660890i | 0.972318 | + | 0.233660i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.79300 | + | 4.06320i | −0.883225 | + | 1.28490i | ||||
\(11\) | 0.116985 | − | 0.0675415i | 0.0352724 | − | 0.0203645i | −0.482260 | − | 0.876028i | \(-0.660184\pi\) |
0.517533 | + | 0.855664i | \(0.326851\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.63890 | − | 1.52357i | −0.731900 | − | 0.422563i | 0.0872168 | − | 0.996189i | \(-0.472203\pi\) |
−0.819117 | + | 0.573627i | \(0.805536\pi\) | |||||||
\(14\) | 2.66496 | − | 1.27088i | 0.712241 | − | 0.339657i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.80386 | + | 1.23719i | 0.950966 | + | 0.309297i | ||||
\(17\) | − | 4.19800i | − | 1.01816i | −0.860718 | − | 0.509082i | \(-0.829985\pi\) | ||
0.860718 | − | 0.509082i | \(-0.170015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.919111 | 0.210858 | 0.105429 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105429 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(20\) | −4.38897 | + | 5.41829i | −0.981403 | + | 1.21157i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.172432 | − | 0.0822305i | 0.0367627 | − | 0.0175316i | ||||
\(23\) | −0.689877 | + | 1.19490i | −0.143849 | + | 0.249154i | −0.928943 | − | 0.370223i | \(-0.879281\pi\) |
0.785094 | + | 0.619377i | \(0.212615\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.57762 | − | 6.19662i | −0.715524 | − | 1.23932i | ||||
\(26\) | −3.55124 | − | 2.44108i | −0.696455 | − | 0.478736i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.89833 | − | 1.49577i | 0.736715 | − | 0.282674i | ||||
\(29\) | −4.24111 | − | 7.34582i | −0.787555 | − | 1.36409i | −0.927461 | − | 0.373921i | \(-0.878013\pi\) |
0.139906 | − | 0.990165i | \(-0.455320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.39877 | − | 2.53963i | −0.790042 | − | 0.456131i | 0.0499352 | − | 0.998752i | \(-0.484099\pi\) |
−0.839977 | + | 0.542621i | \(0.817432\pi\) | |||||||
\(32\) | 5.22546 | + | 2.16671i | 0.923739 | + | 0.383023i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.466236 | − | 5.91853i | 0.0799589 | − | 1.01502i | ||||
\(35\) | 7.27870i | 1.23033i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.61676i | 0.265794i | 0.991130 | + | 0.132897i | \(0.0424280\pi\) | ||||
−0.991130 | + | 0.132897i | \(0.957572\pi\) | |||||||
\(38\) | 1.29580 | + | 0.102078i | 0.210207 | + | 0.0165592i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.78953 | + | 7.15151i | −1.07352 | + | 1.13075i | ||||
\(41\) | −1.79408 | − | 1.03581i | −0.280188 | − | 0.161767i | 0.353320 | − | 0.935502i | \(-0.385053\pi\) |
−0.633509 | + | 0.773736i | \(0.718386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.41106 | + | 9.37224i | 0.825180 | + | 1.42925i | 0.901782 | + | 0.432191i | \(0.142259\pi\) |
−0.0766025 | + | 0.997062i | \(0.524407\pi\) | |||||||
\(44\) | 0.252236 | − | 0.0967817i | 0.0380260 | − | 0.0145904i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.10533 | + | 1.60801i | −0.162972 | + | 0.237088i | ||||
\(47\) | 0.205809 | + | 0.356471i | 0.0300203 | + | 0.0519966i | 0.880645 | − | 0.473776i | \(-0.157109\pi\) |
−0.850625 | + | 0.525773i | \(0.823776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.32071 | + | 2.28754i | −0.188673 | + | 0.326791i | ||||
\(50\) | −4.35568 | − | 9.13361i | −0.615987 | − | 1.29169i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.73559 | − | 3.83596i | −0.656708 | − | 0.531951i | ||||
\(53\) | 0.968137 | 0.132984 | 0.0664919 | − | 0.997787i | \(-0.478819\pi\) | ||||
0.0664919 | + | 0.997787i | \(0.478819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.470958i | 0.0635040i | ||||||||
\(56\) | 5.66217 | − | 1.67585i | 0.756639 | − | 0.223945i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.16348 | − | 10.8275i | −0.677998 | − | 1.42172i | ||||
\(59\) | −3.88770 | − | 2.24457i | −0.506136 | − | 0.292218i | 0.225108 | − | 0.974334i | \(-0.427726\pi\) |
−0.731244 | + | 0.682116i | \(0.761060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.44553 | + | 4.29868i | −0.953303 | + | 0.550390i | −0.894105 | − | 0.447857i | \(-0.852188\pi\) |
−0.0591976 | + | 0.998246i | \(0.518854\pi\) | |||||||
\(62\) | −5.91953 | − | 4.06902i | −0.751781 | − | 0.516766i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.12645 | + | 3.63507i | 0.890806 | + | 0.454384i | ||||
\(65\) | 9.20037 | − | 5.31183i | 1.14117 | − | 0.658852i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.15416 | − | 5.46316i | 0.385342 | − | 0.667432i | −0.606475 | − | 0.795103i | \(-0.707417\pi\) |
0.991817 | + | 0.127671i | \(0.0407502\pi\) | |||||||
\(68\) | 1.31464 | − | 8.29243i | 0.159424 | − | 1.00561i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.808385 | + | 10.2618i | −0.0966205 | + | 1.22653i | ||||
\(71\) | 11.9687 | 1.42042 | 0.710210 | − | 0.703990i | \(-0.248600\pi\) | ||||
0.710210 | + | 0.703990i | \(0.248600\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.06264 | −0.475496 | −0.237748 | − | 0.971327i | \(-0.576409\pi\) | ||||
−0.237748 | + | 0.971327i | \(0.576409\pi\) | |||||||
\(74\) | −0.179560 | + | 2.27939i | −0.0208735 | + | 0.264973i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.81555 | + | 0.287828i | 0.208258 | + | 0.0330162i | ||||
\(77\) | 0.141008 | − | 0.244232i | 0.0160693 | − | 0.0278329i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8672 | − | 6.27416i | 1.22265 | − | 0.705899i | 0.257170 | − | 0.966366i | \(-0.417210\pi\) |
0.965483 | + | 0.260468i | \(0.0838768\pi\) | |||||||
\(80\) | −10.3665 | + | 9.32847i | −1.15900 | + | 1.04296i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.41434 | − | 1.65959i | −0.266619 | − | 0.183271i | ||||
\(83\) | −5.23875 | + | 3.02459i | −0.575027 | + | 0.331992i | −0.759155 | − | 0.650910i | \(-0.774387\pi\) |
0.184128 | + | 0.982902i | \(0.441054\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.6752 | + | 7.31802i | 1.37482 | + | 0.793751i | ||||
\(86\) | 6.58787 | + | 13.8144i | 0.710388 | + | 1.48964i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.366362 | − | 0.108434i | 0.0390544 | − | 0.0115591i | ||||
\(89\) | 8.35848i | 0.885997i | 0.896522 | + | 0.442999i | \(0.146085\pi\) | ||||
−0.896522 | + | 0.442999i | \(0.853915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.36158 | −0.666875 | ||||||||
\(92\) | −1.73693 | + | 2.14428i | −0.181087 | + | 0.223557i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.250568 | + | 0.525426i | 0.0258441 | + | 0.0541936i | ||||
\(95\) | −1.60221 | + | 2.77511i | −0.164383 | + | 0.284720i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.477065 | − | 0.826300i | −0.0484386 | − | 0.0838981i | 0.840790 | − | 0.541362i | \(-0.182091\pi\) |
−0.889228 | + | 0.457464i | \(0.848758\pi\) | |||||||
\(98\) | −2.11606 | + | 3.07840i | −0.213754 | + | 0.310965i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.12645 | − | 13.3607i | −0.512645 | − | 1.33607i | ||||
\(101\) | 5.35926 | + | 9.28250i | 0.533266 | + | 0.923644i | 0.999245 | + | 0.0388479i | \(0.0123688\pi\) |
−0.465979 | + | 0.884796i | \(0.654298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.46070 | + | 4.30743i | 0.735124 | + | 0.424424i | 0.820294 | − | 0.571942i | \(-0.193810\pi\) |
−0.0851696 | + | 0.996366i | \(0.527143\pi\) | |||||||
\(104\) | −6.25042 | − | 5.93405i | −0.612904 | − | 0.581881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.36492 | + | 0.107523i | 0.132573 | + | 0.0104435i | ||||
\(107\) | − | 4.80774i | − | 0.464781i | −0.972623 | − | 0.232391i | \(-0.925345\pi\) | ||
0.972623 | − | 0.232391i | \(-0.0746548\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.16698i | − | 0.686472i | −0.939249 | − | 0.343236i | \(-0.888477\pi\) | ||
0.939249 | − | 0.343236i | \(-0.111523\pi\) | |||||||
\(110\) | −0.0523054 | + | 0.663978i | −0.00498712 | + | 0.0633078i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.16891 | − | 1.73384i | 0.771889 | − | 0.163833i | ||||
\(113\) | 0.213928 | + | 0.123511i | 0.0201246 | + | 0.0116190i | 0.510029 | − | 0.860157i | \(-0.329635\pi\) |
−0.489904 | + | 0.871776i | \(0.662968\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.40521 | − | 4.16595i | −0.224287 | − | 0.388477i | ||||
\(116\) | −6.07719 | − | 15.8386i | −0.564253 | − | 1.47058i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.23178 | − | 3.59627i | −0.481624 | − | 0.331063i | ||||
\(119\) | −4.38212 | − | 7.59006i | −0.401708 | − | 0.695779i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.49088 | + | 9.51048i | −0.499171 | + | 0.864589i | ||||
\(122\) | −10.9745 | + | 5.23356i | −0.993582 | + | 0.473825i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.89371 | − | 6.39413i | −0.708876 | − | 0.574210i | ||||
\(125\) | 7.51409 | 0.672081 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6276i | 1.56420i | 0.623156 | + | 0.782098i | \(0.285850\pi\) | ||||
