Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(49,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.j (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: | \(3.79289409601\) |
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: | \( x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(1.19454 - 0.689667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.49 |
Dual form | 475.2.j.c.349.4 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.950409 | − | 0.548719i | −0.672041 | − | 0.388003i | 0.124809 | − | 0.992181i | \(-0.460168\pi\) |
−0.796850 | + | 0.604178i | \(0.793502\pi\) | |||||||
\(3\) | −0.328513 | − | 0.189667i | −0.189667 | − | 0.109504i | 0.402160 | − | 0.915570i | \(-0.368260\pi\) |
−0.591827 | + | 0.806065i | \(0.701593\pi\) | |||||||
\(4\) | −0.397815 | − | 0.689035i | −0.198907 | − | 0.344518i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.208148 | + | 0.360522i | 0.0849759 | + | 0.147183i | ||||
\(7\) | 1.89307i | 0.715512i | 0.933815 | + | 0.357756i | \(0.116458\pi\) | ||||
−0.933815 | + | 0.357756i | \(0.883542\pi\) | |||||||
\(8\) | 3.06803i | 1.08471i | ||||||||
\(9\) | −1.42805 | − | 2.47346i | −0.476018 | − | 0.824487i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.134400 | 0.0405231 | 0.0202615 | − | 0.999795i | \(-0.493550\pi\) | ||||
0.0202615 | + | 0.999795i | \(0.493550\pi\) | |||||||
\(12\) | 0.301809i | 0.0871248i | ||||||||
\(13\) | −3.04298 | + | 1.75687i | −0.843972 | + | 0.487267i | −0.858612 | − | 0.512626i | \(-0.828673\pi\) |
0.0146407 | + | 0.999893i | \(0.495340\pi\) | |||||||
\(14\) | 1.03876 | − | 1.79919i | 0.277621 | − | 0.480854i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.887858 | − | 1.53781i | 0.221964 | − | 0.384454i | ||||
\(17\) | 1.43867 | + | 0.830615i | 0.348928 | + | 0.201454i | 0.664213 | − | 0.747543i | \(-0.268767\pi\) |
−0.315285 | + | 0.948997i | \(0.602100\pi\) | |||||||
\(18\) | 3.13440i | 0.738785i | ||||||||
\(19\) | −2.10596 | + | 3.81640i | −0.483141 | + | 0.875543i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.359052 | − | 0.621897i | 0.0783516 | − | 0.135709i | ||||
\(22\) | −0.127735 | − | 0.0737478i | −0.0272332 | − | 0.0157231i | ||||
\(23\) | −4.65042 | + | 2.68492i | −0.969679 | + | 0.559844i | −0.899138 | − | 0.437664i | \(-0.855806\pi\) |
−0.0705407 | + | 0.997509i | \(0.522472\pi\) | |||||||
\(24\) | 0.581904 | − | 1.00789i | 0.118781 | − | 0.205734i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.85611 | 0.756245 | ||||||||
\(27\) | 2.22142i | 0.427512i | ||||||||
\(28\) | 1.30439 | − | 0.753090i | 0.246507 | − | 0.142321i | ||||
\(29\) | 2.48530 | + | 4.30466i | 0.461508 | + | 0.799355i | 0.999036 | − | 0.0438905i | \(-0.0139753\pi\) |
−0.537528 | + | 0.843246i | \(0.680642\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.56472 | 1.17906 | 0.589529 | − | 0.807747i | \(-0.299313\pi\) | ||||
0.589529 | + | 0.807747i | \(0.299313\pi\) | |||||||
\(32\) | 3.62633 | − | 2.09366i | 0.641050 | − | 0.370111i | ||||
\(33\) | −0.0441521 | − | 0.0254912i | −0.00768589 | − | 0.00443745i | ||||
\(34\) | −0.911548 | − | 1.57885i | −0.156329 | − | 0.270770i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.13620 | + | 1.96796i | −0.189367 | + | 0.327993i | ||||
\(37\) | − | 1.69819i | − | 0.279181i | −0.990209 | − | 0.139590i | \(-0.955421\pi\) | ||
0.990209 | − | 0.139590i | \(-0.0445786\pi\) | |||||||
\(38\) | 4.09566 | − | 2.47156i | 0.664404 | − | 0.400940i | ||||
\(39\) | 1.33288 | 0.213431 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.31637 | + | 9.20823i | −0.830278 | + | 1.43808i | 0.0675398 | + | 0.997717i | \(0.478485\pi\) |
−0.897818 | + | 0.440367i | \(0.854848\pi\) | |||||||
\(42\) | −0.682493 | + | 0.394038i | −0.105311 | + | 0.0608013i | ||||
\(43\) | 7.36801 | + | 4.25392i | 1.12361 | + | 0.648717i | 0.942320 | − | 0.334713i | \(-0.108639\pi\) |
0.181290 | + | 0.983430i | \(0.441973\pi\) | |||||||
\(44\) | −0.0534662 | − | 0.0926063i | −0.00806034 | − | 0.0139609i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.89307 | 0.868885 | ||||||||
\(47\) | −9.62623 | + | 5.55771i | −1.40413 | + | 0.810675i | −0.994813 | − | 0.101718i | \(-0.967566\pi\) |
−0.409316 | + | 0.912392i | \(0.634233\pi\) | |||||||
\(48\) | −0.583345 | + | 0.336794i | −0.0841986 | + | 0.0486121i | ||||
\(49\) | 3.41630 | 0.488042 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.315080 | − | 0.545735i | −0.0441201 | − | 0.0764182i | ||||
\(52\) | 2.42109 | + | 1.39781i | 0.335744 | + | 0.193842i | ||||
\(53\) | 0.229365 | − | 0.132424i | 0.0315057 | − | 0.0181898i | −0.484164 | − | 0.874977i | \(-0.660876\pi\) |
0.515670 | + | 0.856787i | \(0.327543\pi\) | |||||||
\(54\) | 1.21894 | − | 2.11126i | 0.165876 | − | 0.287306i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.80799 | −0.776125 | ||||||||
\(57\) | 1.41568 | − | 0.854305i | 0.187511 | − | 0.113155i | ||||
\(58\) | − | 5.45492i | − | 0.716266i | ||||||
\(59\) | −3.44833 | + | 5.97269i | −0.448935 | + | 0.777578i | −0.998317 | − | 0.0579932i | \(-0.981530\pi\) |
0.549382 | + | 0.835571i | \(0.314863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.58794 | − | 7.94655i | −0.587426 | − | 1.01745i | −0.994568 | − | 0.104087i | \(-0.966808\pi\) |
0.407142 | − | 0.913365i | \(-0.366525\pi\) | |||||||
\(62\) | −6.23917 | − | 3.60219i | −0.792375 | − | 0.457478i | ||||
\(63\) | 4.68243 | − | 2.70340i | 0.589930 | − | 0.340596i | ||||
\(64\) | −8.14676 | −1.01834 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0279750 | + | 0.0484542i | 0.00344349 | + | 0.00596430i | ||||
\(67\) | −2.55784 | + | 1.47677i | −0.312490 | + | 0.180416i | −0.648040 | − | 0.761606i | \(-0.724411\pi\) |
0.335550 | + | 0.942022i | \(0.391078\pi\) | |||||||
\(68\) | − | 1.32172i | − | 0.160282i | ||||||
\(69\) | 2.03696 | 0.245221 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.664176 | + | 1.15039i | −0.0788232 | + | 0.136526i | −0.902742 | − | 0.430181i | \(-0.858450\pi\) |
0.823919 | + | 0.566707i | \(0.191783\pi\) | |||||||
\(72\) | 7.58865 | − | 4.38131i | 0.894331 | − | 0.516342i | ||||
\(73\) | −5.49266 | − | 3.17119i | −0.642867 | − | 0.371159i | 0.142851 | − | 0.989744i | \(-0.454373\pi\) |
−0.785718 | + | 0.618585i | \(0.787706\pi\) | |||||||
\(74\) | −0.931830 | + | 1.61398i | −0.108323 | + | 0.187621i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.46742 | − | 0.0671384i | 0.397740 | − | 0.00770130i | ||||
\(77\) | 0.254428i | 0.0289948i | ||||||||
\(78\) | −1.26678 | − | 0.731376i | −0.143435 | − | 0.0828120i | ||||
\(79\) | −0.733639 | + | 1.27070i | −0.0825408 | + | 0.142965i | −0.904341 | − | 0.426811i | \(-0.859637\pi\) |
0.821800 | + | 0.569776i | \(0.192970\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.86283 | + | 6.69062i | −0.429203 | + | 0.743402i | ||||
\(82\) | 10.1055 | − | 5.83439i | 1.11596 | − | 0.644301i | ||||
\(83\) | − | 7.44736i | − | 0.817454i | −0.912657 | − | 0.408727i | \(-0.865973\pi\) | ||
0.912657 | − | 0.408727i | \(-0.134027\pi\) | |||||||
\(84\) | −0.571345 | −0.0623388 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.66842 | − | 8.08593i | −0.503408 | − | 0.871929i | ||||
\(87\) | − | 1.88551i | − | 0.202148i | ||||||
\(88\) | 0.412343i | 0.0439559i | ||||||||
\(89\) | 4.86804 | + | 8.43169i | 0.516011 | + | 0.893757i | 0.999827 | + | 0.0185878i | \(0.00591701\pi\) |
−0.483816 | + | 0.875170i | \(0.660750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.32587 | − | 5.76057i | −0.348646 | − | 0.603872i | ||||
\(92\) | 3.70001 | + | 2.13620i | 0.385753 | + | 0.222714i | ||||
\(93\) | −2.15659 | − | 1.24511i | −0.223628 | − | 0.129112i | ||||
\(94\) | 12.1985 | 1.25818 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.58839 | −0.162115 | ||||||||
\(97\) | −15.1285 | − | 8.73447i | −1.53607 | − | 0.886851i | −0.999063 | − | 0.0432737i | \(-0.986221\pi\) |
−0.537008 | − | 0.843577i | \(-0.680445\pi\) | |||||||
\(98\) | −3.24688 | − | 1.87459i | −0.327984 | − | 0.189362i | ||||
\(99\) | −0.191930 | − | 0.332433i | −0.0192897 | − | 0.0334108i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.69865 | − | 4.67420i | −0.268526 | − | 0.465101i | 0.699955 | − | 0.714187i | \(-0.253203\pi\) |
−0.968481 | + | 0.249086i | \(0.919870\pi\) | |||||||
\(102\) | 0.691562i | 0.0684749i | ||||||||
\(103\) | − | 2.14750i | − | 0.211599i | −0.994387 | − | 0.105800i | \(-0.966260\pi\) | ||
0.994387 | − | 0.105800i | \(-0.0337402\pi\) | |||||||
\(104\) | −5.39012 | − | 9.33596i | −0.528545 | − | 0.915467i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.290654 | −0.0282308 | ||||||||
\(107\) | − | 1.00093i | − | 0.0967631i | −0.998829 | − | 0.0483815i | \(-0.984594\pi\) | ||
0.998829 | − | 0.0483815i | \(-0.0154063\pi\) | |||||||
\(108\) | 1.53064 | − | 0.883713i | 0.147285 | − | 0.0850353i | ||||
\(109\) | 8.13145 | − | 14.0841i | 0.778852 | − | 1.34901i | −0.153752 | − | 0.988109i | \(-0.549136\pi\) |
0.932604 | − | 0.360902i | \(-0.117531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.322091 | + | 0.557877i | −0.0305715 | + | 0.0529514i | ||||
\(112\) | 2.91119 | + | 1.68077i | 0.275081 | + | 0.158818i | ||||
