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 | 49.5 | ||
Root | \(-1.19454 + 0.689667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.49 |
Dual form | 475.2.j.c.349.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0.796850 | − | 0.604178i | \(-0.206498\pi\) |
−0.124809 | + | 0.992181i | \(0.539832\pi\) | |||||||
\(3\) | 0.328513 | + | 0.189667i | 0.189667 | + | 0.109504i | 0.591827 | − | 0.806065i | \(-0.298407\pi\) |
−0.402160 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(4\) | −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 | \(-0.883542\pi\) | ||
0.933815 | − | 0.357756i | \(-0.116458\pi\) | |||||||
\(8\) | − | 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 | −0.0146407 | − | 0.999893i | \(-0.504660\pi\) |
0.858612 | + | 0.512626i | \(0.171327\pi\) | |||||||
\(14\) | 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 | 0.315285 | − | 0.948997i | \(-0.397900\pi\) |
−0.664213 | + | 0.747543i | \(0.731233\pi\) | |||||||
\(18\) | − | 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 | 0.0705407 | − | 0.997509i | \(-0.477528\pi\) |
0.899138 | + | 0.437664i | \(0.144194\pi\) | |||||||
\(24\) | 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 | \(0.0445786\pi\) | ||||
−0.990209 | + | 0.139590i | \(0.955421\pi\) | |||||||
\(38\) | −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 | −0.181290 | − | 0.983430i | \(-0.558027\pi\) |
−0.942320 | + | 0.334713i | \(0.891361\pi\) | |||||||
\(44\) | −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 | 0.409316 | − | 0.912392i | \(-0.365767\pi\) |
0.994813 | + | 0.101718i | \(0.0324339\pi\) | |||||||
\(48\) | 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 | −0.515670 | − | 0.856787i | \(-0.672457\pi\) |
0.484164 | + | 0.874977i | \(0.339124\pi\) | |||||||
\(54\) | 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 | −0.335550 | − | 0.942022i | \(-0.608922\pi\) |
0.648040 | + | 0.761606i | \(0.275589\pi\) | |||||||
\(68\) | 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 | 0.785718 | − | 0.618585i | \(-0.212294\pi\) |
−0.142851 | + | 0.989744i | \(0.545627\pi\) | |||||||
\(74\) | −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 | \(0.134027\pi\) | ||||
−0.912657 | + | 0.408727i | \(0.865973\pi\) | |||||||
\(84\) | −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 | \(0.0137788\pi\) |
0.537008 | + | 0.843577i | \(0.319555\pi\) | |||||||
\(98\) | 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 | \(0.0337402\pi\) | ||||
−0.994387 | + | 0.105800i | \(0.966260\pi\) | |||||||
\(104\) | −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 | \(0.0154063\pi\) | ||||
−0.998829 | + | 0.0483815i | \(0.984594\pi\) | |||||||
\(108\) | −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 | \(0.0126249\pi\) | ||||
−0.999214 | + | 0.0396519i | \(0.987375\pi\) | |||||||
\(114\) | −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 | −0.997855 | − | 0.0654584i | \(-0.979149\pi\) |
−0.442239 | + | 0.896897i | \(0.645816\pi\) | |||||||
\(128\) | −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 | 0.399656 | − | 0.916665i | \(-0.369129\pi\) |
0.993683 | + | 0.112220i | \(0.0357961\pi\) | |||||||
\(138\) | 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 | 0.729533 | − | 0.683945i | \(-0.239737\pi\) |
−0.227548 | + | 0.973767i | \(0.573071\pi\) | |||||||
\(158\) | −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 | \(-0.717962\pi\) | ||
0.632478 | − | 0.774578i | \(-0.282038\pi\) | |||||||
\(164\) | 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 | −0.381614 | − | 0.924322i | \(-0.624632\pi\) |
0.609679 | + | 0.792648i | \(0.291298\pi\) | |||||||
\(168\) | −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 | 0.806226 | − | 0.591607i | \(-0.201506\pi\) |