−0.623156 | + | 0.782098i | \(0.714150\pi\) | |||||||
\(128\) | 9.64348 | + | 5.91636i | 0.852371 | + | 0.522938i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.5610 | − | 6.46706i | 1.18938 | − | 0.567199i | ||||
\(131\) | 12.7802 | + | 7.37864i | 1.11661 | + | 0.644675i | 0.940533 | − | 0.339702i | \(-0.110326\pi\) |
0.176076 | + | 0.984377i | \(0.443659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.66177 | − | 0.959423i | 0.144094 | − | 0.0831925i | ||||
\(134\) | 5.05362 | − | 7.35191i | 0.436567 | − | 0.635108i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.77442 | − | 11.5450i | 0.237904 | − | 0.989979i | ||||
\(137\) | −14.8589 | + | 8.57878i | −1.26948 | + | 0.732934i | −0.974889 | − | 0.222689i | \(-0.928516\pi\) |
−0.294590 | + | 0.955624i | \(0.595183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.607862 | + | 1.05285i | −0.0515581 | + | 0.0893013i | −0.890653 | − | 0.454684i | \(-0.849752\pi\) |
0.839095 | + | 0.543986i | \(0.183085\pi\) | |||||||
\(140\) | −2.27940 | + | 14.3778i | −0.192644 | + | 1.21515i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.8740 | + | 1.32926i | 1.41603 | + | 0.111549i | ||||
\(143\) | −0.411617 | −0.0344211 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.5727 | 2.45588 | ||||||||
\(146\) | −5.72770 | − | 0.451204i | −0.474028 | − | 0.0373419i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.506305 | + | 3.19364i | −0.0416180 | + | 0.262516i | ||||
\(149\) | 4.46357 | − | 7.73113i | 0.365670 | − | 0.633359i | −0.623214 | − | 0.782052i | \(-0.714173\pi\) |
0.988883 | + | 0.148693i | \(0.0475066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9453 | + | 10.9381i | −1.54175 | + | 0.890127i | −0.543017 | + | 0.839722i | \(0.682718\pi\) |
−0.998729 | + | 0.0504058i | \(0.983949\pi\) | |||||||
\(152\) | 2.52768 | + | 0.607431i | 0.205022 | + | 0.0492692i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.225924 | − | 0.328670i | 0.0182055 | − | 0.0264850i | ||||
\(155\) | 15.3360 | − | 8.85426i | 1.23182 | − | 0.711191i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.85478 | + | 2.80291i | 0.387454 | + | 0.223697i | 0.681056 | − | 0.732231i | \(-0.261521\pi\) |
−0.293602 | + | 0.955928i | \(0.594854\pi\) | |||||||
\(158\) | 16.0179 | − | 7.63868i | 1.27431 | − | 0.607701i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.6511 | + | 12.0004i | −1.23733 | + | 0.948714i | ||||
\(161\) | 2.88054i | 0.227018i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1763 | −1.34535 | −0.672676 | − | 0.739937i | \(-0.734855\pi\) | ||||
−0.672676 | + | 0.739937i | \(0.734855\pi\) | |||||||
\(164\) | −3.21952 | − | 2.60790i | −0.251403 | − | 0.203643i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.72174 | + | 3.68238i | −0.599323 | + | 0.285808i | ||||
\(167\) | −2.31249 | + | 4.00535i | −0.178946 | + | 0.309943i | −0.941520 | − | 0.336958i | \(-0.890602\pi\) |
0.762574 | + | 0.646901i | \(0.223935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.85746 | − | 3.21721i | −0.142881 | − | 0.247478i | ||||
\(170\) | 17.0573 | + | 11.7250i | 1.30824 | + | 0.899267i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.75363 | + | 20.2078i | 0.591209 | + | 1.54083i | ||||
\(173\) | 1.52076 | + | 2.63404i | 0.115621 | + | 0.200262i | 0.918028 | − | 0.396516i | \(-0.129781\pi\) |
−0.802407 | + | 0.596778i | \(0.796447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9368 | − | 7.46907i | −0.977930 | − | 0.564608i | ||||
\(176\) | 0.528557 | − | 0.112186i | 0.0398415 | − | 0.00845632i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.928307 | + | 11.7842i | −0.0695795 | + | 0.883261i | ||||
\(179\) | − | 17.9997i | − | 1.34536i | −0.739935 | − | 0.672679i | \(-0.765144\pi\) | ||
0.739935 | − | 0.672679i | \(-0.234856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.9507i | − | 1.18561i | −0.805347 | − | 0.592804i | \(-0.798021\pi\) | ||
0.805347 | − | 0.592804i | \(-0.201979\pi\) | |||||||
\(182\) | −8.96885 | − | 0.706528i | −0.664815 | − | 0.0523713i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.68695 | + | 2.83020i | −0.198085 | + | 0.208645i | ||||
\(185\) | −4.88156 | − | 2.81837i | −0.358899 | − | 0.207211i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.283539 | − | 0.491104i | −0.0207344 | − | 0.0359131i | ||||
\(188\) | 0.294908 | + | 0.768599i | 0.0215084 | + | 0.0560558i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.56708 | + | 3.73453i | −0.186235 | + | 0.270931i | ||||
\(191\) | −2.21964 | − | 3.84452i | −0.160607 | − | 0.278180i | 0.774479 | − | 0.632599i | \(-0.218012\pi\) |
−0.935087 | + | 0.354419i | \(0.884679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.673862 | − | 1.16716i | 0.0485057 | − | 0.0840143i | −0.840753 | − | 0.541419i | \(-0.817887\pi\) |
0.889259 | + | 0.457404i | \(0.151221\pi\) | |||||||
\(194\) | −0.580817 | − | 1.21794i | −0.0417003 | − | 0.0874430i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.32521 | + | 4.10505i | −0.237515 | + | 0.293218i | ||||
\(197\) | −9.16835 | −0.653218 | −0.326609 | − | 0.945160i | \(-0.605906\pi\) | ||||
−0.326609 | + | 0.945160i | \(0.605906\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 24.0240i | − | 1.70301i | −0.524344 | − | 0.851507i | \(-0.675689\pi\) | ||
0.524344 | − | 0.851507i | \(-0.324311\pi\) | |||||||
\(200\) | −5.74364 | − | 19.4059i | −0.406136 | − | 1.37221i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.52479 | + | 13.6821i | 0.459083 | + | 0.962670i | ||||
\(203\) | −15.3360 | − | 8.85426i | −1.07638 | − | 0.621447i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.25494 | − | 3.61129i | 0.436864 | − | 0.252224i | ||||
\(206\) | 10.0400 | + | 6.90142i | 0.699523 | + | 0.480844i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.15308 | − | 9.06028i | −0.565314 | − | 0.628217i | ||||
\(209\) | 0.107522 | − | 0.0620781i | 0.00743748 | − | 0.00429403i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1275 | − | 17.5414i | 0.697208 | − | 1.20760i | −0.272223 | − | 0.962234i | \(-0.587759\pi\) |
0.969431 | − | 0.245365i | \(-0.0789078\pi\) | |||||||
\(212\) | 1.91239 | + | 0.303181i | 0.131344 | + | 0.0208226i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.533955 | − | 6.77817i | 0.0365004 | − | 0.463346i | ||||
\(215\) | −37.7307 | −2.57321 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6041 | −0.719852 | ||||||||
\(218\) | 0.795977 | − | 10.1043i | 0.0539104 | − | 0.684352i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.147485 | + | 0.930298i | −0.00994344 | + | 0.0627207i | ||||
\(221\) | −6.39595 | + | 11.0781i | −0.430238 | + | 0.745194i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.521119 | − | 0.300868i | 0.0348967 | − | 0.0201476i | −0.482450 | − | 0.875923i | \(-0.660253\pi\) |
0.517347 | + | 0.855776i | \(0.326920\pi\) | |||||||
\(224\) | 11.7095 | − | 1.53720i | 0.782371 | − | 0.102708i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.287888 | + | 0.197891i | 0.0191500 | + | 0.0131635i | ||||
\(227\) | −9.23720 | + | 5.33310i | −0.613095 | + | 0.353970i | −0.774176 | − | 0.632971i | \(-0.781835\pi\) |
0.161081 | + | 0.986941i | \(0.448502\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1574 | − | 12.7926i | −1.46420 | − | 0.845356i | −0.464998 | − | 0.885312i | \(-0.653945\pi\) |
−0.999201 | + | 0.0399555i | \(0.987278\pi\) | |||||||
\(230\) | −2.92830 | − | 6.14047i | −0.193086 | − | 0.404891i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.80884 | − | 23.0049i | −0.447022 | − | 1.51035i | ||||
\(233\) | 4.71086i | 0.308619i | 0.988023 | + | 0.154309i | \(0.0493152\pi\) | ||||
−0.988023 | + | 0.154309i | \(0.950685\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.43508 | −0.0936141 | ||||||||
\(236\) | −6.97659 | − | 5.65123i | −0.454137 | − | 0.367864i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.33515 | − | 11.1875i | −0.345827 | − | 0.725178i | ||||
\(239\) | 7.51034 | − | 13.0083i | 0.485803 | − | 0.841436i | −0.514064 | − | 0.857752i | \(-0.671861\pi\) |
0.999867 | + | 0.0163162i | \(0.00519384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8731 | + | 22.2969i | 0.829230 | + | 1.43627i | 0.898643 | + | 0.438681i | \(0.144554\pi\) |
−0.0694129 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(242\) | −8.79754 | + | 12.7985i | −0.565527 | + | 0.822717i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.0536 | + | 6.15968i | −1.02772 | + | 0.394333i | ||||
\(245\) | −4.60458 | − | 7.97536i | −0.294176 | − | 0.509527i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.42544 | − | 1.40033i | −0.154327 | − | 0.0891009i | ||||
\(248\) | −10.4188 | − | 9.89142i | −0.661593 | − | 0.628106i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.5937 | + | 0.834527i | 0.670005 | + | 0.0527801i | ||||