\(113\) | − | 0.843010i | − | 0.0793037i | −0.999214 | − | 0.0396519i | \(-0.987375\pi\) | ||
0.999214 | − | 0.0396519i | \(-0.0126249\pi\) | |||||||
\(114\) | −1.81425 | + | 0.0351287i | −0.169920 | + | 0.00329010i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.97737 | − | 3.42491i | 0.183595 | − | 0.317995i | ||||
\(117\) | 8.69108 | + | 5.01780i | 0.803491 | + | 0.463896i | ||||
\(118\) | 6.55466 | − | 3.78433i | 0.603405 | − | 0.348376i | ||||
\(119\) | −1.57241 | + | 2.72349i | −0.144143 | + | 0.249662i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9819 | −0.998358 | ||||||||
\(122\) | 10.0700i | 0.911692i | ||||||||
\(123\) | 3.49299 | − | 2.01668i | 0.314953 | − | 0.181838i | ||||
\(124\) | −2.61154 | − | 4.52332i | −0.234523 | − | 0.406206i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.93363 | −0.528610 | ||||||||
\(127\) | 16.2290 | − | 9.36984i | 1.44009 | − | 0.831439i | 0.442239 | − | 0.896897i | \(-0.354184\pi\) |
0.997855 | + | 0.0654584i | \(0.0208510\pi\) | |||||||
\(128\) | 0.490101 | + | 0.282960i | 0.0433193 | + | 0.0250104i | ||||
\(129\) | −1.61366 | − | 2.79493i | −0.142074 | − | 0.246080i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.44322 | + | 2.49973i | −0.126095 | + | 0.218402i | −0.922160 | − | 0.386808i | \(-0.873578\pi\) |
0.796066 | + | 0.605210i | \(0.206911\pi\) | |||||||
\(132\) | 0.0405631i | 0.00353057i | ||||||||
\(133\) | −7.22471 | − | 3.98673i | −0.626461 | − | 0.345693i | ||||
\(134\) | 3.24133 | 0.280008 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.54835 | + | 4.41387i | −0.218519 | + | 0.378487i | ||||
\(137\) | −16.3086 | + | 9.41579i | −1.39334 | + | 0.804445i | −0.993683 | − | 0.112220i | \(-0.964204\pi\) |
−0.399656 | + | 0.916665i | \(0.630871\pi\) | |||||||
\(138\) | −1.93595 | − | 1.11772i | −0.164799 | − | 0.0951466i | ||||
\(139\) | −9.08974 | − | 15.7439i | −0.770982 | − | 1.33538i | −0.937025 | − | 0.349262i | \(-0.886432\pi\) |
0.166043 | − | 0.986118i | \(-0.446901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.21645 | 0.355089 | ||||||||
\(142\) | 1.26248 | − | 0.728892i | 0.105945 | − | 0.0611672i | ||||
\(143\) | −0.408977 | + | 0.236123i | −0.0342003 | + | 0.0197456i | ||||
\(144\) | −5.07163 | −0.422636 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.48018 | + | 6.02785i | 0.288022 | + | 0.498868i | ||||
\(147\) | −1.12230 | − | 0.647958i | −0.0925655 | − | 0.0534427i | ||||
\(148\) | −1.17011 | + | 0.675565i | −0.0961827 | + | 0.0555311i | ||||
\(149\) | −11.1272 | + | 19.2728i | −0.911573 | + | 1.57889i | −0.0997308 | + | 0.995014i | \(0.531798\pi\) |
−0.811842 | + | 0.583877i | \(0.801535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.33482 | 0.271384 | 0.135692 | − | 0.990751i | \(-0.456674\pi\) | ||||
0.135692 | + | 0.990751i | \(0.456674\pi\) | |||||||
\(152\) | −11.7088 | − | 6.46116i | −0.949712 | − | 0.524069i | ||||
\(153\) | − | 4.74465i | − | 0.383582i | ||||||
\(154\) | 0.139610 | − | 0.241811i | 0.0112501 | − | 0.0194857i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.530238 | − | 0.918400i | −0.0424530 | − | 0.0735308i | ||||
\(157\) | −6.28986 | − | 3.63145i | −0.501986 | − | 0.289822i | 0.227548 | − | 0.973767i | \(-0.426929\pi\) |
−0.729533 | + | 0.683945i | \(0.760263\pi\) | |||||||
\(158\) | 1.39451 | − | 0.805123i | 0.110942 | − | 0.0640522i | ||||
\(159\) | −0.100466 | −0.00796744 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.08273 | − | 8.80355i | −0.400576 | − | 0.693817i | ||||
\(162\) | 7.34254 | − | 4.23922i | 0.576884 | − | 0.333064i | ||||
\(163\) | 19.7783i | 1.54916i | 0.632478 | + | 0.774578i | \(0.282038\pi\) | ||||
−0.632478 | + | 0.774578i | \(0.717962\pi\) | |||||||
\(164\) | 8.45972 | 0.660593 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.08651 | + | 7.07805i | −0.317175 | + | 0.549363i | ||||
\(167\) | −2.94726 | + | 1.70160i | −0.228066 | + | 0.131674i | −0.609679 | − | 0.792648i | \(-0.708702\pi\) |
0.381614 | + | 0.924322i | \(0.375368\pi\) | |||||||
\(168\) | 1.90800 | + | 1.10158i | 0.147205 | + | 0.0849890i | ||||
\(169\) | −0.326838 | + | 0.566100i | −0.0251414 | + | 0.0435461i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.4471 | − | 0.241010i | 0.951857 | − | 0.0184305i | ||||
\(172\) | − | 6.76909i | − | 0.516138i | ||||||
\(173\) | −9.16750 | − | 5.29286i | −0.696992 | − | 0.402409i | 0.109234 | − | 0.994016i | \(-0.465160\pi\) |
−0.806226 | + | 0.591607i | \(0.798494\pi\) | |||||||
\(174\) | −1.03462 | + | 1.79201i | −0.0784341 | + | 0.135852i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.119328 | − | 0.206682i | 0.00899469 | − | 0.0155793i | ||||
\(177\) | 2.26564 | − | 1.30807i | 0.170296 | − | 0.0983205i | ||||
\(178\) | − | 10.6847i | − | 0.800855i | ||||||
\(179\) | 14.6024 | 1.09144 | 0.545718 | − | 0.837969i | \(-0.316257\pi\) | ||||
0.545718 | + | 0.837969i | \(0.316257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.71630 | + | 4.70478i | 0.201901 | + | 0.349703i | 0.949141 | − | 0.314851i | \(-0.101955\pi\) |
−0.747240 | + | 0.664555i | \(0.768621\pi\) | |||||||
\(182\) | 7.29987i | 0.541102i | ||||||||
\(183\) | 3.48072i | 0.257303i | ||||||||
\(184\) | −8.23742 | − | 14.2676i | −0.607270 | − | 1.05182i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.36643 | + | 2.36673i | 0.100192 | + | 0.173537i | ||||
\(187\) | 0.193357 | + | 0.111635i | 0.0141396 | + | 0.00816353i | ||||
\(188\) | 7.65891 | + | 4.42187i | 0.558583 | + | 0.322498i | ||||
\(189\) | −4.20530 | −0.305890 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.4758 | 1.48157 | 0.740787 | − | 0.671740i | \(-0.234453\pi\) | ||||
0.740787 | + | 0.671740i | \(0.234453\pi\) | |||||||
\(192\) | 2.67631 | + | 1.54517i | 0.193146 | + | 0.111513i | ||||
\(193\) | 9.54664 | + | 5.51176i | 0.687182 | + | 0.396745i | 0.802556 | − | 0.596577i | \(-0.203473\pi\) |
−0.115373 | + | 0.993322i | \(0.536806\pi\) | |||||||
\(194\) | 9.58554 | + | 16.6026i | 0.688202 | + | 1.19200i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.35905 | − | 2.35395i | −0.0970752 | − | 0.168139i | ||||
\(197\) | − | 19.8532i | − | 1.41448i | −0.706971 | − | 0.707242i | \(-0.749939\pi\) | ||
0.706971 | − | 0.707242i | \(-0.250061\pi\) | |||||||
\(198\) | 0.421263i | 0.0299379i | ||||||||
\(199\) | 10.5013 | + | 18.1888i | 0.744417 | + | 1.28937i | 0.950467 | + | 0.310826i | \(0.100606\pi\) |
−0.206050 | + | 0.978542i | \(0.566061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.12038 | 0.0790254 | ||||||||
\(202\) | 5.92321i | 0.416756i | ||||||||
\(203\) | −8.14901 | + | 4.70483i | −0.571948 | + | 0.330215i | ||||
\(204\) | −0.250687 | + | 0.434203i | −0.0175516 | + | 0.0304003i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.17837 | + | 2.04100i | −0.0821011 | + | 0.142203i | ||||
\(207\) | 13.2821 | + | 7.66842i | 0.923169 | + | 0.532992i | ||||
\(208\) | 6.23939i | 0.432624i | ||||||||
\(209\) | −0.283041 | + | 0.512924i | −0.0195784 | + | 0.0354797i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.41284 | − | 11.1074i | 0.441478 | − | 0.764663i | −0.556321 | − | 0.830967i | \(-0.687788\pi\) |
0.997799 | + | 0.0663046i | \(0.0211209\pi\) | |||||||
\(212\) | −0.182489 | − | 0.105360i | −0.0125334 | − | 0.00723617i | ||||
\(213\) | 0.436380 | − | 0.251944i | 0.0299003 | − | 0.0172629i | ||||
\(214\) | −0.549227 | + | 0.951289i | −0.0375444 | + | 0.0650288i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.81538 | −0.463728 | ||||||||
\(217\) | 12.4275i | 0.843630i | ||||||||
\(218\) | −15.4564 | + | 8.92377i | −1.04684 | + | 0.604394i | ||||
\(219\) | 1.20294 | + | 2.08355i | 0.0812870 | + | 0.140793i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.83712 | −0.392647 | ||||||||
\(222\) | 0.612236 | − | 0.353475i | 0.0410906 | − | 0.0237237i | ||||
\(223\) | 17.6621 | + | 10.1972i | 1.18274 | + | 0.682856i | 0.956647 | − | 0.291249i | \(-0.0940708\pi\) |
0.226095 | + | 0.974105i | \(0.427404\pi\) | |||||||
\(224\) | 3.96344 | + | 6.86488i | 0.264819 | + | 0.458679i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.462576 | + | 0.801205i | −0.0307701 | + | 0.0532954i | ||||
\(227\) | 25.4172i | 1.68700i | 0.537129 | + | 0.843500i | \(0.319509\pi\) | ||||
−0.537129 | + | 0.843500i | \(0.680491\pi\) | |||||||
\(228\) | −1.15182 | − | 0.635598i | −0.0762814 | − | 0.0420935i | ||||
\(229\) | −2.21553 | −0.146406 | −0.0732030 | − | 0.997317i | \(-0.523322\pi\) | ||||
−0.0732030 | + | 0.997317i | \(0.523322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0482566 | − | 0.0835829i | 0.00317505 | − | 0.00549935i | ||||
\(232\) | −13.2068 | + | 7.62496i | −0.867071 | + | 0.500603i | ||||
\(233\) | −12.2609 | − | 7.07882i | −0.803236 | − | 0.463749i | 0.0413652 | − | 0.999144i | \(-0.486829\pi\) |
−0.844602 | + | 0.535395i | \(0.820163\pi\) | |||||||
\(234\) | −5.50672 | − | 9.53792i | −0.359986 | − | 0.623514i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.48719 | 0.357186 | ||||||||
\(237\) | 0.482019 | − | 0.278294i | 0.0313105 | − | 0.0180771i | ||||
\(238\) | 2.98887 | − | 1.72562i | 0.193739 | − | 0.111855i | ||||