−0.109234 | + | 0.994016i | \(0.534840\pi\) | |||||||
\(174\) | −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 | 0.115373 | − | 0.993322i | \(-0.463194\pi\) |
−0.802556 | + | 0.596577i | \(0.796527\pi\) | |||||||
\(194\) | 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 | \(0.250061\pi\) | ||||
−0.706971 | + | 0.707242i | \(0.749939\pi\) | |||||||
\(198\) | − | 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 | −0.226095 | − | 0.974105i | \(-0.572596\pi\) |
−0.956647 | + | 0.291249i | \(0.905929\pi\) | |||||||
\(224\) | 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 | \(-0.680491\pi\) | ||
0.537129 | − | 0.843500i | \(-0.319509\pi\) | |||||||
\(228\) | 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 | 0.844602 | − | 0.535395i | \(-0.179837\pi\) |
−0.0413652 | + | 0.999144i | \(0.513171\pi\) | |||||||
\(234\) | −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 | 0.131481 | − | 0.991319i | \(-0.458027\pi\) |
0.924248 | + | 0.381794i | \(0.124693\pi\) | |||||||
\(258\) | − | 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 | 0.245857 | − | 0.969306i | \(-0.420931\pi\) |
−0.716515 | + | 0.697571i | \(0.754264\pi\) | |||||||
\(264\) | 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 | \(0.0422463\pi\) | ||||
−0.991206 | + | 0.132331i | \(0.957754\pi\) | |||||||
\(278\) | − | 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 | 0.533816 | − | 0.845600i | \(-0.320757\pi\) |
−0.465403 | + | 0.885099i | \(0.654091\pi\) | |||||||
\(284\) | 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 | \(-0.927562\pi\) | ||
0.974218 | − | 0.225610i | \(-0.0724375\pi\) | |||||||
\(294\) | 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 | 0.257955 | − | 0.966157i | \(-0.416951\pi\) |
−0.707739 | + | 0.706474i | \(0.750285\pi\) | |||||||
\(308\) | −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 | −0.449099 | − | 0.893482i | \(-0.648255\pi\) |
0.549229 | + | 0.835672i | \(0.314922\pi\) | |||||||
\(314\) | 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 | −0.948038 | − | 0.318157i | \(-0.896936\pi\) |
−0.198487 | + | 0.980103i | \(0.563603\pi\) | |||||||
\(318\) | −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 | \(-0.983817\pi\) |
−0.543365 | − | 0.839497i | \(-0.682850\pi\) | |||||||
\(338\) | −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 | 0.439149 | − | 0.898414i | \(-0.355280\pi\) |
−0.558475 | + | 0.829521i | \(0.688613\pi\) | |||||||
\(348\) | 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 | \(0.272268\pi\) | ||||
−0.655951 | + | 0.754803i | \(0.727732\pi\) | |||||||
\(354\) | −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 | −0.952862 | − | 0.303404i | \(-0.901877\pi\) |
−0.213676 | + | 0.976905i | \(0.568544\pi\) | |||||||
\(368\) | − | 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 | \(0.247138\pi\) | ||||
−0.713437 | + | 0.700719i | \(0.752862\pi\) | |||||||
\(374\) | −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 | 0.613873 | − | 0.789405i | \(-0.289611\pi\) |
−0.376709 | + | 0.926332i | \(0.622944\pi\) | |||||||
\(384\) | −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 | 0.250502 | − | 0.968116i | \(-0.419404\pi\) |
−0.713162 | + | 0.700999i | \(0.752738\pi\) | |||||||
\(398\) | 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 | −0.833673 | − | 0.552258i | \(-0.813766\pi\) |
0.0614325 | + | 0.998111i | \(0.480433\pi\) | |||||||
\(434\) | 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 | −0.997808 | − | 0.0661770i | \(-0.978920\pi\) |
−0.441593 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(444\) | 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 | \(-0.988067\pi\) | ||