\(251\) | 5.30436i | 0.334808i | 0.985888 | + | 0.167404i | \(0.0535385\pi\) | ||||
−0.985888 | + | 0.167404i | \(0.946462\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.186381i | 0.0117177i | ||||||||
\(254\) | −1.95775 | + | 24.8522i | −0.122840 | + | 1.55936i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.9387 | + | 9.41218i | 0.808671 | + | 0.588261i | ||||
\(257\) | 21.4984 | + | 12.4121i | 1.34104 | + | 0.774248i | 0.986959 | − | 0.160969i | \(-0.0514619\pi\) |
0.354077 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68767 | + | 2.92314i | 0.104867 | + | 0.181635i | ||||
\(260\) | 19.8372 | − | 7.61145i | 1.23025 | − | 0.472042i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.1986 | + | 11.8221i | 1.06253 | + | 0.730374i | ||||
\(263\) | 9.95859 | + | 17.2488i | 0.614073 | + | 1.06361i | 0.990546 | + | 0.137178i | \(0.0438033\pi\) |
−0.376473 | + | 0.926427i | \(0.622863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.68767 | + | 2.92314i | −0.103673 | + | 0.179567i | ||||
\(266\) | 2.44939 | − | 1.16808i | 0.150182 | − | 0.0716196i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.94135 | − | 9.80380i | 0.485095 | − | 0.598862i | ||||
\(269\) | −2.35540 | −0.143611 | −0.0718057 | − | 0.997419i | \(-0.522876\pi\) | ||||
−0.0718057 | + | 0.997419i | \(0.522876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0774i | 0.733648i | 0.930290 | + | 0.366824i | \(0.119555\pi\) | ||||
−0.930290 | + | 0.366824i | \(0.880445\pi\) | |||||||
\(272\) | 5.19371 | − | 15.9686i | 0.314915 | − | 0.968239i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.9015 | + | 10.4445i | −1.32312 | + | 0.630975i | ||||
\(275\) | −0.837057 | − | 0.483275i | −0.0504764 | − | 0.0291426i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5504 | + | 8.40069i | −0.874250 | + | 0.504748i | −0.868758 | − | 0.495237i | \(-0.835081\pi\) |
−0.00549164 | + | 0.999985i | \(0.501748\pi\) | |||||||
\(278\) | −0.973922 | + | 1.41684i | −0.0584120 | + | 0.0849765i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.81042 | + | 20.0174i | −0.287478 | + | 1.19627i | ||||
\(281\) | −11.9853 | + | 6.91973i | −0.714984 | + | 0.412796i | −0.812904 | − | 0.582398i | \(-0.802115\pi\) |
0.0979194 | + | 0.995194i | \(0.468781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.58123 | − | 4.47082i | 0.153438 | − | 0.265763i | −0.779051 | − | 0.626960i | \(-0.784299\pi\) |
0.932489 | + | 0.361198i | \(0.117632\pi\) | |||||||
\(284\) | 23.6421 | + | 3.74810i | 1.40290 | + | 0.222409i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.580317 | − | 0.0457149i | −0.0343148 | − | 0.00270318i | ||||
\(287\) | −4.32497 | −0.255295 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.623177 | −0.0366574 | ||||||||
\(290\) | 41.6930 | + | 3.28440i | 2.44830 | + | 0.192866i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.02506 | − | 1.27226i | −0.469631 | − | 0.0744531i | ||||
\(293\) | 5.41881 | − | 9.38566i | 0.316571 | − | 0.548316i | −0.663200 | − | 0.748443i | \(-0.730802\pi\) |
0.979770 | + | 0.200126i | \(0.0641353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.5542 | − | 7.82554i | 0.789158 | − | 0.455620i | ||||
\(296\) | −1.06850 | + | 4.44631i | −0.0621054 | + | 0.258436i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.15158 | − | 10.4040i | 0.414280 | − | 0.602686i | ||||
\(299\) | 3.64104 | − | 2.10215i | 0.210567 | − | 0.121571i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5666 | + | 11.2968i | 1.12780 | + | 0.651136i | ||||
\(302\) | −27.9247 | + | 13.3169i | −1.60689 | + | 0.766301i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.49617 | + | 1.13711i | 0.200519 | + | 0.0652179i | ||||
\(305\) | − | 29.9742i | − | 1.71632i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.6551 | 0.950557 | 0.475279 | − | 0.879835i | \(-0.342347\pi\) | ||||
0.475279 | + | 0.879835i | \(0.342347\pi\) | |||||||
\(308\) | 0.355021 | − | 0.438282i | 0.0202292 | − | 0.0249734i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.6048 | − | 10.7799i | 1.28387 | − | 0.612257i | ||||
\(311\) | 6.47216 | − | 11.2101i | 0.367002 | − | 0.635667i | −0.622093 | − | 0.782943i | \(-0.713717\pi\) |
0.989095 | + | 0.147277i | \(0.0470508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3593 | − | 23.1390i | −0.755112 | − | 1.30789i | −0.945318 | − | 0.326149i | \(-0.894249\pi\) |
0.190206 | − | 0.981744i | \(-0.439084\pi\) | |||||||
\(314\) | 6.53320 | + | 4.49085i | 0.368690 | + | 0.253433i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.4311 | − | 8.99039i | 1.31810 | − | 0.505749i | ||||
\(317\) | 12.5342 | + | 21.7098i | 0.703990 | + | 1.21935i | 0.967055 | + | 0.254568i | \(0.0819332\pi\) |
−0.263065 | + | 0.964778i | \(0.584733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.992296 | − | 0.572902i | −0.0555579 | − | 0.0320764i | ||||
\(320\) | −23.3985 | + | 15.1805i | −1.30801 | + | 0.848614i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.319918 | + | 4.06112i | −0.0178283 | + | 0.226317i | ||||
\(323\) | − | 3.85842i | − | 0.214688i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.8030i | 1.20941i | ||||||||
\(326\) | −24.2160 | − | 1.90763i | −1.34120 | − | 0.105654i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.24940 | − | 4.03431i | −0.234634 | − | 0.222757i | ||||
\(329\) | 0.744211 | + | 0.429671i | 0.0410297 | + | 0.0236885i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.47956 | − | 14.6870i | −0.466079 | − | 0.807272i | 0.533171 | − | 0.846008i | \(-0.321000\pi\) |
−0.999249 | + | 0.0387357i | \(0.987667\pi\) | |||||||
\(332\) | −11.2954 | + | 4.33400i | −0.619917 | + | 0.237859i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.70510 | + | 5.39010i | −0.202734 | + | 0.294933i | ||||
\(335\) | 10.9968 | + | 19.0470i | 0.600818 | + | 1.04065i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.47220 | − | 7.74608i | 0.243616 | − | 0.421956i | −0.718125 | − | 0.695914i | \(-0.755000\pi\) |
0.961742 | + | 0.273958i | \(0.0883329\pi\) | |||||||
\(338\) | −2.26142 | − | 4.74207i | −0.123005 | − | 0.257934i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 22.7460 | + | 18.4249i | 1.23357 | + | 0.999229i | ||||
\(341\) | −0.686122 | −0.0371556 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1286i | 1.08684i | ||||||||
\(344\) | 8.68712 | + | 29.3510i | 0.468378 | + | 1.58250i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.85150 | + | 3.88248i | 0.0995372 | + | 0.208724i | ||||
\(347\) | 4.29330 | + | 2.47874i | 0.230476 | + | 0.133066i | 0.610792 | − | 0.791791i | \(-0.290851\pi\) |
−0.380315 | + | 0.924857i | \(0.624185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9731 | − | 13.2635i | 1.22972 | − | 0.709980i | 0.262749 | − | 0.964864i | \(-0.415371\pi\) |
0.966972 | + | 0.254884i | \(0.0820374\pi\) | |||||||
\(350\) | −17.4094 | − | 11.9670i | −0.930570 | − | 0.639664i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.757644 | − | 0.0994621i | 0.0403825 | − | 0.00530135i | ||||
\(353\) | 28.7458 | − | 16.5964i | 1.52998 | − | 0.883337i | 0.530623 | − | 0.847608i | \(-0.321958\pi\) |
0.999362 | − | 0.0357291i | \(-0.0113753\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.8640 | + | 36.1375i | −1.10735 | + | 1.91798i | ||||
\(356\) | −2.61754 | + | 16.5108i | −0.138729 | + | 0.875069i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.99907 | − | 25.3767i | 0.105654 | − | 1.34120i | ||||
\(359\) | 20.6138 | 1.08795 | 0.543977 | − | 0.839100i | \(-0.316918\pi\) | ||||
0.543977 | + | 0.839100i | \(0.316918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1552 | −0.955539 | ||||||||
\(362\) | 1.77151 | − | 22.4881i | 0.0931087 | − | 1.18195i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.5662 | − | 1.99219i | −0.658649 | − | 0.104419i | ||||
\(365\) | 7.08207 | − | 12.2665i | 0.370693 | − | 0.642058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1478 | − | 5.85881i | 0.529708 | − | 0.305827i | −0.211189 | − | 0.977445i | \(-0.567734\pi\) |
0.740898 | + | 0.671618i | \(0.234400\pi\) | |||||||
\(368\) | −4.10251 | + | 3.69174i | −0.213858 | + | 0.192445i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.56923 | − | 4.51562i | −0.341518 | − | 0.234756i | ||||
\(371\) | 1.75041 | − | 1.01060i | 0.0908767 | − | 0.0524677i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.02771 | − | 1.74805i | −0.156769 | − | 0.0905105i | 0.419563 | − | 0.907726i | \(-0.362183\pi\) |
−0.576332 | + | 0.817216i | \(0.695517\pi\) | |||||||
\(374\) | −0.345203 | − | 0.723871i | −0.0178500 | − | 0.0374305i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.330412 | + | 1.11636i | 0.0170397 | + | 0.0575718i | ||||
\(377\) | 25.8466i | 1.33117i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1604 | 1.03557 | 0.517785 | − | 0.855511i | \(-0.326757\pi\) | ||||
0.517785 | + | 0.855511i | \(0.326757\pi\) | |||||||