\(239\) | −3.01476 | −0.195008 | −0.0975042 | − | 0.995235i | \(-0.531086\pi\) | ||||
−0.0975042 | + | 0.995235i | \(0.531086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.8896 | + | 20.5934i | 0.765877 | + | 1.32654i | 0.939781 | + | 0.341776i | \(0.111028\pi\) |
−0.173904 | + | 0.984763i | \(0.555638\pi\) | |||||||
\(242\) | 10.4373 | + | 6.02600i | 0.670937 | + | 0.387366i | ||||
\(243\) | 8.30939 | − | 4.79743i | 0.533048 | − | 0.307755i | ||||
\(244\) | −3.65030 | + | 6.32251i | −0.233687 | + | 0.404757i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.42636 | −0.282215 | ||||||||
\(247\) | −0.296503 | − | 15.3131i | −0.0188660 | − | 0.974352i | ||||
\(248\) | 20.1407i | 1.27894i | ||||||||
\(249\) | −1.41252 | + | 2.44655i | −0.0895147 | + | 0.155044i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.59495 | − | 14.8869i | −0.542509 | − | 0.939653i | −0.998759 | − | 0.0498012i | \(-0.984141\pi\) |
0.456250 | − | 0.889851i | \(-0.349192\pi\) | |||||||
\(252\) | −3.72548 | − | 2.15090i | −0.234683 | − | 0.135494i | ||||
\(253\) | −0.625016 | + | 0.360853i | −0.0392944 | + | 0.0226866i | ||||
\(254\) | −20.5656 | −1.29040 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.83623 | + | 13.5727i | 0.489764 | + | 0.848297i | ||||
\(257\) | −16.9246 | + | 9.77143i | −1.05573 | + | 0.609525i | −0.924248 | − | 0.381794i | \(-0.875307\pi\) |
−0.131481 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(258\) | 3.54178i | 0.220501i | ||||||||
\(259\) | 3.21479 | 0.199757 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.09827 | − | 12.2946i | 0.439372 | − | 0.761014i | ||||
\(262\) | 2.74330 | − | 1.58384i | 0.169482 | − | 0.0978502i | ||||
\(263\) | 7.63280 | + | 4.40680i | 0.470659 | + | 0.271735i | 0.716515 | − | 0.697571i | \(-0.245736\pi\) |
−0.245857 | + | 0.969306i | \(0.579069\pi\) | |||||||
\(264\) | 0.0782078 | − | 0.135460i | 0.00481336 | − | 0.00833698i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.67883 | + | 7.75336i | 0.286878 | + | 0.475389i | ||||
\(267\) | − | 3.69322i | − | 0.226022i | ||||||
\(268\) | 2.03510 | + | 1.17496i | 0.124313 | + | 0.0717723i | ||||
\(269\) | 0.144181 | − | 0.249729i | 0.00879088 | − | 0.0152263i | −0.861596 | − | 0.507594i | \(-0.830535\pi\) |
0.870387 | + | 0.492368i | \(0.163868\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4356 | − | 21.5391i | 0.755409 | − | 1.30841i | −0.189761 | − | 0.981830i | \(-0.560771\pi\) |
0.945171 | − | 0.326577i | \(-0.105895\pi\) | |||||||
\(272\) | 2.55466 | − | 1.47494i | 0.154899 | − | 0.0894311i | ||||
\(273\) | 2.52323i | 0.152713i | ||||||||
\(274\) | 20.6665 | 1.24851 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.810333 | − | 1.40354i | −0.0487763 | − | 0.0844831i | ||||
\(277\) | − | 4.40486i | − | 0.264662i | −0.991206 | − | 0.132331i | \(-0.957754\pi\) | ||
0.991206 | − | 0.132331i | \(-0.0422463\pi\) | |||||||
\(278\) | 19.9509i | 1.19657i | ||||||||
\(279\) | −9.37476 | − | 16.2376i | −0.561252 | − | 0.972118i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3607 | + | 28.3376i | 0.975998 | + | 1.69048i | 0.676600 | + | 0.736350i | \(0.263452\pi\) |
0.299398 | + | 0.954128i | \(0.403214\pi\) | |||||||
\(282\) | −4.00736 | − | 2.31365i | −0.238635 | − | 0.137776i | ||||
\(283\) | −1.15088 | − | 0.664463i | −0.0684129 | − | 0.0394982i | 0.465403 | − | 0.885099i | \(-0.345909\pi\) |
−0.533816 | + | 0.845600i | \(0.679243\pi\) | |||||||
\(284\) | 1.05688 | 0.0627140 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.518260 | 0.0306454 | ||||||||
\(287\) | −17.4318 | − | 10.0643i | −1.02897 | − | 0.594074i | ||||
\(288\) | −10.3572 | − | 5.97972i | −0.610302 | − | 0.352358i | ||||
\(289\) | −7.12016 | − | 12.3325i | −0.418833 | − | 0.725440i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.31328 | + | 5.73877i | 0.194228 | + | 0.336413i | ||||
\(292\) | 5.04618i | 0.295305i | ||||||||
\(293\) | 7.72365i | 0.451220i | 0.974218 | + | 0.225610i | \(0.0724375\pi\) | ||||
−0.974218 | + | 0.225610i | \(0.927562\pi\) | |||||||
\(294\) | 0.711094 | + | 1.23165i | 0.0414718 | + | 0.0718313i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.21010 | 0.302831 | ||||||||
\(297\) | 0.298558i | 0.0173241i | ||||||||
\(298\) | 21.1507 | − | 12.2114i | 1.22523 | − | 0.707386i | ||||
\(299\) | 9.43409 | − | 16.3403i | 0.545588 | − | 0.944986i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.05296 | + | 13.9481i | −0.464165 | + | 0.803957i | ||||
\(302\) | −3.16944 | − | 1.82988i | −0.182381 | − | 0.105298i | ||||
\(303\) | 2.04738i | 0.117619i | ||||||||
\(304\) | 3.99912 | + | 6.62700i | 0.229366 | + | 0.380085i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.60348 | + | 4.50936i | −0.148831 | + | 0.257783i | ||||
\(307\) | 7.88085 | + | 4.55001i | 0.449784 | + | 0.259683i | 0.707739 | − | 0.706474i | \(-0.249715\pi\) |
−0.257955 | + | 0.966157i | \(0.583049\pi\) | |||||||
\(308\) | 0.175310 | − | 0.101215i | 0.00998921 | − | 0.00576727i | ||||
\(309\) | −0.407309 | + | 0.705480i | −0.0231710 | + | 0.0401333i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4569 | −0.706364 | −0.353182 | − | 0.935555i | \(-0.614900\pi\) | ||||
−0.353182 | + | 0.935555i | \(0.614900\pi\) | |||||||
\(312\) | 4.08931i | 0.231512i | ||||||||
\(313\) | −1.77148 | + | 1.02277i | −0.100130 | + | 0.0578101i | −0.549229 | − | 0.835672i | \(-0.685078\pi\) |
0.449099 | + | 0.893482i | \(0.351745\pi\) | |||||||
\(314\) | 3.98530 | + | 6.90274i | 0.224903 | + | 0.389544i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.16741 | 0.0656719 | ||||||||
\(317\) | 20.4133 | − | 11.7856i | 1.14653 | − | 0.661947i | 0.198487 | − | 0.980103i | \(-0.436397\pi\) |
0.948038 | + | 0.318157i | \(0.103064\pi\) | |||||||
\(318\) | 0.0954834 | + | 0.0551274i | 0.00535445 | + | 0.00309139i | ||||
\(319\) | 0.334024 | + | 0.578546i | 0.0187017 | + | 0.0323923i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.189842 | + | 0.328817i | −0.0105960 | + | 0.0183528i | ||||
\(322\) | 11.1560i | 0.621698i | ||||||||
\(323\) | −6.19974 | + | 3.74129i | −0.344963 | + | 0.208171i | ||||
\(324\) | 6.14676 | 0.341487 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.8527 | − | 18.7975i | 0.601077 | − | 1.04110i | ||||
\(327\) | −5.34257 | + | 3.08454i | −0.295445 | + | 0.170575i | ||||
\(328\) | −28.2511 | − | 16.3108i | −1.55991 | − | 0.900613i | ||||
\(329\) | −10.5211 | − | 18.2231i | −0.580048 | − | 1.00467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7175 | −1.02881 | −0.514403 | − | 0.857549i | \(-0.671986\pi\) | ||||
−0.514403 | + | 0.857549i | \(0.671986\pi\) | |||||||
\(332\) | −5.13150 | + | 2.96267i | −0.281627 | + | 0.162598i | ||||
\(333\) | −4.20041 | + | 2.42511i | −0.230181 | + | 0.132895i | ||||
\(334\) | 3.73480 | 0.204359 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.637575 | − | 1.10431i | −0.0347826 | − | 0.0602451i | ||||
\(337\) | 28.3087 | + | 16.3440i | 1.54207 | + | 0.890316i | 0.998708 | + | 0.0508197i | \(0.0161834\pi\) |
0.543365 | + | 0.839497i | \(0.317150\pi\) | |||||||
\(338\) | 0.621259 | − | 0.358684i | 0.0337921 | − | 0.0195098i | ||||
\(339\) | −0.159891 | + | 0.276940i | −0.00868409 | + | 0.0150413i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.882297 | 0.0477791 | ||||||||
\(342\) | −11.9621 | − | 6.60093i | −0.646838 | − | 0.356937i | ||||
\(343\) | 19.7188i | 1.06471i | ||||||||
\(344\) | −13.0512 | + | 22.6053i | −0.703671 | + | 1.21879i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.80859 | + | 10.0608i | 0.312271 | + | 0.540870i | ||||
\(347\) | 2.22279 | + | 1.28333i | 0.119326 | + | 0.0688927i | 0.558475 | − | 0.829521i | \(-0.311387\pi\) |
−0.439149 | + | 0.898414i | \(0.644720\pi\) | |||||||
\(348\) | −1.29919 | + | 0.750085i | −0.0696436 | + | 0.0402088i | ||||
\(349\) | −16.6195 | −0.889619 | −0.444810 | − | 0.895625i | \(-0.646729\pi\) | ||||
−0.444810 | + | 0.895625i | \(0.646729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.90274 | − | 6.75974i | −0.208313 | − | 0.360808i | ||||
\(352\) | 0.487378 | − | 0.281388i | 0.0259773 | − | 0.0149980i | ||||
\(353\) | − | 28.3629i | − | 1.50961i | −0.655951 | − | 0.754803i | \(-0.727732\pi\) | ||
0.655951 | − | 0.754803i | \(-0.272268\pi\) | |||||||
\(354\) | −2.87105 | −0.152595 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.87315 | − | 6.70850i | 0.205277 | − | 0.355550i | ||||
\(357\) | 1.03311 | − | 0.596468i | 0.0546781 | − | 0.0315684i | ||||
\(358\) | −13.8783 | − | 8.01262i | −0.733489 | − | 0.423480i | ||||
\(359\) | 8.69427 | − | 15.0589i | 0.458866 | − | 0.794780i | −0.540035 | − | 0.841643i | \(-0.681589\pi\) |
0.998901 | + | 0.0468628i | \(0.0149224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.1298 | − | 16.0744i | −0.533150 | − | 0.846021i | ||||
\(362\) | − | 5.96195i | − | 0.313353i | ||||||
\(363\) | 3.60771 | + | 2.08291i | 0.189355 | + | 0.109324i | ||||
\(364\) | −2.64616 | + | 4.58328i | −0.138696 | + | 0.240229i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.90994 | − | 3.30811i | 0.0998342 | − | 0.172918i | ||||