0.999297 | − | 0.0374789i | \(-0.0119327\pi\) | |||||||
\(458\) | −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 | \(0.163865\pi\) | ||||
−0.870392 | + | 0.492359i | \(0.836135\pi\) | |||||||
\(464\) | 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 | \(-0.843101\pi\) | ||
0.880958 | − | 0.473194i | \(-0.156899\pi\) | |||||||
\(468\) | 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 | \(-0.695886\pi\) | ||
0.577280 | − | 0.816546i | \(-0.304114\pi\) | |||||||
\(488\) | −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 | −0.855884 | − | 0.517167i | \(-0.826987\pi\) |
0.0199377 | + | 0.999801i | \(0.493653\pi\) | |||||||
\(504\) | 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 | −0.489876 | − | 0.871792i | \(-0.662958\pi\) |
0.510056 | + | 0.860141i | \(0.329625\pi\) | |||||||
\(524\) | 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 | −0.856568 | − | 0.516035i | \(-0.827408\pi\) |
0.0186154 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(548\) | −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 | −0.979306 | − | 0.202387i | \(-0.935130\pi\) |
−0.314381 | + | 0.949297i | \(0.601797\pi\) | |||||||
\(558\) | − | 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 | \(-0.826302\pi\) | ||
0.854771 | − | 0.519005i | \(-0.173698\pi\) | |||||||
\(564\) | −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 | \(-0.916567\pi\) | ||
0.965845 | − | 0.259122i | \(-0.0834331\pi\) | |||||||
\(578\) | − | 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 | 0.578458 | − | 0.815712i | \(-0.303655\pi\) |
−0.417198 | + | 0.908816i | \(0.636988\pi\) | |||||||
\(588\) | − | 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 | −0.109019 | − | 0.994040i | \(-0.534771\pi\) |
0.806354 | + | 0.591433i | \(0.201438\pi\) | |||||||
\(594\) | 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 | \(-0.829195\pi\) | ||
0.859452 | − | 0.511217i | \(-0.170805\pi\) | |||||||
\(608\) | −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 | 0.188424 | − | 0.982088i | \(-0.439662\pi\) |
−0.756301 | + | 0.654224i | \(0.772995\pi\) | |||||||
\(614\) | −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 | −0.609307 | − | 0.792935i | \(-0.708552\pi\) |
0.382048 | + | 0.924142i | \(0.375219\pi\) | |||||||
\(618\) | −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 | 0.755185 | − | 0.655512i | \(-0.227547\pi\) |
−0.190098 | + | 0.981765i | \(0.560880\pi\) | |||||||
\(644\) | −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 | \(-0.803235\pi\) | ||
0.814949 | − | 0.579533i | \(-0.196765\pi\) | |||||||
\(648\) | 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 | \(0.0410594\pi\) | ||||
−0.991692 | + | 0.128634i | \(0.958941\pi\) | |||||||
\(654\) | 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 | \(-0.867071\pi\) | ||
0.914062 | − | 0.405575i | \(-0.132929\pi\) | |||||||
\(674\) | −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 | \(0.0948273\pi\) | ||||
−0.955952 | + | 0.293522i | \(0.905173\pi\) | |||||||
\(678\) | −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 | \(-0.947374\pi\) | ||
0.986364 | − | 0.164578i | \(-0.0526262\pi\) | |||||||
\(684\) | −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 | 0.487413 | − | 0.873172i | \(-0.337941\pi\) |
−0.512482 | + | 0.858698i | \(0.671274\pi\) | |||||||
\(728\) | −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 | \(-0.834925\pi\) | ||
0.868515 | − | 0.495663i | \(-0.165075\pi\) | |||||||
\(734\) | −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 | 0.476415 | − | 0.879220i | \(-0.341936\pi\) |
−0.523220 | + | 0.852198i | \(0.675269\pi\) | |||||||
\(744\) | 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 | 0.782706 | − | 0.622392i | \(-0.213839\pi\) |