\(380\) | −4.03395 | + | 4.98001i | −0.206937 | + | 0.255469i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.70237 | − | 5.66670i | −0.138265 | − | 0.289934i | ||||
\(383\) | −5.33120 | + | 9.23391i | −0.272412 | + | 0.471831i | −0.969479 | − | 0.245175i | \(-0.921155\pi\) |
0.697067 | + | 0.717006i | \(0.254488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.491614 | + | 0.851501i | 0.0250550 | + | 0.0433965i | ||||
\(386\) | 1.07967 | − | 1.57068i | 0.0549537 | − | 0.0799455i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.683597 | − | 1.78161i | −0.0347044 | − | 0.0904477i | ||||
\(389\) | −8.34122 | − | 14.4474i | −0.422917 | − | 0.732513i | 0.573307 | − | 0.819341i | \(-0.305660\pi\) |
−0.996223 | + | 0.0868277i | \(0.972327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.01619 | + | 2.89610i | 0.253680 | + | 0.146462i | ||||
\(392\) | −5.14394 | + | 5.41819i | −0.259808 | + | 0.273660i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.9260 | − | 1.01825i | −0.651200 | − | 0.0512988i | ||||
\(395\) | 43.7489i | 2.20125i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.9869i | 1.15368i | 0.816857 | + | 0.576840i | \(0.195715\pi\) | ||||
−0.816857 | + | 0.576840i | \(0.804285\pi\) | |||||||
\(398\) | 2.66814 | − | 33.8701i | 0.133742 | − | 1.69775i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.94239 | − | 27.9973i | −0.297119 | − | 1.39986i | ||||
\(401\) | −27.3094 | − | 15.7671i | −1.36377 | − | 0.787371i | −0.373644 | − | 0.927572i | \(-0.621892\pi\) |
−0.990123 | + | 0.140201i | \(0.955225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.73862 | + | 13.4037i | 0.385488 | + | 0.667685i | ||||
\(404\) | 7.67940 | + | 20.0143i | 0.382064 | + | 0.995749i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.6381 | − | 14.1864i | −1.02425 | − | 0.704058i | ||||
\(407\) | 0.109199 | + | 0.189137i | 0.00541277 | + | 0.00937519i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.59259 | − | 6.22255i | 0.177642 | − | 0.307686i | −0.763430 | − | 0.645890i | \(-0.776486\pi\) |
0.941073 | + | 0.338205i | \(0.109820\pi\) | |||||||
\(410\) | 9.21958 | − | 4.39668i | 0.455323 | − | 0.217137i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.3884 | + | 10.8450i | 0.659600 | + | 0.534295i | ||||
\(413\) | −9.37205 | −0.461169 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 21.0901i | − | 1.03527i | ||||||
\(416\) | −10.4883 | − | 13.6791i | −0.514233 | − | 0.670672i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.158485 | − | 0.0755789i | 0.00775173 | − | 0.00369669i | ||||
\(419\) | 12.5999 | + | 7.27453i | 0.615543 | + | 0.355384i | 0.775132 | − | 0.631800i | \(-0.217683\pi\) |
−0.159589 | + | 0.987184i | \(0.551017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.38587 | − | 5.41893i | 0.457439 | − | 0.264103i | −0.253528 | − | 0.967328i | \(-0.581591\pi\) |
0.710967 | + | 0.703225i | \(0.248258\pi\) | |||||||
\(422\) | 16.2264 | − | 23.6059i | 0.789890 | − | 1.14912i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.66250 | + | 0.639832i | 0.129303 | + | 0.0310730i | ||||
\(425\) | −26.0134 | + | 15.0188i | −1.26183 | + | 0.728520i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.97444 | + | 15.5442i | −0.434304 | + | 0.752236i | ||||
\(428\) | 1.50559 | − | 9.49687i | 0.0727754 | − | 0.459048i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −53.1944 | − | 4.19043i | −2.56526 | − | 0.202080i | ||||
\(431\) | 10.8604 | 0.523129 | 0.261565 | − | 0.965186i | \(-0.415762\pi\) | ||||
0.261565 | + | 0.965186i | \(0.415762\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.41382 | 0.452399 | 0.226200 | − | 0.974081i | \(-0.427370\pi\) | ||||
0.226200 | + | 0.974081i | \(0.427370\pi\) | |||||||
\(434\) | −14.9501 | − | 1.17771i | −0.717628 | − | 0.0565317i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.24441 | − | 14.1572i | 0.107488 | − | 0.678005i | ||||
\(437\) | −0.634073 | + | 1.09825i | −0.0303318 | + | 0.0525363i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.25745 | + | 5.34479i | −0.441834 | + | 0.255093i | −0.704375 | − | 0.709828i | \(-0.748773\pi\) |
0.262541 | + | 0.964921i | \(0.415439\pi\) | |||||||
\(440\) | −0.311252 | + | 1.29520i | −0.0148383 | + | 0.0617461i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.2477 | + | 14.9081i | −0.487431 | + | 0.709105i | ||||
\(443\) | −18.9818 | + | 10.9592i | −0.901854 | + | 0.520686i | −0.877801 | − | 0.479025i | \(-0.840990\pi\) |
−0.0240526 | + | 0.999711i | \(0.507657\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.2371 | − | 14.5707i | −1.19635 | − | 0.690715i | ||||
\(446\) | 0.768113 | − | 0.366302i | 0.0363712 | − | 0.0173449i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.6793 | − | 0.866739i | 0.788021 | − | 0.0409496i | ||||
\(449\) | − | 18.7436i | − | 0.884565i | −0.896876 | − | 0.442282i | \(-0.854169\pi\) | ||
0.896876 | − | 0.442282i | \(-0.145831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.279841 | −0.0131772 | ||||||||
\(452\) | 0.383899 | + | 0.310969i | 0.0180571 | + | 0.0146267i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.6153 | + | 6.49295i | −0.638999 | + | 0.304729i | ||||
\(455\) | 11.0896 | − | 19.2078i | 0.519890 | − | 0.900475i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.00912370 | − | 0.0158027i | −0.000426789 | − | 0.000739220i | 0.865812 | − | 0.500370i | \(-0.166803\pi\) |
−0.866239 | + | 0.499630i | \(0.833469\pi\) | |||||||
\(458\) | −29.8177 | − | 20.4964i | −1.39329 | − | 0.957732i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.44648 | − | 8.98234i | −0.160693 | − | 0.418804i | ||||
\(461\) | 1.25915 | + | 2.18091i | 0.0586444 | + | 0.101575i | 0.893857 | − | 0.448352i | \(-0.147989\pi\) |
−0.835213 | + | 0.549927i | \(0.814656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.9003 | + | 13.7988i | 1.11074 | + | 0.641286i | 0.939021 | − | 0.343860i | \(-0.111735\pi\) |
0.171719 | + | 0.985146i | \(0.445068\pi\) | |||||||
\(464\) | −7.04445 | − | 33.1896i | −0.327030 | − | 1.54079i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.523196 | + | 6.64159i | −0.0242366 | + | 0.307666i | ||||
\(467\) | − | 28.4629i | − | 1.31711i | −0.752533 | − | 0.658554i | \(-0.771168\pi\) | ||
0.752533 | − | 0.658554i | \(-0.228832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13.1700i | − | 0.608134i | ||||||
\(470\) | −2.02324 | − | 0.159382i | −0.0933250 | − | 0.00735174i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.20828 | − | 8.74220i | −0.423846 | − | 0.402392i | ||||
\(473\) | 1.26603 | + | 0.730942i | 0.0582121 | + | 0.0336088i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.28823 | − | 5.69538i | −0.150874 | − | 0.261322i | ||||
\(476\) | −6.27924 | − | 16.3652i | −0.287808 | − | 0.750097i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0331 | − | 17.5056i | 0.550383 | − | 0.800686i | ||||
\(479\) | −19.1602 | − | 33.1865i | −0.875454 | − | 1.51633i | −0.856279 | − | 0.516514i | \(-0.827229\pi\) |
−0.0191747 | − | 0.999816i | \(-0.506104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.46325 | − | 4.26648i | 0.112315 | − | 0.194535i | ||||
\(482\) | 15.6728 | + | 32.8649i | 0.713875 | + | 1.49695i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.8246 | + | 17.0668i | −0.628391 | + | 0.775764i | ||||
\(485\) | 3.32651 | 0.151049 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.25659i | − | 0.102256i | −0.998692 | − | 0.0511280i | \(-0.983718\pi\) | ||
0.998692 | − | 0.0511280i | \(-0.0162817\pi\) | |||||||
\(488\) | −23.3172 | + | 6.90126i | −1.05552 | + | 0.312405i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.60599 | − | 11.7554i | −0.253253 | − | 0.531056i | ||||
\(491\) | 17.7659 | + | 10.2572i | 0.801765 | + | 0.462899i | 0.844088 | − | 0.536205i | \(-0.180142\pi\) |
−0.0423228 | + | 0.999104i | \(0.513476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.8377 | + | 17.8042i | −1.38886 | + | 0.801860i | ||||
\(494\) | −3.26398 | − | 2.24362i | −0.146853 | − | 0.100945i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.5903 | − | 15.1025i | −0.610223 | − | 0.678123i | ||||
\(497\) | 21.6396 | − | 12.4936i | 0.970667 | − | 0.560415i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.87815 | − | 3.25306i | 0.0840777 | − | 0.145627i | −0.820920 | − | 0.571043i | \(-0.806539\pi\) |
0.904998 | + | 0.425416i | \(0.139872\pi\) | |||||||
\(500\) | 14.8428 | + | 2.35311i | 0.663791 | + | 0.105234i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.589111 | + | 7.47833i | −0.0262933 | + | 0.333774i | ||||
\(503\) | 33.3322 | 1.48621 | 0.743104 | − | 0.669175i | \(-0.233353\pi\) | ||||
0.743104 | + | 0.669175i | \(0.233353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.3694 | −1.66292 | ||||||||
\(506\) | −0.0206998 | + | 0.262769i | −0.000920219 | + | 0.0116815i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.52025 | + | 34.8203i | −0.244921 | + | 1.54490i | ||||