\(367\) | 22.3477 | − | 12.9024i | 1.16654 | − | 0.673501i | 0.213676 | − | 0.976905i | \(-0.431456\pi\) |
0.952862 | + | 0.303404i | \(0.0981231\pi\) | |||||||
\(368\) | 9.53531i | 0.497062i | ||||||||
\(369\) | 30.3683 | 1.58091 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.250687 | + | 0.434203i | 0.0130150 | + | 0.0225427i | ||||
\(372\) | 1.98129i | 0.102725i | ||||||||
\(373\) | − | 27.0663i | − | 1.40144i | −0.713437 | − | 0.700719i | \(-0.752862\pi\) | ||
0.713437 | − | 0.700719i | \(-0.247138\pi\) | |||||||
\(374\) | −0.122512 | − | 0.212197i | −0.00633495 | − | 0.0109724i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.0512 | − | 29.5336i | −0.879349 | − | 1.52308i | ||||
\(377\) | −15.1254 | − | 8.73267i | −0.778999 | − | 0.449755i | ||||
\(378\) | 3.99675 | + | 2.30753i | 0.205571 | + | 0.118686i | ||||
\(379\) | −12.4028 | −0.637092 | −0.318546 | − | 0.947907i | \(-0.603194\pi\) | ||||
−0.318546 | + | 0.947907i | \(0.603194\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.10859 | −0.364184 | ||||||||
\(382\) | −19.4604 | − | 11.2354i | −0.995678 | − | 0.574855i | ||||
\(383\) | −4.64139 | − | 2.67971i | −0.237164 | − | 0.136927i | 0.376709 | − | 0.926332i | \(-0.377056\pi\) |
−0.613873 | + | 0.789405i | \(0.710389\pi\) | |||||||
\(384\) | −0.107336 | − | 0.185912i | −0.00547749 | − | 0.00948728i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.04881 | − | 10.4769i | −0.307877 | − | 0.533258i | ||||
\(387\) | − | 24.2993i | − | 1.23520i | ||||||
\(388\) | 13.8988i | 0.705605i | ||||||||
\(389\) | 4.28467 | + | 7.42126i | 0.217241 | + | 0.376273i | 0.953964 | − | 0.299923i | \(-0.0969608\pi\) |
−0.736722 | + | 0.676195i | \(0.763628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.92053 | −0.451131 | ||||||||
\(392\) | 10.4813i | 0.529386i | ||||||||
\(393\) | 0.948232 | − | 0.547462i | 0.0478320 | − | 0.0276158i | ||||
\(394\) | −10.8939 | + | 18.8687i | −0.548824 | + | 0.950592i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.152705 | + | 0.264493i | −0.00767373 | + | 0.0132913i | ||||
\(397\) | 9.21844 | + | 5.32227i | 0.462660 | + | 0.267117i | 0.713162 | − | 0.700999i | \(-0.247262\pi\) |
−0.250502 | + | 0.968116i | \(0.580596\pi\) | |||||||
\(398\) | − | 23.0490i | − | 1.15534i | ||||||
\(399\) | 1.61726 | + | 2.67998i | 0.0809641 | + | 0.134167i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.82604 | + | 6.62690i | −0.191063 | + | 0.330932i | −0.945603 | − | 0.325323i | \(-0.894527\pi\) |
0.754539 | + | 0.656255i | \(0.227860\pi\) | |||||||
\(402\) | −1.06482 | − | 0.614773i | −0.0531083 | − | 0.0306621i | ||||
\(403\) | −19.9763 | + | 11.5333i | −0.995091 | + | 0.574516i | ||||
\(404\) | −2.14713 | + | 3.71893i | −0.106824 | + | 0.185024i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.3265 | 0.512497 | ||||||||
\(407\) | − | 0.228237i | − | 0.0113133i | ||||||
\(408\) | 1.67433 | − | 0.966676i | 0.0828918 | − | 0.0478576i | ||||
\(409\) | −8.84435 | − | 15.3189i | −0.437325 | − | 0.757469i | 0.560157 | − | 0.828386i | \(-0.310741\pi\) |
−0.997482 | + | 0.0709173i | \(0.977407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.14345 | 0.352361 | ||||||||
\(412\) | −1.47970 | + | 0.854305i | −0.0728996 | + | 0.0420886i | ||||
\(413\) | −11.3067 | − | 6.52793i | −0.556367 | − | 0.321218i | ||||
\(414\) | −8.41561 | − | 14.5763i | −0.413605 | − | 0.716384i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.35657 | + | 12.7420i | −0.360685 | + | 0.624726i | ||||
\(417\) | 6.89609i | 0.337703i | ||||||||
\(418\) | 0.550456 | − | 0.332178i | 0.0269237 | − | 0.0162473i | ||||
\(419\) | −1.18732 | −0.0580045 | −0.0290023 | − | 0.999579i | \(-0.509233\pi\) | ||||
−0.0290023 | + | 0.999579i | \(0.509233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6836 | + | 28.8969i | −0.813111 | + | 1.40835i | 0.0975661 | + | 0.995229i | \(0.468894\pi\) |
−0.910677 | + | 0.413120i | \(0.864439\pi\) | |||||||
\(422\) | −12.1896 | + | 7.03770i | −0.593383 | + | 0.342590i | ||||
\(423\) | 27.4935 | + | 15.8734i | 1.33678 | + | 0.771791i | ||||
\(424\) | 0.406280 | + | 0.703698i | 0.0197307 | + | 0.0341746i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.552987 | −0.0267923 | ||||||||
\(427\) | 15.0434 | − | 8.68529i | 0.727999 | − | 0.420311i | ||||
\(428\) | −0.689673 | + | 0.398183i | −0.0333366 | + | 0.0192469i | ||||
\(429\) | 0.179139 | 0.00864890 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.08799 | + | 5.34855i | 0.148743 | + | 0.257631i | 0.930763 | − | 0.365623i | \(-0.119144\pi\) |
−0.782020 | + | 0.623253i | \(0.785811\pi\) | |||||||
\(432\) | 3.41613 | + | 1.97230i | 0.164359 | + | 0.0948925i | ||||
\(433\) | 16.0693 | − | 9.27761i | 0.772241 | − | 0.445854i | −0.0614325 | − | 0.998111i | \(-0.519567\pi\) |
0.833673 | + | 0.552258i | \(0.186234\pi\) | |||||||
\(434\) | 6.81918 | − | 11.8112i | 0.327331 | − | 0.566954i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.9392 | −0.619677 | ||||||||
\(437\) | −0.453129 | − | 23.4022i | −0.0216761 | − | 1.11948i | ||||
\(438\) | − | 2.64030i | − | 0.126158i | ||||||
\(439\) | −0.113656 | + | 0.196858i | −0.00542450 | + | 0.00939550i | −0.868725 | − | 0.495295i | \(-0.835060\pi\) |
0.863300 | + | 0.504690i | \(0.168393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.87865 | − | 8.45007i | −0.232317 | − | 0.402384i | ||||
\(442\) | 5.54765 | + | 3.20294i | 0.263875 | + | 0.152348i | ||||
\(443\) | 30.2959 | − | 17.4913i | 1.43940 | − | 0.831038i | 0.441593 | − | 0.897216i | \(-0.354414\pi\) |
0.997808 | + | 0.0661770i | \(0.0210802\pi\) | |||||||
\(444\) | 0.512529 | 0.0243236 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.1908 | − | 19.3831i | −0.529901 | − | 0.917815i | ||||
\(447\) | 7.31083 | − | 4.22091i | 0.345791 | − | 0.199642i | ||||
\(448\) | − | 15.4224i | − | 0.728638i | ||||||
\(449\) | 16.9509 | 0.799961 | 0.399980 | − | 0.916524i | \(-0.369017\pi\) | ||||
0.399980 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.714520 | + | 1.23759i | −0.0336454 | + | 0.0582756i | ||||
\(452\) | −0.580864 | + | 0.335362i | −0.0273215 | + | 0.0157741i | ||||
\(453\) | −1.09553 | − | 0.632505i | −0.0514725 | − | 0.0297177i | ||||
\(454\) | 13.9469 | − | 24.1568i | 0.654561 | − | 1.13373i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.62103 | + | 4.34335i | 0.122741 | + | 0.203396i | ||||
\(457\) | 1.60241i | 0.0749578i | 0.999297 | + | 0.0374789i | \(0.0119327\pi\) | ||||
−0.999297 | + | 0.0374789i | \(0.988067\pi\) | |||||||
\(458\) | 2.10566 | + | 1.21570i | 0.0983909 | + | 0.0568060i | ||||
\(459\) | −1.84514 | + | 3.19588i | −0.0861239 | + | 0.149171i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.37081 | − | 7.57046i | 0.203569 | − | 0.352592i | −0.746107 | − | 0.665826i | \(-0.768079\pi\) |
0.949676 | + | 0.313234i | \(0.101413\pi\) | |||||||
\(462\) | −0.0917270 | + | 0.0529586i | −0.00426753 | + | 0.00246386i | ||||
\(463\) | − | 21.1886i | − | 0.984718i | −0.870392 | − | 0.492359i | \(-0.836135\pi\) | ||
0.870392 | − | 0.492359i | \(-0.163865\pi\) | |||||||
\(464\) | 8.82636 | 0.409753 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.76857 | + | 13.4556i | 0.359872 | + | 0.623316i | ||||
\(467\) | 20.4516i | 0.946388i | 0.880958 | + | 0.473194i | \(0.156899\pi\) | ||||
−0.880958 | + | 0.473194i | \(0.843101\pi\) | |||||||
\(468\) | − | 7.98461i | − | 0.369089i | ||||||
\(469\) | −2.79563 | − | 4.84217i | −0.129090 | − | 0.223591i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.37753 | + | 2.38596i | 0.0634734 | + | 0.109939i | ||||
\(472\) | −18.3244 | − | 10.5796i | −0.843449 | − | 0.486965i | ||||
\(473\) | 0.990259 | + | 0.571727i | 0.0455322 | + | 0.0262880i | ||||
\(474\) | −0.610821 | −0.0280559 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.50211 | 0.114684 | ||||||||
\(477\) | −0.655090 | − | 0.378216i | −0.0299945 | − | 0.0173173i | ||||
\(478\) | 2.86525 | + | 1.65425i | 0.131054 | + | 0.0756639i | ||||
\(479\) | 11.7746 | + | 20.3942i | 0.537994 | + | 0.931833i | 0.999012 | + | 0.0444419i | \(0.0141510\pi\) |
−0.461018 | + | 0.887391i | \(0.652516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.98350 | + | 5.16757i | 0.136036 | + | 0.235621i | ||||
\(482\) | − | 26.0962i | − | 1.18865i | ||||||
\(483\) | 3.85611i | 0.175459i | ||||||||
\(484\) | 4.36877 | + | 7.56694i | 0.198581 | + | 0.343952i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.5298 | −0.477640 | ||||||||
\(487\) | 36.0392i | 1.63309i | 0.577280 | + | 0.816546i | \(0.304114\pi\) | ||||
−0.577280 | + | 0.816546i | \(0.695886\pi\) | |||||||
\(488\) | 24.3803 | − | 14.0760i | 1.10364 | − | 0.637188i | ||||
\(489\) | 3.75129 | − | 6.49742i | 0.169639 | − | 0.293824i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0297 | + | 17.3720i | −0.452635 | + | 0.783988i | −0.998549 | − | 0.0538541i | \(-0.982849\pi\) |
0.545913 | + | 0.837842i | \(0.316183\pi\) | |||||||
\(492\) | −2.77913 | − | 1.60453i | −0.125293 | − | 0.0723378i | ||||
\(493\) | 8.25729i | 0.371890i | ||||||||
\(494\) | −8.12081 | + | 14.7164i | −0.365373 | + | 0.662124i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.82853 | − | 10.0953i | 0.261709 | − | 0.453293i | ||||
\(497\) | −2.17776 | − | 1.25733i | −0.0976858 | − | 0.0563989i | ||||
\(498\) | 2.68494 | − | 1.55015i | 0.120315 | − | 0.0694640i | ||||
\(499\) | −18.4364 | + | 31.9328i | −0.825328 | + | 1.42951i | 0.0763399 | + | 0.997082i | \(0.475677\pi\) |
−0.901668 | + | 0.432429i | \(0.857657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.29095 | 0.0576753 | ||||||||
\(502\) | 18.8649i | 0.841980i | ||||||||
\(503\) | 18.7483 | − | 10.8244i | 0.835947 | − | 0.482634i | −0.0199377 | − | 0.999801i | \(-0.506347\pi\) |
0.855884 | + | 0.517167i | \(0.173013\pi\) | |||||||
\(504\) | 8.29412 | + | 14.3658i | 0.369449 | + | 0.639905i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.792028 | 0.0352099 | ||||||||
\(507\) | 0.214741 | − | 0.123981i | 0.00953697 | − | 0.00550617i | ||||
\(508\) | −12.9123 | − | 7.45492i | −0.572891 | − | 0.330759i | ||||
\(509\) | −18.2279 | − | 31.5717i | −0.807938 | − | 1.39939i | −0.914289 | − | 0.405062i | \(-0.867250\pi\) |
0.106351 | − | 0.994329i | \(-0.466083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00327 | − | 10.3980i | 0.265569 | − | 0.459979i | ||||
\(512\) | − | 18.3314i | − | 0.810141i | ||||||
\(513\) | −8.47783 | − | 4.67822i | −0.374305 | − | 0.206549i | ||||
\(514\) | 21.4471 | 0.945990 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.28387 | + | 2.22373i | −0.0565193 | + | 0.0978943i | ||||
\(517\) | −1.29376 | + | 0.746955i | −0.0568997 | + | 0.0328511i | ||||
\(518\) | −3.05537 | − | 1.76402i | −0.134245 | − | 0.0775065i | ||||
\(519\) | 2.00776 | + | 3.47754i | 0.0881309 | + | 0.152647i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.6092 | −0.990528 | −0.495264 | − | 0.868742i | \(-0.664929\pi\) | ||||
−0.495264 | + | 0.868742i | \(0.664929\pi\) | |||||||
\(522\) | −13.4925 | + | 7.78991i | −0.590552 | + | 0.340955i | ||||
\(523\) | −0.461515 | + | 0.266456i | −0.0201806 | + | 0.0116513i | −0.510056 | − | 0.860141i | \(-0.670375\pi\) |
0.489876 | + | 0.871792i | \(0.337042\pi\) | |||||||
\(524\) | 2.29654 | 0.100325 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.83619 | − | 8.37653i | −0.210868 | − | 0.365234i | ||||
\(527\) | 9.44444 | + | 5.45275i | 0.411406 | + | 0.237525i | ||||
\(528\) | −0.0784015 | + | 0.0452651i | −0.00341199 | + | 0.00196991i | ||||
\(529\) | 2.91759 | − | 5.05341i | 0.126852 | − | 0.219714i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.6976 | 0.854804 | ||||||||
\(532\) | 0.127098 | + | 6.56406i | 0.00551038 | + | 0.284588i | ||||
\(533\) | − | 37.3606i | − | 1.61827i | ||||||
\(534\) | −2.02654 | + | 3.51007i | −0.0876971 | + | 0.151896i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.53078 | − | 7.84754i | −0.195700 | − | 0.338962i | ||||
\(537\) | −4.79708 | − | 2.76959i | −0.207009 | − | 0.119517i | ||||
\(538\) | −0.274062 | + | 0.158230i | −0.0118157 | + | 0.00682178i | ||||
\(539\) | 0.459150 | 0.0197770 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.50820 | − | 4.34433i | −0.107836 | − | 0.186777i | 0.807057 | − | 0.590473i | \(-0.201059\pi\) |
−0.914893 | + | 0.403696i | \(0.867725\pi\) | |||||||
\(542\) | −23.6378 | + | 13.6473i | −1.01533 | + | 0.586202i | ||||
\(543\) | − | 2.06077i | − | 0.0884362i | ||||||
\(544\) | 6.95610 | 0.298240 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.38454 | − | 2.39810i | 0.0592530 | − | 0.102629i | ||||
\(547\) | 19.5981 | − | 11.3149i | 0.837952 | − | 0.483792i | −0.0186154 | − | 0.999827i | \(-0.505926\pi\) |
0.856568 | + | 0.516035i | \(0.172592\pi\) | |||||||
\(548\) | 12.9756 | + | 7.49148i | 0.554291 | + | 0.320020i | ||||
\(549\) | −13.1037 | + | 22.6962i | −0.559250 | + | 0.968650i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.6622 | + | 0.419439i | −0.922843 | + | 0.0178687i | ||||
\(552\) | 6.24946i | 0.265995i | ||||||||
\(553\) | −2.40552 | − | 1.38883i | −0.102293 | − | 0.0590590i | ||||
\(554\) | −2.41703 | + | 4.18642i | −0.102690 | + | 0.177864i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.23207 | + | 12.5263i | −0.306708 | + | 0.531234i | ||||
\(557\) | 30.5321 | − | 17.6277i | 1.29369 | − | 0.746910i | 0.314381 | − | 0.949297i | \(-0.398203\pi\) |
0.979306 | + | 0.202387i | \(0.0648698\pi\) | |||||||
\(558\) | 20.5764i | 0.871070i | ||||||||
\(559\) | −29.8943 | −1.26439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0423468 | − | 0.0733467i | −0.00178788 | − | 0.00309670i | ||||
\(562\) | − | 35.9097i | − | 1.51476i | ||||||
\(563\) | 24.6295i | 1.03801i | 0.854771 | + | 0.519005i | \(0.173698\pi\) | ||||
−0.854771 | + | 0.519005i | \(0.826302\pi\) | |||||||
\(564\) | −1.67737 | − | 2.90528i | −0.0706298 | − | 0.122334i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.729207 | + | 1.26302i | 0.0306509 | + | 0.0530888i | ||||
\(567\) | −12.6658 | − | 7.31260i | −0.531913 | − | 0.307100i | ||||
\(568\) | −3.52942 | − | 2.03771i | −0.148091 | − | 0.0855005i | ||||
\(569\) | 20.0193 | 0.839252 | 0.419626 | − | 0.907697i | \(-0.362161\pi\) | ||||
0.419626 | + | 0.907697i | \(0.362161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6121 | −0.695195 | −0.347597 | − | 0.937644i | \(-0.613002\pi\) | ||||
−0.347597 | + | 0.937644i | \(0.613002\pi\) | |||||||
\(572\) | 0.325394 | + | 0.187866i | 0.0136054 | + | 0.00785508i | ||||
\(573\) | −6.72655 | − | 3.88357i | −0.281006 | − | 0.162239i | ||||
\(574\) | 11.0449 | + | 19.1303i | 0.461005 | + | 0.798484i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11.6340 | + | 20.1507i | 0.484750 | + | 0.839612i | ||||
\(577\) | 12.4486i | 0.518244i | 0.965845 | + | 0.259122i | \(0.0834331\pi\) | ||||
−0.965845 | + | 0.259122i | \(0.916567\pi\) | |||||||
\(578\) | 15.6279i | 0.650034i | ||||||||
\(579\) | −2.09080 | − | 3.62136i | −0.0868905 | − | 0.150499i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.0984 | 0.584899 | ||||||||
\(582\) | − | 7.27224i | − | 0.301444i | ||||||
\(583\) | 0.0308266 | − | 0.0177977i | 0.00127671 | − | 0.000737107i | ||||
\(584\) | 9.72930 | − | 16.8516i | 0.402601 | − | 0.697326i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.23811 | − | 7.34063i | 0.175075 | − | 0.303238i | ||||
\(587\) | −3.90702 | − | 2.25572i | −0.161260 | − | 0.0931036i | 0.417198 | − | 0.908816i | \(-0.363012\pi\) |
−0.578458 | + | 0.815712i | \(0.696345\pi\) | |||||||
\(588\) | 1.03107i | 0.0425206i | ||||||||
\(589\) | −13.8250 | + | 25.0536i | −0.569651 | + | 1.03232i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.76550 | + | 6.52204i | −0.154892 | + | 0.268281i | ||||
\(592\) | −2.61150 | − | 1.50775i | −0.107332 | − | 0.0619682i | ||||
\(593\) | −16.9812 | + | 9.80411i | −0.697335 | + | 0.402606i | −0.806354 | − | 0.591433i | \(-0.798562\pi\) |
0.109019 | + | 0.994040i | \(0.465229\pi\) | |||||||
\(594\) | 0.163825 | − | 0.283753i | 0.00672181 | − | 0.0116425i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.7062 | 0.725274 | ||||||||
\(597\) | − | 7.96699i | − | 0.326067i | ||||||
\(598\) | −17.9325 | + | 10.3533i | −0.733315 | + | 0.423379i | ||||
\(599\) | 5.38795 | + | 9.33221i | 0.220146 | + | 0.381304i | 0.954852 | − | 0.297082i | \(-0.0960134\pi\) |
−0.734706 | + | 0.678385i | \(0.762680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0244 | 0.612860 | 0.306430 | − | 0.951893i | \(-0.400866\pi\) | ||||
0.306430 | + | 0.951893i | \(0.400866\pi\) | |||||||
\(602\) | 15.3072 | − | 8.83763i | 0.623876 | − | 0.360195i | ||||
\(603\) | 7.30547 | + | 4.21782i | 0.297502 | + | 0.171763i | ||||
\(604\) | −1.32664 | − | 2.29781i | −0.0539802 | − | 0.0934964i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.12344 | − | 1.94585i | 0.0456365 | − | 0.0790448i | ||||
\(607\) | 25.1901i | 1.02243i | 0.859452 | + | 0.511217i | \(0.170805\pi\) | ||||
−0.859452 | + | 0.511217i | \(0.829195\pi\) | |||||||
\(608\) | 0.353343 | + | 18.2487i | 0.0143300 | + | 0.740082i | ||||
\(609\) | 3.56940 | 0.144640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.5283 | − | 33.8240i | 0.790030 | − | 1.36837i | ||||
\(612\) | −3.26923 | + | 1.88749i | −0.132151 | + | 0.0762973i | ||||
\(613\) | 14.0600 | + | 8.11753i | 0.567877 | + | 0.327864i | 0.756301 | − | 0.654224i | \(-0.227005\pi\) |
−0.188424 | + | 0.982088i | \(0.560338\pi\) | |||||||
\(614\) | −4.99336 | − | 8.64875i | −0.201516 | − | 0.349035i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.780593 | −0.0314510 | ||||||||
\(617\) | 5.64498 | − | 3.25913i | 0.227258 | − | 0.131208i | −0.382048 | − | 0.924142i | \(-0.624781\pi\) |
0.609307 | + | 0.792935i | \(0.291448\pi\) | |||||||
\(618\) | 0.774220 | − | 0.446996i | 0.0311437 | − | 0.0179808i | ||||
\(619\) | 4.39112 | 0.176494 | 0.0882470 | − | 0.996099i | \(-0.471874\pi\) | ||||
0.0882470 | + | 0.996099i | \(0.471874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.96433 | − | 10.3305i | −0.239340 | − | 0.414550i | ||||
\(622\) | 11.8391 | + | 6.83532i | 0.474705 | + | 0.274071i | ||||
\(623\) | −15.9618 | + | 9.21553i | −0.639494 | + | 0.369212i | ||||
\(624\) | 1.18341 | − | 2.04972i | 0.0473742 | − | 0.0820545i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.24484 | 0.0897220 | ||||||||