\(509\) | −3.41788 | + | 5.91994i | −0.151495 | + | 0.262397i | −0.931777 | − | 0.363031i | \(-0.881742\pi\) |
0.780282 | + | 0.625427i | \(0.215075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.34533 | + | 4.24083i | −0.324938 | + | 0.187603i | ||||
\(512\) | 17.1963 | + | 14.7067i | 0.759976 | + | 0.649951i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.9310 | + | 19.8868i | 1.27609 | + | 0.877171i | ||||
\(515\) | −26.0112 | + | 15.0176i | −1.14619 | + | 0.661754i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0481531 | + | 0.0278012i | 0.00211777 | + | 0.00122270i | ||||
\(518\) | 2.05471 | + | 4.30861i | 0.0902788 | + | 0.189309i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 28.8128 | − | 8.52781i | 1.26352 | − | 0.373969i | ||||
\(521\) | − | 19.9468i | − | 0.873887i | −0.899489 | − | 0.436943i | \(-0.856061\pi\) | ||
0.899489 | − | 0.436943i | \(-0.143939\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.50358 | −0.240655 | −0.120327 | − | 0.992734i | \(-0.538394\pi\) | ||||
−0.120327 | + | 0.992734i | \(0.538394\pi\) | |||||||
\(524\) | 22.9344 | + | 18.5775i | 1.00189 | + | 0.811561i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.1244 | + | 25.4241i | 0.528649 | + | 1.10855i | ||||
\(527\) | −10.6614 | + | 18.4660i | −0.464416 | + | 0.804392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5481 | + | 18.2699i | 0.458615 | + | 0.794344i | ||||
\(530\) | −2.70401 | + | 3.93374i | −0.117455 | + | 0.170871i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.58300 | − | 1.37478i | 0.155343 | − | 0.0596042i | ||||
\(533\) | 3.15627 | + | 5.46682i | 0.136713 | + | 0.236794i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.5162 | + | 8.38093i | 0.627590 | + | 0.362339i | ||||
\(536\) | 12.2849 | − | 12.9399i | 0.530627 | − | 0.558917i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.32075 | − | 0.261595i | −0.143168 | − | 0.0112782i | ||||
\(539\) | 0.356811i | 0.0153690i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1375i | 0.521831i | 0.965362 | + | 0.260915i | \(0.0840243\pi\) | ||||
−0.965362 | + | 0.260915i | \(0.915976\pi\) | |||||||
\(542\) | −1.34133 | + | 17.0272i | −0.0576152 | + | 0.731382i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.09583 | − | 21.9364i | 0.389980 | − | 0.940517i | ||||
\(545\) | 21.6396 | + | 12.4936i | 0.926937 | + | 0.535167i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.02439 | + | 8.70250i | 0.214827 | + | 0.372092i | 0.953219 | − | 0.302280i | \(-0.0977477\pi\) |
−0.738392 | + | 0.674372i | \(0.764414\pi\) | |||||||
\(548\) | −32.0377 | + | 12.2927i | −1.36858 | + | 0.525119i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.12645 | − | 0.774308i | −0.0480319 | − | 0.0330166i | ||||
\(551\) | −3.89805 | − | 6.75163i | −0.166063 | − | 0.287629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0987 | − | 22.6876i | 0.557013 | − | 0.964775i | ||||
\(554\) | −21.4468 | + | 10.2277i | −0.911189 | + | 0.434533i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.53044 | + | 1.88936i | −0.0649050 | + | 0.0801269i | ||||
\(557\) | −15.4323 | −0.653887 | −0.326944 | − | 0.945044i | \(-0.606019\pi\) | ||||
−0.326944 | + | 0.945044i | \(0.606019\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 32.9766i | − | 1.39476i | ||||||
\(560\) | −9.00512 | + | 27.6872i | −0.380536 | + | 1.17000i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.6660 | + | 8.42464i | −0.745194 | + | 0.355372i | ||||
\(563\) | −5.08901 | − | 2.93814i | −0.214476 | − | 0.123828i | 0.388914 | − | 0.921274i | \(-0.372850\pi\) |
−0.603390 | + | 0.797446i | \(0.706184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.745845 | + | 0.430614i | −0.0313779 | + | 0.0181161i | ||||
\(566\) | 4.13567 | − | 6.01649i | 0.173835 | − | 0.252892i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 32.9154 | + | 7.90997i | 1.38110 | + | 0.331895i | ||||
\(569\) | 28.3228 | − | 16.3522i | 1.18735 | − | 0.685519i | 0.229650 | − | 0.973273i | \(-0.426242\pi\) |
0.957704 | + | 0.287754i | \(0.0929087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4253 | − | 28.4495i | 0.687377 | − | 1.19057i | −0.285306 | − | 0.958437i | \(-0.592095\pi\) |
0.972683 | − | 0.232136i | \(-0.0745715\pi\) | |||||||
\(572\) | −0.813080 | − | 0.128902i | −0.0339966 | − | 0.00538966i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.09754 | − | 0.480338i | −0.254507 | − | 0.0200489i | ||||
\(575\) | 9.87246 | 0.411710 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.7158 | −0.695887 | −0.347943 | − | 0.937516i | \(-0.613120\pi\) | ||||
−0.347943 | + | 0.937516i | \(0.613120\pi\) | |||||||
\(578\) | −0.878583 | − | 0.0692110i | −0.0365442 | − | 0.00287880i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 58.4159 | + | 9.26099i | 2.42559 | + | 0.384542i | ||||
\(581\) | −6.31450 | + | 10.9370i | −0.261970 | + | 0.453745i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.113258 | − | 0.0653894i | 0.00469066 | − | 0.00270815i | ||||
\(584\) | −11.1728 | − | 2.68496i | −0.462334 | − | 0.111104i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.68208 | − | 12.6305i | 0.358653 | − | 0.521762i | ||||
\(587\) | 23.7005 | − | 13.6835i | 0.978222 | − | 0.564777i | 0.0764895 | − | 0.997070i | \(-0.475629\pi\) |
0.901733 | + | 0.432293i | \(0.142296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.04296 | − | 2.33420i | −0.166587 | − | 0.0961791i | ||||
\(590\) | 19.9785 | − | 9.52744i | 0.822501 | − | 0.392239i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.00024 | + | 6.14994i | −0.0822093 | + | 0.252761i | ||||
\(593\) | 25.6865i | 1.05482i | 0.849612 | + | 0.527408i | \(0.176836\pi\) | ||||
−0.849612 | + | 0.527408i | \(0.823164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.5560 | 1.25267 | ||||||||
\(596\) | 11.2381 | − | 13.8737i | 0.460331 | − | 0.568290i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.36677 | − | 2.55933i | 0.219464 | − | 0.104659i | ||||
\(599\) | −19.9859 | + | 34.6166i | −0.816601 | + | 1.41439i | 0.0915718 | + | 0.995798i | \(0.470811\pi\) |
−0.908173 | + | 0.418596i | \(0.862522\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.01867 | + | 3.49645i | 0.0823434 | + | 0.142623i | 0.904256 | − | 0.426991i | \(-0.140426\pi\) |
−0.821913 | + | 0.569613i | \(0.807093\pi\) | |||||||
\(602\) | 26.3313 | + | 18.0998i | 1.07318 | + | 0.737694i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −40.8486 | + | 15.6734i | −1.66210 | + | 0.637742i | ||||
\(605\) | −19.1436 | − | 33.1577i | −0.778298 | − | 1.34805i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2251 | − | 6.48081i | −0.455612 | − | 0.263048i | 0.254585 | − | 0.967050i | \(-0.418061\pi\) |
−0.710198 | + | 0.704002i | \(0.751394\pi\) | |||||||
\(608\) | 4.80277 | + | 1.99144i | 0.194778 | + | 0.0807637i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.32898 | − | 42.2589i | 0.134786 | − | 1.71101i | ||||
\(611\) | − | 1.25426i | − | 0.0507418i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0890i | 0.892167i | 0.894991 | + | 0.446084i | \(0.147182\pi\) | ||||
−0.894991 | + | 0.446084i | \(0.852818\pi\) | |||||||
\(614\) | 23.4811 | + | 1.84974i | 0.947622 | + | 0.0746496i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.549201 | − | 0.578481i | 0.0221279 | − | 0.0233077i | ||||
\(617\) | −20.0171 | − | 11.5569i | −0.805859 | − | 0.465263i | 0.0396569 | − | 0.999213i | \(-0.487374\pi\) |
−0.845516 | + | 0.533951i | \(0.820707\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.24675 | − | 3.89149i | −0.0903046 | − | 0.156412i | 0.817335 | − | 0.576163i | \(-0.195451\pi\) |
−0.907639 | + | 0.419751i | \(0.862117\pi\) | |||||||
\(620\) | 33.0665 | − | 12.6875i | 1.32798 | − | 0.509541i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.3698 | − | 15.0857i | 0.415789 | − | 0.604882i | ||||
\(623\) | 8.72509 | + | 15.1123i | 0.349563 | + | 0.605461i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.78939 | − | 8.29547i | 0.191576 | − | 0.331819i | ||||
\(626\) | −16.2647 | − | 34.1061i | −0.650068 | − | 1.36315i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.71204 | + | 7.05700i | 0.347648 | + | 0.281605i | ||||
\(629\) | 6.78716 | 0.270622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.8693i | − | 1.22889i | −0.788961 | − | 0.614443i | \(-0.789381\pi\) | ||
0.788961 | − | 0.614443i | \(-0.210619\pi\) | |||||||
\(632\) | 34.0327 | − | 10.0728i | 1.35375 | − | 0.400673i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.2601 | + | 31.9996i | 0.606057 | + | 1.27087i | ||||
\(635\) | −53.2237 | − | 30.7287i | −2.11212 | − | 1.21943i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.97046 | − | 4.02440i | 0.276180 | − | 0.159452i | ||||