\(627\) | 0.190267 | − | 0.114819i | 0.00759855 | − | 0.00458541i | ||||
\(628\) | 5.77858i | 0.230590i | ||||||||
\(629\) | 1.41054 | − | 2.44313i | 0.0562420 | − | 0.0974140i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3104 | + | 29.9826i | 0.689118 | + | 1.19359i | 0.972124 | + | 0.234469i | \(0.0753350\pi\) |
−0.283006 | + | 0.959118i | \(0.591332\pi\) | |||||||
\(632\) | −3.89855 | − | 2.25083i | −0.155076 | − | 0.0895331i | ||||
\(633\) | −4.21340 | + | 2.43261i | −0.167468 | + | 0.0966875i | ||||
\(634\) | −25.8680 | −1.02735 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0399667 | + | 0.0692243i | 0.00158478 | + | 0.00274492i | ||||
\(637\) | −10.3957 | + | 6.00198i | −0.411894 | + | 0.237807i | ||||
\(638\) | − | 0.733141i | − | 0.0290253i | ||||||
\(639\) | 3.79391 | 0.150085 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.70621 | + | 6.41934i | −0.146386 | + | 0.253549i | −0.929889 | − | 0.367839i | \(-0.880098\pi\) |
0.783503 | + | 0.621388i | \(0.213431\pi\) | |||||||
\(642\) | 0.360856 | − | 0.208340i | 0.0142418 | − | 0.00822253i | ||||
\(643\) | −14.3292 | − | 8.27294i | −0.565087 | − | 0.326253i | 0.190098 | − | 0.981765i | \(-0.439120\pi\) |
−0.755185 | + | 0.655512i | \(0.772453\pi\) | |||||||
\(644\) | −4.04397 | + | 7.00437i | −0.159355 | + | 0.276011i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.94520 | − | 0.153840i | 0.312600 | − | 0.00605276i | ||||
\(647\) | 29.4822i | 1.15907i | 0.814949 | + | 0.579533i | \(0.196765\pi\) | ||||
−0.814949 | + | 0.579533i | \(0.803235\pi\) | |||||||
\(648\) | −20.5270 | − | 11.8513i | −0.806377 | − | 0.465562i | ||||
\(649\) | −0.463456 | + | 0.802729i | −0.0181922 | + | 0.0315099i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.35708 | − | 4.08258i | 0.0923811 | − | 0.160009i | ||||
\(652\) | 13.6279 | − | 7.86810i | 0.533712 | − | 0.308138i | ||||
\(653\) | − | 6.57421i | − | 0.257269i | −0.991692 | − | 0.128634i | \(-0.958941\pi\) | ||
0.991692 | − | 0.128634i | \(-0.0410594\pi\) | |||||||
\(654\) | 6.77017 | 0.264735 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.44037 | + | 16.3512i | 0.368584 | + | 0.638407i | ||||
\(657\) | 18.1145i | 0.706713i | ||||||||
\(658\) | 23.0925i | 0.900241i | ||||||||
\(659\) | −13.1685 | − | 22.8085i | −0.512972 | − | 0.888494i | −0.999887 | − | 0.0150445i | \(-0.995211\pi\) |
0.486915 | − | 0.873450i | \(-0.338122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.89210 | − | 3.27721i | −0.0735941 | − | 0.127469i | 0.826880 | − | 0.562378i | \(-0.190114\pi\) |
−0.900474 | + | 0.434910i | \(0.856780\pi\) | |||||||
\(662\) | 17.7893 | + | 10.2706i | 0.691399 | + | 0.399180i | ||||
\(663\) | 1.91757 | + | 1.10711i | 0.0744721 | + | 0.0429965i | ||||
\(664\) | 22.8487 | 0.886703 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.32281 | 0.206255 | ||||||||
\(667\) | −23.1153 | − | 13.3456i | −0.895029 | − | 0.516745i | ||||
\(668\) | 2.34492 | + | 1.35384i | 0.0907278 | + | 0.0523817i | ||||
\(669\) | −3.86815 | − | 6.69983i | −0.149551 | − | 0.259031i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.616619 | − | 1.06802i | −0.0238043 | − | 0.0412303i | ||||
\(672\) | − | 3.00694i | − | 0.115995i | ||||||
\(673\) | 21.0431i | 0.811150i | 0.914062 | + | 0.405575i | \(0.132929\pi\) | ||||
−0.914062 | + | 0.405575i | \(0.867071\pi\) | |||||||
\(674\) | −17.9366 | − | 31.0670i | −0.690891 | − | 1.19666i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.520083 | 0.0200032 | ||||||||
\(677\) | − | 15.2744i | − | 0.587043i | −0.955952 | − | 0.293522i | \(-0.905173\pi\) | ||
0.955952 | − | 0.293522i | \(-0.0948273\pi\) | |||||||
\(678\) | 0.303924 | − | 0.175471i | 0.0116721 | − | 0.00673891i | ||||
\(679\) | 16.5349 | − | 28.6394i | 0.634553 | − | 1.09908i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.82081 | − | 8.34988i | 0.184734 | − | 0.319968i | ||||
\(682\) | −0.838544 | − | 0.484133i | −0.0321095 | − | 0.0185384i | ||||
\(683\) | 8.60225i | 0.329156i | 0.986364 | + | 0.164578i | \(0.0526262\pi\) | ||||
−0.986364 | + | 0.164578i | \(0.947374\pi\) | |||||||
\(684\) | −5.11772 | − | 8.48064i | −0.195681 | − | 0.324265i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.8201 | − | 18.7409i | 0.413112 | − | 0.715530i | ||||
\(687\) | 0.727828 | + | 0.420212i | 0.0277684 | + | 0.0160321i | ||||
\(688\) | 13.0835 | − | 7.55375i | 0.498803 | − | 0.287984i | ||||
\(689\) | −0.465302 | + | 0.805926i | −0.0177266 | + | 0.0307033i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.1079 | 1.29753 | 0.648763 | − | 0.760990i | \(-0.275286\pi\) | ||||
0.648763 | + | 0.760990i | \(0.275286\pi\) | |||||||
\(692\) | 8.42231i | 0.320168i | ||||||||
\(693\) | 0.629318 | − | 0.363337i | 0.0239058 | − | 0.0138020i | ||||
\(694\) | −1.40837 | − | 2.43937i | −0.0534611 | − | 0.0925974i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.78481 | 0.219273 | ||||||||
\(697\) | −15.2970 | + | 8.83172i | −0.579414 | + | 0.334525i | ||||
\(698\) | 15.7953 | + | 9.11942i | 0.597861 | + | 0.345175i | ||||
\(699\) | 2.68523 | + | 4.65096i | 0.101565 | + | 0.175916i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.36463 | + | 9.29181i | −0.202619 | + | 0.350947i | −0.949372 | − | 0.314155i | \(-0.898279\pi\) |
0.746752 | + | 0.665102i | \(0.231612\pi\) | |||||||
\(702\) | 8.56603i | 0.323304i | ||||||||
\(703\) | 6.48098 | + | 3.57633i | 0.244435 | + | 0.134884i | ||||
\(704\) | −1.09492 | −0.0412665 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.5633 | + | 26.9564i | −0.585732 | + | 1.01452i | ||||
\(707\) | 8.84859 | − | 5.10873i | 0.332785 | − | 0.192134i | ||||
\(708\) | −1.80261 | − | 1.04074i | −0.0677463 | − | 0.0391134i | ||||
\(709\) | −14.4238 | − | 24.9828i | −0.541697 | − | 0.938247i | −0.998807 | − | 0.0488369i | \(-0.984449\pi\) |
0.457109 | − | 0.889410i | \(-0.348885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.19070 | 0.157164 | ||||||||
\(712\) | −25.8687 | + | 14.9353i | −0.969470 | + | 0.559724i | ||||
\(713\) | −30.5287 | + | 17.6257i | −1.14331 | + | 0.660089i | ||||
\(714\) | −1.30917 | −0.0489946 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.80905 | − | 10.0616i | −0.217095 | − | 0.376019i | ||||
\(717\) | 0.990386 | + | 0.571800i | 0.0369866 | + | 0.0213542i | ||||
\(718\) | −16.5262 | + | 9.54143i | −0.616754 | + | 0.356083i | ||||
\(719\) | −10.0278 | + | 17.3686i | −0.373972 | + | 0.647739i | −0.990173 | − | 0.139851i | \(-0.955338\pi\) |
0.616200 | + | 0.787589i | \(0.288671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.06535 | 0.151402 | ||||||||
\(722\) | 0.807171 | + | 20.8357i | 0.0300398 | + | 0.775424i | ||||
\(723\) | − | 9.02026i | − | 0.335467i | ||||||
\(724\) | 2.16117 | − | 3.74326i | 0.0803193 | − | 0.139117i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.28587 | − | 3.95923i | −0.0848364 | − | 0.146941i | ||||
\(727\) | 0.675951 | + | 0.390261i | 0.0250697 | + | 0.0144740i | 0.512482 | − | 0.858698i | \(-0.328726\pi\) |
−0.487413 | + | 0.873172i | \(0.662059\pi\) | |||||||
\(728\) | 17.6736 | − | 10.2039i | 0.655028 | − | 0.378180i | ||||
\(729\) | 19.5373 | 0.723604 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.06674 | + | 12.2399i | 0.261373 | + | 0.452711i | ||||
\(732\) | 2.39834 | − | 1.38468i | 0.0886452 | − | 0.0511794i | ||||
\(733\) | 26.8391i | 0.991326i | 0.868515 | + | 0.495663i | \(0.165075\pi\) | ||||
−0.868515 | + | 0.495663i | \(0.834925\pi\) | |||||||
\(734\) | −28.3192 | −1.04528 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.2426 | + | 19.4728i | −0.414409 | + | 0.717777i | ||||
\(737\) | −0.343774 | + | 0.198478i | −0.0126631 | + | 0.00731103i | ||||
\(738\) | −28.8623 | − | 16.6636i | −1.06243 | − | 0.613397i | ||||
\(739\) | 10.3265 | − | 17.8861i | 0.379867 | − | 0.657949i | −0.611175 | − | 0.791495i | \(-0.709303\pi\) |
0.991043 | + | 0.133546i | \(0.0426363\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.80699 | + | 5.08680i | −0.103117 | + | 0.186868i | ||||
\(742\) | − | 0.550227i | − | 0.0201995i | ||||||
\(743\) | 1.27580 | + | 0.736585i | 0.0468047 | + | 0.0270227i | 0.523220 | − | 0.852198i | \(-0.324731\pi\) |
−0.476415 | + | 0.879220i | \(0.658064\pi\) | |||||||
\(744\) | 3.82003 | − | 6.61649i | 0.140049 | − | 0.242572i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.8518 | + | 25.7240i | −0.543762 | + | 0.941824i | ||||
\(747\) | −18.4208 | + | 10.6352i | −0.673980 | + | 0.389123i | ||||
\(748\) | − | 0.177639i | − | 0.00649514i | ||||||
\(749\) | 1.89482 | 0.0692352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.78121 | − | 13.4775i | −0.283940 | − | 0.491799i | 0.688411 | − | 0.725321i | \(-0.258308\pi\) |
−0.972352 | + | 0.233521i | \(0.924975\pi\) | |||||||
\(752\) | 19.7378i | 0.719764i | ||||||||
\(753\) | 6.52071i | 0.237628i | ||||||||
\(754\) | 9.58356 | + | 16.5992i | 0.349013 | + | 0.604508i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.67293 | + | 2.89760i | 0.0608438 | + | 0.105385i | ||||
\(757\) | −17.4726 | − | 10.0878i | −0.635052 | − | 0.366647i | 0.147654 | − | 0.989039i | \(-0.452828\pi\) |