\(638\) | −1.33536 | − | 0.917910i | −0.0528673 | − | 0.0363404i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.6742 | + | 18.8034i | −1.37062 | + | 0.743271i | ||||
\(641\) | −23.7137 | + | 13.6911i | −0.936633 | + | 0.540766i | −0.888903 | − | 0.458095i | \(-0.848532\pi\) |
−0.0477300 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.9857 | + | 34.6162i | −0.788158 | + | 1.36513i | 0.138937 | + | 0.990301i | \(0.455631\pi\) |
−0.927094 | + | 0.374828i | \(0.877702\pi\) | |||||||
\(644\) | −0.902069 | + | 5.69002i | −0.0355465 | + | 0.224218i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.428523 | − | 5.43978i | 0.0168600 | − | 0.214025i | ||||
\(647\) | −30.9768 | −1.21782 | −0.608912 | − | 0.793238i | \(-0.708394\pi\) | ||||
−0.608912 | + | 0.793238i | \(0.708394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.606405 | −0.0238035 | ||||||||
\(650\) | −2.42148 | + | 30.7389i | −0.0949783 | + | 1.20568i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.9289 | − | 5.37893i | −1.32876 | − | 0.210655i | ||||
\(653\) | 2.78891 | − | 4.83053i | 0.109138 | − | 0.189033i | −0.806283 | − | 0.591530i | \(-0.798524\pi\) |
0.915421 | + | 0.402497i | \(0.131857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.5573 | + | 25.7252i | −1.74100 | + | 1.00517i | ||||
\(656\) | −5.54294 | − | 6.15970i | −0.216415 | − | 0.240496i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.00150 | + | 0.688423i | 0.0390427 | + | 0.0268375i | ||||
\(659\) | 5.69959 | − | 3.29066i | 0.222025 | − | 0.128186i | −0.384863 | − | 0.922974i | \(-0.625751\pi\) |
0.606887 | + | 0.794788i | \(0.292418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.9562 | + | 15.5632i | 1.04847 | + | 0.605337i | 0.922222 | − | 0.386661i | \(-0.126372\pi\) |
0.126253 | + | 0.991998i | \(0.459705\pi\) | |||||||
\(662\) | −10.3237 | − | 21.6482i | −0.401242 | − | 0.841381i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.4062 | + | 4.85579i | −0.636683 | + | 0.188441i | ||||
\(665\) | 6.68993i | 0.259425i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7034 | 0.453157 | ||||||||
\(668\) | −5.82225 | + | 7.18771i | −0.225270 | + | 0.278101i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.3884 | + | 28.0746i | 0.517238 | + | 1.08462i | ||||
\(671\) | −0.580679 | + | 1.00576i | −0.0224168 | + | 0.0388271i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.54087 | − | 6.13297i | −0.136491 | − | 0.236409i | 0.789675 | − | 0.613525i | \(-0.210249\pi\) |
−0.926166 | + | 0.377116i | \(0.876916\pi\) | |||||||
\(674\) | 7.16541 | − | 10.4241i | 0.276001 | − | 0.401521i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.66159 | − | 6.93674i | −0.102369 | − | 0.266798i | ||||
\(677\) | 3.18253 | + | 5.51231i | 0.122315 | + | 0.211855i | 0.920680 | − | 0.390318i | \(-0.127635\pi\) |
−0.798365 | + | 0.602173i | \(0.794302\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.72508 | − | 0.995978i | −0.0662026 | − | 0.0382221i | ||||
\(680\) | 30.0220 | + | 28.5024i | 1.15129 | + | 1.09302i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.967326 | − | 0.0762018i | −0.0370408 | − | 0.00291792i | ||||
\(683\) | 51.9104i | 1.98630i | 0.116864 | + | 0.993148i | \(0.462716\pi\) | ||||
−0.116864 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 59.8187i | − | 2.28556i | ||||||
\(686\) | −2.23552 | + | 28.3782i | −0.0853524 | + | 1.08349i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.98773 | + | 42.3452i | 0.342654 | + | 1.61440i | ||||
\(689\) | −2.55482 | − | 1.47503i | −0.0973309 | − | 0.0561940i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9150 | − | 31.0297i | −0.681519 | − | 1.18043i | −0.974517 | − | 0.224313i | \(-0.927986\pi\) |
0.292998 | − | 0.956113i | \(-0.405347\pi\) | |||||||
\(692\) | 2.17913 | + | 5.67933i | 0.0828382 | + | 0.215896i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.77760 | + | 3.97146i | 0.219315 | + | 0.150755i | ||||
\(695\) | −2.11927 | − | 3.67068i | −0.0803885 | − | 0.139237i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.34834 | + | 7.53154i | −0.164705 | + | 0.285277i | ||||
\(698\) | 33.8616 | − | 16.1481i | 1.28168 | − | 0.611214i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −23.2154 | − | 18.8052i | −0.877461 | − | 0.710768i | ||||
\(701\) | 19.0081 | 0.717927 | 0.358964 | − | 0.933352i | \(-0.383130\pi\) | ||||
0.358964 | + | 0.933352i | \(0.383130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.48598i | 0.0560449i | ||||||||
\(704\) | 1.07921 | − | 0.0560811i | 0.0406742 | − | 0.00211364i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.3704 | − | 20.2058i | 1.59463 | − | 0.760455i | ||||
\(707\) | 19.3793 | + | 11.1886i | 0.728832 | + | 0.420792i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.5758 | − | 22.2717i | 1.44874 | − | 0.836433i | 0.450337 | − | 0.892859i | \(-0.351304\pi\) |
0.998407 | + | 0.0564260i | \(0.0179705\pi\) | |||||||
\(710\) | −33.4285 | + | 48.6311i | −1.25455 | + | 1.82509i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.52404 | + | 22.9869i | −0.207022 | + | 0.861472i | ||||
\(713\) | 6.06922 | − | 3.50407i | 0.227294 | − | 0.131228i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.717538 | − | 1.24281i | 0.0268344 | − | 0.0464786i | ||||
\(716\) | 5.63676 | − | 35.5553i | 0.210656 | − | 1.32876i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.0623 | + | 2.28940i | 1.08459 | + | 0.0854397i | ||||
\(719\) | −40.5385 | −1.51183 | −0.755915 | − | 0.654670i | \(-0.772808\pi\) | ||||
−0.755915 | + | 0.654670i | \(0.772808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.9854 | 0.669813 | ||||||||
\(722\) | −25.5961 | − | 2.01635i | −0.952588 | − | 0.0750408i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.99512 | − | 31.5080i | 0.185642 | − | 1.17098i | ||||
\(725\) | −30.3462 | + | 52.5611i | −1.12703 | + | 1.95207i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5719 | − | 9.56779i | 0.614618 | − | 0.354850i | −0.160153 | − | 0.987092i | \(-0.551199\pi\) |
0.774770 | + | 0.632243i | \(0.217865\pi\) | |||||||
\(728\) | −17.4952 | − | 4.20431i | −0.648415 | − | 0.155822i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.3470 | − | 16.5073i | 0.419970 | − | 0.610964i | ||||
\(731\) | 39.3446 | − | 22.7156i | 1.45521 | − | 0.840168i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4597 | − | 14.6992i | −0.940377 | − | 0.542927i | −0.0502985 | − | 0.998734i | \(-0.516017\pi\) |
−0.890078 | + | 0.455807i | \(0.849351\pi\) | |||||||
\(734\) | 14.9575 | − | 7.13299i | 0.552090 | − | 0.263283i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.19392 | + | 4.74915i | −0.228311 | + | 0.175056i | ||||
\(737\) | − | 0.852146i | − | 0.0313892i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.807511 | −0.0297048 | −0.0148524 | − | 0.999890i | \(-0.504728\pi\) | ||||
−0.0148524 | + | 0.999890i | \(0.504728\pi\) | |||||||
\(740\) | −8.76009 | − | 7.09592i | −0.322027 | − | 0.260851i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.58005 | − | 1.23039i | 0.0947165 | − | 0.0451689i | ||||
\(743\) | −13.2127 | + | 22.8850i | −0.484725 | + | 0.839569i | −0.999846 | − | 0.0175489i | \(-0.994414\pi\) |
0.515121 | + | 0.857118i | \(0.327747\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.5620 | + | 26.9541i | 0.570146 | + | 0.987521i | ||||
\(746\) | −4.07446 | − | 2.80074i | −0.149177 | − | 0.102542i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.406289 | − | 1.05889i | −0.0148554 | − | 0.0387167i | ||||
\(749\) | −5.01860 | − | 8.69248i | −0.183376 | − | 0.317616i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.08658 | + | 1.20469i | 0.0761405 | + | 0.0439597i | 0.537587 | − | 0.843208i | \(-0.319336\pi\) |
−0.461446 | + | 0.887168i | \(0.652669\pi\) | |||||||
\(752\) | 0.341846 | + | 1.61059i | 0.0124658 | + | 0.0587322i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.87056 | + | 36.4397i | −0.104540 | + | 1.32705i | ||||
\(755\) | − | 76.2698i | − | 2.77574i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3.61528i | − | 0.131400i | −0.997839 | − | 0.0656998i | \(-0.979072\pi\) | ||
0.997839 | − | 0.0656998i | \(-0.0209280\pi\) | |||||||
\(758\) | 28.4231 | + | 2.23905i | 1.03237 | + | 0.0813258i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.24033 | + | 6.57303i | −0.226361 | + | 0.238429i | ||||
\(761\) | −7.79878 | − | 4.50263i | −0.282706 | − | 0.163220i | 0.351942 | − | 0.936022i | \(-0.385521\pi\) |
−0.634648 | + | 0.772802i | \(0.718855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.48133 | − | 12.9580i | −0.270842 | − | 0.469112i | ||||
\(764\) | −3.18057 | − | 8.28930i | −0.115069 | − | 0.299896i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.54171 | + | 12.4263i | −0.308624 | + | 0.448981i | ||||
\(767\) | 6.83951 | + | 11.8464i | 0.246961 | + | 0.427748i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.58489 | − | 13.1374i | 0.273518 | − | 0.473747i | −0.696242 | − | 0.717807i | \(-0.745146\pi\) |