−0.782706 | + | 0.622392i | \(0.786161\pi\) | |||||||
\(758\) | 11.7878 | + | 6.80568i | 0.428152 | + | 0.247193i | ||||
\(759\) | 0.273767 | 0.00993713 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.1076 | −0.547649 | −0.273825 | − | 0.961780i | \(-0.588289\pi\) | ||||
−0.273825 | + | 0.961780i | \(0.588289\pi\) | |||||||
\(762\) | 6.75607 | + | 3.90062i | 0.244747 | + | 0.141305i | ||||
\(763\) | 26.6621 | + | 15.3934i | 0.965234 | + | 0.557278i | ||||
\(764\) | −8.14556 | − | 14.1085i | −0.294696 | − | 0.510428i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.94082 | + | 5.09364i | 0.106256 | + | 0.184041i | ||||
\(767\) | − | 24.2331i | − | 0.875005i | ||||||
\(768\) | − | 5.94509i | − | 0.214525i | ||||||
\(769\) | 25.8290 | + | 44.7372i | 0.931418 | + | 1.61326i | 0.780900 | + | 0.624656i | \(0.214761\pi\) |
0.150518 | + | 0.988607i | \(0.451906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.41327 | 0.266982 | ||||||||
\(772\) | − | 8.77063i | − | 0.315662i | ||||||
\(773\) | −26.1157 | + | 15.0779i | −0.939316 | + | 0.542314i | −0.889746 | − | 0.456457i | \(-0.849118\pi\) |
−0.0495699 | + | 0.998771i | \(0.515785\pi\) | |||||||
\(774\) | −13.3335 | + | 23.0943i | −0.479262 | + | 0.830107i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.7976 | − | 46.4148i | 0.961978 | − | 1.66620i | ||||
\(777\) | −1.05610 | − | 0.609739i | −0.0378874 | − | 0.0218743i | ||||
\(778\) | − | 9.40431i | − | 0.337161i | ||||||
\(779\) | −23.9462 | − | 39.6816i | −0.857962 | − | 1.42174i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0892652 | + | 0.154612i | −0.00319416 | + | 0.00553244i | ||||
\(782\) | 8.47816 | + | 4.89487i | 0.303178 | + | 0.175040i | ||||
\(783\) | −9.56245 | + | 5.52088i | −0.341734 | + | 0.197300i | ||||
\(784\) | 3.03318 | − | 5.25363i | 0.108328 | − | 0.187630i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.20161 | −0.0428601 | ||||||||
\(787\) | 43.0969i | 1.53624i | 0.640307 | + | 0.768119i | \(0.278807\pi\) | ||||
−0.640307 | + | 0.768119i | \(0.721193\pi\) | |||||||
\(788\) | −13.6796 | + | 7.89791i | −0.487315 | + | 0.281351i | ||||
\(789\) | −1.67165 | − | 2.89538i | −0.0595123 | − | 0.103078i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.59588 | 0.0567428 | ||||||||
\(792\) | 1.01991 | − | 0.588848i | 0.0362411 | − | 0.0209238i | ||||
\(793\) | 27.9221 | + | 16.1208i | 0.991542 | + | 0.572467i | ||||
\(794\) | −5.84086 | − | 10.1167i | −0.207284 | − | 0.359027i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.35514 | − | 14.4715i | 0.296140 | − | 0.512929i | ||||
\(797\) | − | 50.5062i | − | 1.78902i | −0.447048 | − | 0.894510i | \(-0.647525\pi\) | ||
0.447048 | − | 0.894510i | \(-0.352475\pi\) | |||||||
\(798\) | −0.0665010 | − | 3.43450i | −0.00235411 | − | 0.121580i | ||||
\(799\) | −18.4652 | −0.653253 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9036 | − | 24.0818i | 0.491261 | − | 0.850889i | ||||
\(802\) | 7.27261 | − | 4.19885i | 0.256805 | − | 0.148266i | ||||
\(803\) | −0.738212 | − | 0.426207i | −0.0260509 | − | 0.0150405i | ||||
\(804\) | −0.445703 | − | 0.771981i | −0.0157187 | − | 0.0272257i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.3142 | 0.891656 | ||||||||
\(807\) | −0.0947307 | + | 0.0546928i | −0.00333468 | + | 0.00192528i | ||||
\(808\) | 14.3406 | − | 8.27955i | 0.504501 | − | 0.291274i | ||||
\(809\) | 30.0872 | 1.05781 | 0.528905 | − | 0.848681i | \(-0.322603\pi\) | ||||
0.528905 | + | 0.848681i | \(0.322603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.4755 | − | 19.8761i | −0.402958 | − | 0.697944i | 0.591123 | − | 0.806581i | \(-0.298685\pi\) |
−0.994081 | + | 0.108637i | \(0.965351\pi\) | |||||||
\(812\) | 6.48359 | + | 3.74330i | 0.227529 | + | 0.131364i | ||||
\(813\) | −8.17051 | + | 4.71725i | −0.286552 | + | 0.165441i | ||||
\(814\) | −0.125238 | + | 0.216918i | −0.00438958 | + | 0.00760298i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.11899 | −0.0391723 | ||||||||
\(817\) | −31.7514 | + | 19.1607i | −1.11084 | + | 0.670347i | ||||
\(818\) | 19.4123i | 0.678734i | ||||||||
\(819\) | −9.49903 | + | 16.4528i | −0.331923 | + | 0.574907i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.0403 | + | 32.9788i | 0.664513 | + | 1.15097i | 0.979417 | + | 0.201846i | \(0.0646941\pi\) |
−0.314905 | + | 0.949123i | \(0.601973\pi\) | |||||||
\(822\) | −6.78921 | − | 3.91975i | −0.236801 | − | 0.136717i | ||||
\(823\) | −46.5862 | + | 26.8966i | −1.62389 | + | 0.937556i | −0.638030 | + | 0.770012i | \(0.720250\pi\) |
−0.985865 | + | 0.167544i | \(0.946416\pi\) | |||||||
\(824\) | 6.58858 | 0.229524 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.16400 | + | 12.4084i | 0.249267 | + | 0.431744i | ||||
\(827\) | 28.0672 | − | 16.2046i | 0.975993 | − | 0.563490i | 0.0749347 | − | 0.997188i | \(-0.476125\pi\) |
0.901058 | + | 0.433699i | \(0.142792\pi\) | |||||||
\(828\) | − | 12.2024i | − | 0.424064i | ||||||
\(829\) | 18.5305 | 0.643592 | 0.321796 | − | 0.946809i | \(-0.395713\pi\) | ||||
0.321796 | + | 0.946809i | \(0.395713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.835456 | + | 1.44705i | −0.0289817 | + | 0.0501977i | ||||
\(832\) | 24.7904 | − | 14.3128i | 0.859454 | − | 0.496206i | ||||
\(833\) | 4.91491 | + | 2.83763i | 0.170292 | + | 0.0983179i | ||||
\(834\) | 3.78402 | − | 6.55411i | 0.131030 | − | 0.226950i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.466021 | − | 0.00902339i | 0.0161177 | − | 0.000312081i | ||||
\(837\) | 14.5830i | 0.504062i | ||||||||
\(838\) | 1.12844 | + | 0.651507i | 0.0389814 | + | 0.0225059i | ||||
\(839\) | 0.413304 | − | 0.715864i | 0.0142688 | − | 0.0247144i | −0.858803 | − | 0.512306i | \(-0.828791\pi\) |
0.873072 | + | 0.487592i | \(0.162125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.14661 | − | 3.71803i | 0.0740209 | − | 0.128208i | ||||
\(842\) | 31.7126 | − | 18.3093i | 1.09289 | − | 0.630979i | ||||
\(843\) | − | 12.4123i | − | 0.427504i | ||||||
\(844\) | −10.2045 | −0.351253 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.4201 | − | 30.1725i | −0.598914 | − | 1.03735i | ||||
\(847\) | − | 20.7895i | − | 0.714337i | ||||||
\(848\) | − | 0.470294i | − | 0.0161500i | ||||||
\(849\) | 0.252053 | + | 0.436569i | 0.00865044 | + | 0.0149830i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.55951 | + | 7.89730i | 0.156298 | + | 0.270716i | ||||
\(852\) | −0.347197 | − | 0.200454i | −0.0118948 | − | 0.00686745i | ||||
\(853\) | −6.36475 | − | 3.67469i | −0.217925 | − | 0.125819i | 0.387064 | − | 0.922053i | \(-0.373489\pi\) |
−0.604989 | + | 0.796234i | \(0.706823\pi\) | |||||||
\(854\) | −19.0631 | −0.652327 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.07087 | 0.104960 | ||||||||
\(857\) | 39.2739 | + | 22.6748i | 1.34157 | + | 0.774556i | 0.987038 | − | 0.160488i | \(-0.0513069\pi\) |
0.354532 | + | 0.935044i | \(0.384640\pi\) | |||||||
\(858\) | −0.170255 | − | 0.0982968i | −0.00581241 | − | 0.00335580i | ||||
\(859\) | 14.8143 | + | 25.6590i | 0.505456 | + | 0.875475i | 0.999980 | + | 0.00631148i | \(0.00200902\pi\) |
−0.494524 | + | 0.869164i | \(0.664658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.81771 | + | 6.61247i | 0.130107 | + | 0.225352i | ||||
\(862\) | − | 6.77775i | − | 0.230851i | ||||||
\(863\) | − | 41.0807i | − | 1.39840i | −0.714925 | − | 0.699201i | \(-0.753539\pi\) | ||
0.714925 | − | 0.699201i | \(-0.246461\pi\) | |||||||
\(864\) | 4.65090 | + | 8.05559i | 0.158227 | + | 0.274057i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.3632 | −0.691970 | ||||||||
\(867\) | 5.40183i | 0.183456i | ||||||||
\(868\) | 8.56295 | − | 4.94382i | 0.290645 | − | 0.167804i | ||||
\(869\) | −0.0986010 | + | 0.170782i | −0.00334481 | + | 0.00579338i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.18898 | − | 8.98758i | 0.175822 | − | 0.304533i | ||||
\(872\) | 43.2104 | + | 24.9475i | 1.46329 | + | 0.844831i | ||||
\(873\) | 49.8931i | 1.68863i | ||||||||
\(874\) | −12.4106 | + | 22.4903i | −0.419794 | + | 0.760746i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.957093 | − | 1.65773i | 0.0323372 | − | 0.0560096i | ||||
\(877\) | −47.3116 | − | 27.3154i | −1.59760 | − | 0.922374i | −0.991948 | − | 0.126643i | \(-0.959580\pi\) |
−0.605650 | − | 0.795731i | \(-0.707087\pi\) | |||||||
\(878\) | 0.216039 | − | 0.124730i | 0.00729097 | − | 0.00420944i | ||||
\(879\) | 1.46492 | − | 2.53732i | 0.0494105 | − | 0.0855815i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.4805 | −0.521552 | −0.260776 | − | 0.965399i | \(-0.583978\pi\) | ||||
−0.260776 | + | 0.965399i | \(0.583978\pi\) | |||||||
\(882\) | 10.7080i | 0.360558i | ||||||||
\(883\) | 39.2738 | − | 22.6747i | 1.32167 | − | 0.763066i | 0.337674 | − | 0.941263i | \(-0.390360\pi\) |
0.983995 | + | 0.178197i | \(0.0570265\pi\) | |||||||
\(884\) | 2.32209 | + | 4.02198i | 0.0781004 | + | 0.135274i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.3913 | −1.28978 | ||||||||
\(887\) | −26.9680 | + | 15.5700i | −0.905496 | + | 0.522788i | −0.878979 | − | 0.476860i | \(-0.841775\pi\) |
−0.0265165 | + | 0.999648i | \(0.508441\pi\) | |||||||
\(888\) | −1.71158 | − | 0.988184i | −0.0574370 | − | 0.0331613i | ||||
\(889\) | 17.7377 | + | 30.7227i | 0.594905 | + | 1.03041i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.519164 | + | 0.899218i | −0.0173926 | + | 0.0301249i | ||||
\(892\) | − | 16.2264i | − | 0.543301i | ||||||
\(893\) | −0.937963 | − | 48.4419i | −0.0313877 | − | 1.62105i | ||||
\(894\) | −9.26438 | −0.309847 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.535663 | + | 0.927795i | −0.0178952 | + | 0.0309955i | ||||
\(897\) | −6.19844 | + | 3.57867i | −0.206960 | + | 0.119488i | ||||
\(898\) | −16.1103 | − | 9.30127i | −0.537606 | − | 0.310387i | ||||
\(899\) | 16.3153 | + | 28.2589i | 0.544145 | + | 0.942486i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.439972 | 0.0146576 | ||||||||
\(902\) | 1.35817 | − | 0.784142i | 0.0452222 | − | 0.0261091i | ||||
\(903\) | 5.29100 | − | 3.05476i | 0.176073 | − | 0.101656i | ||||
\(904\) | 2.58638 | 0.0860218 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.694135 | + | 1.20228i | 0.0230611 | + | 0.0399430i | ||||
\(907\) | −37.7080 | − | 21.7707i | −1.25207 | − | 0.722886i | −0.280554 | − | 0.959838i | \(-0.590518\pi\) |
−0.971521 | + | 0.236952i | \(0.923851\pi\) | |||||||
\(908\) | 17.5134 | − | 10.1113i | 0.581201 | − | 0.335557i | ||||
\(909\) | −7.70764 | + | 13.3500i | −0.255646 | + | 0.442792i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.72789 | 0.189774 | 0.0948868 | − | 0.995488i | \(-0.469751\pi\) | ||||
0.0948868 | + | 0.995488i | \(0.469751\pi\) | |||||||
\(912\) | −0.0568401 | − | 2.93556i | −0.00188217 | − | 0.0972060i | ||||
\(913\) | − | 1.00093i | − | 0.0331258i | ||||||
\(914\) | 0.879275 | − | 1.52295i | 0.0290838 | − | 0.0503747i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.881369 | + | 1.52658i | 0.0291212 | + | 0.0504395i | ||||
\(917\) | −4.73216 | − | 2.73211i | −0.156270 | − | 0.0902223i | ||||
\(918\) | 3.50728 | − | 2.02493i | 0.115758 | − | 0.0668327i | ||||
\(919\) | −7.93860 | −0.261870 | −0.130935 | − | 0.991391i | \(-0.541798\pi\) | ||||
−0.130935 | + | 0.991391i | \(0.541798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.72597 | − | 2.98947i | −0.0568728 | − | 0.0985065i | ||||
\(922\) | −8.30812 | + | 4.79669i | −0.273613 | + | 0.157971i | ||||
\(923\) | − | 4.66747i | − | 0.153632i | ||||||
\(924\) | −0.0767887 | −0.00252616 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.6266 | + | 20.1378i | −0.382073 | + | 0.661771i | ||||
\(927\) | −5.31174 | + | 3.06674i | −0.174461 | + | 0.100725i | ||||
\(928\) | 18.0250 | + | 10.4067i | 0.591700 | + | 0.341618i | ||||
\(929\) | −14.4784 | + | 25.0772i | −0.475019 | + | 0.822758i | −0.999591 | − | 0.0286089i | \(-0.990892\pi\) |
0.524571 | + | 0.851366i | \(0.324226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.19459 | + | 13.0380i | −0.235793 | + | 0.427302i | ||||
\(932\) | 11.2642i | 0.368972i | ||||||||
\(933\) | 4.09224 | + | 2.36265i | 0.133974 | + | 0.0773498i | ||||
\(934\) | 11.2222 | − | 19.4374i | 0.367201 | − | 0.636011i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.3948 | + | 26.6645i | −0.503193 | + | 0.871556i | ||||
\(937\) | −12.7146 | + | 7.34080i | −0.415369 | + | 0.239813i | −0.693094 | − | 0.720847i | \(-0.743753\pi\) |
0.277725 | + | 0.960661i | \(0.410420\pi\) | |||||||
\(938\) | 6.13606i | 0.200349i | ||||||||
\(939\) | 0.775939 | 0.0253218 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.0773773 | + | 0.134021i | 0.00252243 | + | 0.00436897i | 0.867284 | − | 0.497814i | \(-0.165864\pi\) |
−0.864761 | + | 0.502183i | \(0.832530\pi\) | |||||||
\(942\) | − | 3.02352i | − | 0.0985114i | ||||||
\(943\) | − | 57.0961i | − | 1.85931i | ||||||
\(944\) | 6.12326 | + | 10.6058i | 0.199295 | + | 0.345189i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.627435 | − | 1.08675i | −0.0203997 | − | 0.0353332i | ||||
\(947\) | 6.51084 | + | 3.75904i | 0.211574 | + | 0.122152i | 0.602043 | − | 0.798464i | \(-0.294354\pi\) |
−0.390469 | + | 0.920616i | \(0.627687\pi\) | |||||||
\(948\) | −0.383509 | − | 0.221419i | −0.0124558 | − | 0.00719135i | ||||
\(949\) | 22.2854 | 0.723415 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.94137 | −0.289944 | ||||||||
\(952\) | −8.35576 | − | 4.82420i | −0.270812 | − | 0.156353i | ||||
\(953\) | 19.6365 | + | 11.3372i | 0.636090 | + | 0.367247i | 0.783107 | − | 0.621887i | \(-0.213634\pi\) |
−0.147017 | + | 0.989134i | \(0.546967\pi\) | |||||||
\(954\) | 0.415069 | + | 0.718920i | 0.0134384 | + | 0.0232759i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.19931 | + | 2.07727i | 0.0387886 | + | 0.0671838i | ||||
\(957\) | − | 0.253413i | − | 0.00819167i | ||||||
\(958\) | − | 25.8437i | − | 0.834973i | ||||||
\(959\) | −17.8247 | − | 30.8733i | −0.575590 | − | 0.996952i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0955 | 0.390177 | ||||||||
\(962\) | − | 6.54840i | − | 0.211129i | ||||||
\(963\) | −2.47575 | + | 1.42937i | −0.0797799 | + | 0.0460609i | ||||
\(964\) | 9.45972 | − | 16.3847i | 0.304677 | − | 0.527716i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.11592 | − | 3.66488i | 0.0680786 | − | 0.117916i | ||||
\(967\) | −24.9714 | − | 14.4172i | −0.803025 | − | 0.463627i | 0.0415030 | − | 0.999138i | \(-0.486785\pi\) |
−0.844528 | + | 0.535512i | \(0.820119\pi\) | |||||||
\(968\) | − | 33.6929i | − | 1.08293i | ||||||
\(969\) | 2.74629 | − | 0.0531755i | 0.0882236 | − | 0.00170824i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.1831 | + | 22.8338i | −0.423065 | + | 0.732770i | −0.996238 | − | 0.0866647i | \(-0.972379\pi\) |
0.573173 | + | 0.819435i | \(0.305712\pi\) | |||||||
\(972\) | −6.61120 | − | 3.81698i | −0.212054 | − | 0.122430i | ||||
\(973\) | 29.8043 | − | 17.2075i | 0.955481 | − | 0.551647i | ||||
\(974\) | 19.7754 | − | 34.2520i | 0.633645 | − | 1.09750i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.2938 | −0.521551 | ||||||||
\(977\) | 4.59218i | 0.146917i | 0.997298 | + | 0.0734585i | \(0.0234036\pi\) | ||||
−0.997298 | + | 0.0734585i | \(0.976596\pi\) | |||||||
\(978\) | −7.13052 | + | 4.11681i | −0.228009 | + | 0.131641i | ||||
\(979\) | 0.654264 | + | 1.13322i | 0.0209104 | + | 0.0362178i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.4486 | −1.48299 | ||||||||
\(982\) | 19.0647 | − | 11.0070i | 0.608379 | − | 0.351248i | ||||
\(983\) | 5.98833 | + | 3.45737i | 0.190998 | + | 0.110273i | 0.592450 | − | 0.805607i | \(-0.298161\pi\) |
−0.401452 | + | 0.915880i | \(0.631494\pi\) | |||||||
\(984\) | 6.18724 | + | 10.7166i | 0.197242 | + | 0.341633i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.53094 | − | 7.84781i | 0.144294 | − | 0.249925i | ||||
\(987\) | 7.98203i | 0.254071i | ||||||||
\(988\) | −10.4333 | + | 6.29609i | −0.331929 | + | 0.200305i | ||||
\(989\) | −45.6857 | −1.45272 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0035 | − | 32.9150i | 0.603666 | − | 1.04558i | −0.388594 | − | 0.921409i | \(-0.627039\pi\) |
0.992261 | − | 0.124172i | \(-0.0396274\pi\) | |||||||
\(992\) | 23.8058 | − | 13.7443i | 0.755835 | − | 0.436382i | ||||
\(993\) | 6.14893 | + | 3.55009i | 0.195130 | + | 0.112659i | ||||
\(994\) | 1.37984 | + | 2.38996i | 0.0437659 | + | 0.0758048i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.24768 | 0.0712205 | ||||||||
\(997\) | 14.0526 | − | 8.11326i | 0.445050 | − | 0.256950i | −0.260688 | − | 0.965423i | \(-0.583949\pi\) |
0.705737 | + | 0.708474i | \(0.250616\pi\) | |||||||
\(998\) | 35.0443 | − | 20.2329i | 1.10931 | − | 0.640460i | ||||
\(999\) | 3.77239 | 0.119353 |
(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 | 475.2.j.c.49.4 | 16 | ||
5.2 | odd | 4 | 475.2.e.e.201.3 | 8 | |||
5.3 | odd | 4 | 95.2.e.c.11.2 | ✓ | 8 | ||
5.4 | even | 2 | inner | 475.2.j.c.49.5 | 16 | ||
15.8 | even | 4 | 855.2.k.h.676.3 | 8 | |||
19.7 | even | 3 | inner | 475.2.j.c.349.5 | 16 | ||
20.3 | even | 4 | 1520.2.q.o.961.2 | 8 | |||
95.7 | odd | 12 | 475.2.e.e.26.3 | 8 | |||
95.8 | even | 12 | 1805.2.a.i.1.2 | 4 | |||
95.27 | even | 12 | 9025.2.a.bp.1.3 | 4 | |||
95.64 | even | 6 | inner | 475.2.j.c.349.4 | 16 | ||
95.68 | odd | 12 | 1805.2.a.o.1.3 | 4 | |||
95.83 | odd | 12 | 95.2.e.c.26.2 | yes | 8 | ||
95.87 | odd | 12 | 9025.2.a.bg.1.2 | 4 | |||
285.83 | even | 12 | 855.2.k.h.406.3 | 8 | |||
380.83 | even | 12 | 1520.2.q.o.881.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.c.11.2 | ✓ | 8 | 5.3 | odd | 4 | ||
95.2.e.c.26.2 | yes | 8 | 95.83 | odd | 12 | ||
475.2.e.e.26.3 | 8 | 95.7 | odd | 12 | |||
475.2.e.e.201.3 | 8 | 5.2 | odd | 4 | |||
475.2.j.c.49.4 | 16 | 1.1 | even | 1 | trivial | ||
475.2.j.c.49.5 | 16 | 5.4 | even | 2 | inner | ||
475.2.j.c.349.4 | 16 | 95.64 | even | 6 | inner | ||
475.2.j.c.349.5 | 16 | 19.7 | even | 3 | inner | ||
855.2.k.h.406.3 | 8 | 285.83 | even | 12 | |||
855.2.k.h.676.3 | 8 | 15.8 | even | 4 | |||
1520.2.q.o.881.2 | 8 | 380.83 | even | 12 | |||
1520.2.q.o.961.2 | 8 | 20.3 | even | 4 | |||
1805.2.a.i.1.2 | 4 | 95.8 | even | 12 | |||
1805.2.a.o.1.3 | 4 | 95.68 | odd | 12 | |||
9025.2.a.bg.1.2 | 4 | 95.87 | odd | 12 | |||
9025.2.a.bp.1.3 | 4 | 95.27 | even | 12 |