0.969760 | + | 0.244060i | \(0.0784794\pi\) | |||||||
\(770\) | 0.598531 | + | 1.25508i | 0.0215696 | + | 0.0452301i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.69661 | − | 2.09451i | 0.0610623 | − | 0.0753830i | ||||
\(773\) | 31.6926 | 1.13990 | 0.569952 | − | 0.821678i | \(-0.306962\pi\) | ||||
0.569952 | + | 0.821678i | \(0.306962\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.3433i | 1.30549i | ||||||||
\(776\) | −0.765897 | − | 2.58772i | −0.0274941 | − | 0.0928938i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.1553 | − | 21.2950i | −0.364084 | − | 0.763463i | ||||
\(779\) | −1.64896 | − | 0.952026i | −0.0590800 | − | 0.0341099i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.40016 | − | 0.808381i | 0.0501016 | − | 0.0289262i | ||||
\(782\) | 6.75042 | + | 4.64016i | 0.241394 | + | 0.165932i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.85392 | + | 7.06752i | −0.280497 | + | 0.252411i | ||||
\(785\) | −16.9259 | + | 9.77217i | −0.604111 | + | 0.348784i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.3290 | − | 17.8904i | 0.368189 | − | 0.637723i | −0.621093 | − | 0.783737i | \(-0.713311\pi\) |
0.989283 | + | 0.146014i | \(0.0466444\pi\) | |||||||
\(788\) | −18.1105 | − | 2.87116i | −0.645161 | − | 0.102281i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.85883 | + | 61.6793i | −0.172869 | + | 2.19445i | ||||
\(791\) | 0.515713 | 0.0183367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1974 | 0.930297 | ||||||||
\(794\) | −2.55297 | + | 32.4080i | −0.0906014 | + | 1.15012i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.52333 | − | 47.4553i | 0.266657 | − | 1.68201i | ||||
\(797\) | 17.8453 | − | 30.9089i | 0.632112 | − | 1.09485i | −0.355007 | − | 0.934864i | \(-0.615521\pi\) |
0.987119 | − | 0.159987i | \(-0.0511452\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.49646 | − | 0.863984i | 0.0529411 | − | 0.0305655i | ||||
\(800\) | −5.26843 | − | 40.1318i | −0.186267 | − | 1.41887i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.7510 | − | 25.2622i | −1.29772 | − | 0.892040i | ||||
\(803\) | −0.475269 | + | 0.274397i | −0.0167719 | + | 0.00968325i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.69734 | − | 5.02141i | −0.306541 | − | 0.176981i | ||||
\(806\) | 9.42162 | + | 19.7566i | 0.331863 | + | 0.695896i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.60394 | + | 29.0700i | 0.302686 | + | 1.02268i | ||||
\(809\) | 18.7528i | 0.659314i | 0.944101 | + | 0.329657i | \(0.106933\pi\) | ||||
−0.944101 | + | 0.329657i | \(0.893067\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.9206 | −1.19111 | −0.595556 | − | 0.803314i | \(-0.703068\pi\) | ||||
−0.595556 | + | 0.803314i | \(0.703068\pi\) | |||||||
\(812\) | −27.5209 | − | 22.2927i | −0.965795 | − | 0.782321i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.132947 | + | 0.278782i | 0.00465980 | + | 0.00977131i | ||||
\(815\) | 29.9421 | − | 51.8612i | 1.04882 | − | 1.81662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.97337 | + | 8.61412i | 0.173996 | + | 0.301370i | ||||
\(818\) | 5.75609 | − | 8.37384i | 0.201257 | − | 0.292785i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.4865 | − | 5.17470i | 0.470969 | − | 0.180708i | ||||
\(821\) | 5.34636 | + | 9.26017i | 0.186589 | + | 0.323182i | 0.944111 | − | 0.329628i | \(-0.106923\pi\) |
−0.757522 | + | 0.652810i | \(0.773590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.4172 | − | 19.2934i | −1.16485 | − | 0.672527i | −0.212390 | − | 0.977185i | \(-0.568125\pi\) |
−0.952462 | + | 0.304658i | \(0.901458\pi\) | |||||||
\(824\) | 17.6712 | + | 16.7767i | 0.615604 | + | 0.584445i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.2131 | − | 1.04088i | −0.459744 | − | 0.0362167i | ||||
\(827\) | − | 0.214418i | − | 0.00745604i | −0.999993 | − | 0.00372802i | \(-0.998813\pi\) | ||
0.999993 | − | 0.00372802i | \(-0.00118667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.5733i | 1.23551i | 0.786369 | + | 0.617757i | \(0.211958\pi\) | ||||
−0.786369 | + | 0.617757i | \(0.788042\pi\) | |||||||
\(830\) | 2.34230 | − | 29.7338i | 0.0813024 | − | 1.03207i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.2677 | − | 20.4503i | −0.459975 | − | 0.708985i | ||||
\(833\) | 9.60309 | + | 5.54434i | 0.332727 | + | 0.192100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.06235 | − | 13.9644i | −0.279009 | − | 0.483258i | ||||
\(836\) | 0.231833 | − | 0.0889531i | 0.00801810 | − | 0.00307651i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.9559 | + | 11.6553i | 0.585733 | + | 0.402627i | ||||
\(839\) | −20.5867 | − | 35.6571i | −0.710730 | − | 1.23102i | −0.964583 | − | 0.263778i | \(-0.915031\pi\) |
0.253853 | − | 0.967243i | \(-0.418302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4741 | + | 37.1942i | −0.740486 | + | 1.28256i | ||||
\(842\) | 13.8345 | − | 6.59745i | 0.476767 | − | 0.227363i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.4985 | − | 31.4785i | 0.877693 | − | 1.08353i | ||||
\(845\) | 12.9518 | 0.445556 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.9268i | 0.787775i | ||||||||
\(848\) | 3.68266 | + | 1.19777i | 0.126463 | + | 0.0411315i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −38.3429 | + | 18.2851i | −1.31515 | + | 0.627175i | ||||
\(851\) | −1.93187 | − | 1.11537i | −0.0662237 | − | 0.0382343i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.9858 | + | 17.8897i | −1.06093 | + | 0.612530i | −0.925690 | − | 0.378282i | \(-0.876515\pi\) |
−0.135243 | + | 0.990812i | \(0.543181\pi\) | |||||||
\(854\) | −14.3789 | + | 20.9182i | −0.492037 | + | 0.715806i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.17739 | − | 13.2219i | 0.108601 | − | 0.451915i | ||||
\(857\) | −26.3688 | + | 15.2241i | −0.900742 | + | 0.520044i | −0.877441 | − | 0.479685i | \(-0.840751\pi\) |
−0.0233014 | + | 0.999728i | \(0.507418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.7147 | + | 20.2904i | −0.399700 | + | 0.692301i | −0.993689 | − | 0.112172i | \(-0.964219\pi\) |
0.593989 | + | 0.804473i | \(0.297552\pi\) | |||||||
\(860\) | −74.5305 | − | 11.8157i | −2.54147 | − | 0.402913i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.3115 | + | 1.20618i | 0.521513 | + | 0.0410826i | ||||
\(863\) | 32.2240 | 1.09692 | 0.548458 | − | 0.836178i | \(-0.315215\pi\) | ||||
0.548458 | + | 0.836178i | \(0.315215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.6041 | −0.360549 | ||||||||
\(866\) | 13.2720 | + | 1.04551i | 0.451002 | + | 0.0355280i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.9466 | − | 3.32077i | −0.710972 | − | 0.112714i | ||||
\(869\) | 0.847532 | − | 1.46797i | 0.0287506 | − | 0.0497974i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.6470 | + | 9.61117i | −0.564063 | + | 0.325662i | ||||
\(872\) | 4.73659 | − | 19.7101i | 0.160401 | − | 0.667470i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.01592 | + | 1.47794i | −0.0343640 | + | 0.0499920i | ||||
\(875\) | 13.5856 | − | 7.84366i | 0.459278 | − | 0.265164i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.74081 | − | 1.00506i | −0.0587829 | − | 0.0339384i | 0.470320 | − | 0.882496i | \(-0.344138\pi\) |
−0.529103 | + | 0.848557i | \(0.677472\pi\) | |||||||
\(878\) | −13.6452 | + | 6.50718i | −0.460502 | + | 0.219607i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.582663 | + | 1.79146i | −0.0196416 | + | 0.0603901i | ||||
\(881\) | 21.6545i | 0.729558i | 0.931094 | + | 0.364779i | \(0.118855\pi\) | ||||
−0.931094 | + | 0.364779i | \(0.881145\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.3462 | −0.785664 | −0.392832 | − | 0.919610i | \(-0.628505\pi\) | ||||
−0.392832 | + | 0.919610i | \(0.628505\pi\) | |||||||
\(884\) | −16.1033 | + | 19.8800i | −0.541614 | + | 0.668636i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.9786 | + | 13.3426i | −0.939959 | + | 0.448253i | ||||
\(887\) | 24.4901 | − | 42.4181i | 0.822297 | − | 1.42426i | −0.0816710 | − | 0.996659i | \(-0.526026\pi\) |
0.903968 | − | 0.427600i | \(-0.140641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.4007 | + | 31.8710i | 0.617141 | + | 1.06892i | ||||
\(890\) | −33.9622 | − | 23.3453i | −1.13842 | − | 0.782535i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.12360 | − | 0.431121i | 0.0376210 | − | 0.0144350i | ||||
\(893\) | 0.189161 | + | 0.327636i | 0.00633003 | + | 0.0109639i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.3471 | + | 31.3773i | 1.81662 | + | 1.04883i | ||||
\(896\) | 23.6114 | + | 0.630457i | 0.788803 | + | 0.0210621i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.08169 | − | 26.4256i | 0.0694670 | − | 0.881833i | ||||
\(899\) | 43.0834i | 1.43691i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 4.06424i | − | 0.135399i | ||||||
\(902\) | −0.394533 | − | 0.0310796i | −0.0131365 | − | 0.00103484i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.506702 | + | 0.481055i | 0.0168526 | + | 0.0159996i | ||||
\(905\) | 48.1607 | + | 27.8056i | 1.60092 | + | 0.924289i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.93443 | − | 17.2069i | −0.329867 | − | 0.571347i | 0.652618 | − | 0.757687i | \(-0.273671\pi\) |
−0.982485 | + | 0.186340i | \(0.940337\pi\) | |||||||
\(908\) | −19.9166 | + | 7.64192i | −0.660957 | + | 0.253606i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.7679 | − | 25.8484i | 0.589001 | − | 0.856866i | ||||
\(911\) | −24.0672 | − | 41.6857i | −0.797383 | − | 1.38111i | −0.921315 | − | 0.388817i | \(-0.872884\pi\) |
0.123932 | − | 0.992291i | \(-0.460450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.408571 | + | 0.707665i | −0.0135217 | + | 0.0234203i | ||||
\(914\) | −0.0111079 | − | 0.0232927i | −0.000367418 | − | 0.000770453i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −39.7620 | − | 32.2083i | −1.31377 | − | 1.06419i | ||||
\(917\) | 30.8091 | 1.01741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.3644i | 1.13358i | 0.823864 | + | 0.566788i | \(0.191814\pi\) | ||||
−0.823864 | + | 0.566788i | \(0.808186\pi\) | |||||||
\(920\) | −3.86141 | − | 13.0465i | −0.127307 | − | 0.430130i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.53299 | + | 3.21459i | 0.0504864 | + | 0.105867i | ||||
\(923\) | −31.5841 | − | 18.2351i | −1.03960 | − | 0.600216i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0185 | − | 5.78416i | 0.329405 | − | 0.190182i | ||||
\(926\) | 32.1632 | + | 22.1086i | 1.05695 | + | 0.726535i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.24550 | − | 47.5745i | −0.205019 | − | 1.56171i | ||||
\(929\) | −15.1165 | + | 8.72750i | −0.495955 | + | 0.286340i | −0.727042 | − | 0.686593i | \(-0.759105\pi\) |
0.231086 | + | 0.972933i | \(0.425772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.21388 | + | 2.10250i | −0.0397833 | + | 0.0689067i | ||||
\(932\) | −1.47525 | + | 9.30551i | −0.0483235 | + | 0.304812i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.16114 | − | 40.1284i | 0.103436 | − | 1.31304i | ||||
\(935\) | 1.97708 | 0.0646574 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.3068 | 1.38210 | 0.691051 | − | 0.722806i | \(-0.257148\pi\) | ||||
0.691051 | + | 0.722806i | \(0.257148\pi\) | |||||||
\(938\) | 1.46268 | − | 18.5677i | 0.0477583 | − | 0.606256i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.83475 | − | 0.449408i | −0.0924594 | − | 0.0146581i | ||||
\(941\) | −11.6752 | + | 20.2221i | −0.380602 | + | 0.659222i | −0.991148 | − | 0.132758i | \(-0.957617\pi\) |
0.610546 | + | 0.791980i | \(0.290950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.47539 | − | 1.42917i | 0.0806097 | − | 0.0465400i | ||||
\(944\) | −12.0113 | − | 13.3478i | −0.390936 | − | 0.434435i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.70373 | + | 1.17112i | 0.0553929 | + | 0.0380765i | ||||
\(947\) | −28.1206 | + | 16.2354i | −0.913796 | + | 0.527580i | −0.881651 | − | 0.471903i | \(-0.843567\pi\) |
−0.0321454 | + | 0.999483i | \(0.510234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7209 | + | 6.18973i | 0.348016 | + | 0.200927i | ||||
\(950\) | −4.00335 | − | 8.39480i | −0.129886 | − | 0.272363i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.03522 | − | 23.7698i | −0.228013 | − | 0.770382i | ||||
\(953\) | − | 11.0705i | − | 0.358607i | −0.983794 | − | 0.179304i | \(-0.942616\pi\) | ||
0.983794 | − | 0.179304i | \(-0.0573844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.4772 | 0.500832 | ||||||||
\(956\) | 18.9091 | − | 23.3437i | 0.611563 | − | 0.754990i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.3272 | − | 48.9158i | −0.753669 | − | 1.58040i | ||||
\(959\) | −17.9101 | + | 31.0212i | −0.578347 | + | 1.00173i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.60055 | − | 4.50429i | −0.0838888 | − | 0.145300i | ||||
\(962\) | 3.94665 | − | 5.74151i | 0.127245 | − | 0.185114i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.4462 | + | 48.0751i | 0.594111 | + | 1.54839i | ||||
\(965\) | 2.34938 | + | 4.06924i | 0.0756291 | + | 0.130993i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.9201 | − | 23.6252i | −1.31590 | − | 0.759736i | −0.332835 | − | 0.942985i | \(-0.608005\pi\) |
−0.983066 | + | 0.183249i | \(0.941338\pi\) | |||||||
\(968\) | −21.3860 | + | 22.5262i | −0.687373 | + | 0.724019i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.68987 | + | 0.369448i | 0.150583 | + | 0.0118623i | ||||
\(971\) | − | 33.9428i | − | 1.08928i | −0.838671 | − | 0.544638i | \(-0.816667\pi\) | ||
0.838671 | − | 0.544638i | \(-0.183333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.53809i | 0.0813674i | ||||||||
\(974\) | 0.250621 | − | 3.18145i | 0.00803042 | − | 0.101940i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.6401 | + | 7.14007i | −1.07679 | + | 0.228548i | ||||
\(977\) | −26.9476 | − | 15.5582i | −0.862131 | − | 0.497752i | 0.00259421 | − | 0.999997i | \(-0.499174\pi\) |
−0.864725 | + | 0.502245i | \(0.832508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.564544 | + | 0.977819i | 0.0180429 | + | 0.0312512i | ||||
\(980\) | −6.59800 | − | 17.1959i | −0.210765 | − | 0.549304i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.9080 | + | 16.4341i | 0.762936 | + | 0.524434i | ||||
\(983\) | 18.2288 | + | 31.5733i | 0.581410 | + | 1.00703i | 0.995313 | + | 0.0967103i | \(0.0308320\pi\) |
−0.413903 | + | 0.910321i | \(0.635835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.9824 | − | 27.6824i | 0.509243 | − | 0.882034i | ||||
\(986\) | −45.4538 | + | 21.6763i | −1.44754 | + | 0.690313i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.35253 | − | 3.52567i | −0.138472 | − | 0.112166i | ||||
\(989\) | −14.9319 | −0.474806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 21.5164i | − | 0.683490i | −0.939793 | − | 0.341745i | \(-0.888982\pi\) | ||
0.939793 | − | 0.341745i | \(-0.111018\pi\) | |||||||
\(992\) | −17.4829 | − | 22.8016i | −0.555084 | − | 0.723951i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 31.8960 | − | 15.2107i | 1.01168 | − | 0.482455i | ||||
\(995\) | 72.5365 | + | 41.8790i | 2.29956 | + | 1.32765i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.4923 | − | 28.5744i | 1.56744 | − | 0.904961i | 0.570971 | − | 0.820970i | \(-0.306567\pi\) |
0.996467 | − | 0.0839906i | \(-0.0267666\pi\) | |||||||
\(998\) | 3.00920 | − | 4.37772i | 0.0952544 | − | 0.138574i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 216.2.l.b.179.8 | 16 | ||
3.2 | odd | 2 | 72.2.l.b.59.1 | yes | 16 | ||
4.3 | odd | 2 | 864.2.p.b.719.1 | 16 | |||
8.3 | odd | 2 | inner | 216.2.l.b.179.5 | 16 | ||
8.5 | even | 2 | 864.2.p.b.719.8 | 16 | |||
9.2 | odd | 6 | inner | 216.2.l.b.35.5 | 16 | ||
9.4 | even | 3 | 648.2.f.b.323.8 | 16 | |||
9.5 | odd | 6 | 648.2.f.b.323.9 | 16 | |||
9.7 | even | 3 | 72.2.l.b.11.4 | yes | 16 | ||
12.11 | even | 2 | 288.2.p.b.239.8 | 16 | |||
24.5 | odd | 2 | 288.2.p.b.239.7 | 16 | |||
24.11 | even | 2 | 72.2.l.b.59.4 | yes | 16 | ||
36.7 | odd | 6 | 288.2.p.b.47.7 | 16 | |||
36.11 | even | 6 | 864.2.p.b.143.8 | 16 | |||
36.23 | even | 6 | 2592.2.f.b.1295.1 | 16 | |||
36.31 | odd | 6 | 2592.2.f.b.1295.15 | 16 | |||
72.5 | odd | 6 | 2592.2.f.b.1295.16 | 16 | |||
72.11 | even | 6 | inner | 216.2.l.b.35.8 | 16 | ||
72.13 | even | 6 | 2592.2.f.b.1295.2 | 16 | |||
72.29 | odd | 6 | 864.2.p.b.143.1 | 16 | |||
72.43 | odd | 6 | 72.2.l.b.11.1 | ✓ | 16 | ||
72.59 | even | 6 | 648.2.f.b.323.7 | 16 | |||
72.61 | even | 6 | 288.2.p.b.47.8 | 16 | |||
72.67 | odd | 6 | 648.2.f.b.323.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.l.b.11.1 | ✓ | 16 | 72.43 | odd | 6 | ||
72.2.l.b.11.4 | yes | 16 | 9.7 | even | 3 | ||
72.2.l.b.59.1 | yes | 16 | 3.2 | odd | 2 | ||
72.2.l.b.59.4 | yes | 16 | 24.11 | even | 2 | ||
216.2.l.b.35.5 | 16 | 9.2 | odd | 6 | inner | ||
216.2.l.b.35.8 | 16 | 72.11 | even | 6 | inner | ||
216.2.l.b.179.5 | 16 | 8.3 | odd | 2 | inner | ||
216.2.l.b.179.8 | 16 | 1.1 | even | 1 | trivial | ||
288.2.p.b.47.7 | 16 | 36.7 | odd | 6 | |||
288.2.p.b.47.8 | 16 | 72.61 | even | 6 | |||
288.2.p.b.239.7 | 16 | 24.5 | odd | 2 | |||
288.2.p.b.239.8 | 16 | 12.11 | even | 2 | |||
648.2.f.b.323.7 | 16 | 72.59 | even | 6 | |||
648.2.f.b.323.8 | 16 | 9.4 | even | 3 | |||
648.2.f.b.323.9 | 16 | 9.5 | odd | 6 | |||
648.2.f.b.323.10 | 16 | 72.67 | odd | 6 | |||
864.2.p.b.143.1 | 16 | 72.29 | odd | 6 | |||
864.2.p.b.143.8 | 16 | 36.11 | even | 6 | |||
864.2.p.b.719.1 | 16 | 4.3 | odd | 2 | |||
864.2.p.b.719.8 | 16 | 8.5 | even | 2 | |||
2592.2.f.b.1295.1 | 16 | 36.23 | even | 6 | |||
2592.2.f.b.1295.2 | 16 | 72.13 | even | 6 | |||
2592.2.f.b.1295.15 | 16 | 36.31 | odd | 6 | |||
2592.2.f.b.1295.16 | 16 | 72.5 | odd | 6 |