−0.147654 | + | 0.989039i | \(0.547172\pi\) | |||||||
\(758\) | −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 | 0.0495699 | − | 0.998771i | \(-0.484215\pi\) |
0.889746 | + | 0.456457i | \(0.150882\pi\) | |||||||
\(774\) | −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 | \(-0.721193\pi\) | ||
0.640307 | − | 0.768119i | \(-0.278807\pi\) | |||||||
\(788\) | 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 | \(0.352475\pi\) | ||||
−0.447048 | + | 0.894510i | \(0.647525\pi\) | |||||||
\(798\) | 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 | \(-0.279750\pi\) |
0.985865 | − | 0.167544i | \(-0.0535836\pi\) | |||||||
\(824\) | 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 | −0.901058 | − | 0.433699i | \(-0.857208\pi\) |
−0.0749347 | + | 0.997188i | \(0.523875\pi\) | |||||||
\(828\) | 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 | 0.604989 | − | 0.796234i | \(-0.293177\pi\) |
−0.387064 | + | 0.922053i | \(0.626511\pi\) | |||||||
\(854\) | −19.0631 | −0.652327 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.07087 | 0.104960 | ||||||||
\(857\) | −39.2739 | − | 22.6748i | −1.34157 | − | 0.774556i | −0.354532 | − | 0.935044i | \(-0.615360\pi\) |
−0.987038 | + | 0.160488i | \(0.948693\pi\) | |||||||
\(858\) | 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 | \(0.246461\pi\) | ||||
−0.714925 | + | 0.699201i | \(0.753539\pi\) | |||||||
\(864\) | 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 | \(0.0404204\pi\) |
0.605650 | + | 0.795731i | \(0.292913\pi\) | |||||||
\(878\) | −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 | −0.983995 | − | 0.178197i | \(-0.942973\pi\) |
−0.337674 | + | 0.941263i | \(0.609640\pi\) | |||||||
\(884\) | 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 | 0.0265165 | − | 0.999648i | \(-0.491559\pi\) |
0.878979 | + | 0.476860i | \(0.158225\pi\) | |||||||
\(888\) | 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 | 0.971521 | − | 0.236952i | \(-0.0761486\pi\) |
0.280554 | + | 0.959838i | \(0.409482\pi\) | |||||||
\(908\) | −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 | −0.277725 | − | 0.960661i | \(-0.589580\pi\) |
0.693094 | + | 0.720847i | \(0.256247\pi\) | |||||||
\(938\) | − | 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 | 0.390469 | − | 0.920616i | \(-0.372313\pi\) |
−0.602043 | + | 0.798464i | \(0.705646\pi\) | |||||||
\(948\) | 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 | 0.147017 | − | 0.989134i | \(-0.453033\pi\) |
−0.783107 | + | 0.621887i | \(0.786366\pi\) | |||||||
\(954\) | 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 | 0.844528 | − | 0.535512i | \(-0.179881\pi\) |
−0.0415030 | + | 0.999138i | \(0.513215\pi\) | |||||||
\(968\) | 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 | \(-0.976596\pi\) | ||
0.997298 | − | 0.0734585i | \(-0.0234036\pi\) | |||||||
\(978\) | 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 | 0.401452 | − | 0.915880i | \(-0.368506\pi\) |
−0.592450 | + | 0.805607i | \(0.701839\pi\) | |||||||
\(984\) | 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 | −0.705737 | − | 0.708474i | \(-0.749384\pi\) |
0.260688 | + | 0.965423i | \(0.416051\pi\) | |||||||
\(998\) | −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.49.5 | 16 | ||
5.2 | odd | 4 | 95.2.e.c.11.2 | ✓ | 8 | ||
5.3 | odd | 4 | 475.2.e.e.201.3 | 8 | |||
5.4 | even | 2 | inner | 475.2.j.c.49.4 | 16 | ||
15.2 | even | 4 | 855.2.k.h.676.3 | 8 | |||
19.7 | even | 3 | inner | 475.2.j.c.349.4 | 16 | ||
20.7 | even | 4 | 1520.2.q.o.961.2 | 8 | |||
95.7 | odd | 12 | 95.2.e.c.26.2 | yes | 8 | ||
95.8 | even | 12 | 9025.2.a.bp.1.3 | 4 | |||
95.27 | even | 12 | 1805.2.a.i.1.2 | 4 | |||
95.64 | even | 6 | inner | 475.2.j.c.349.5 | 16 | ||
95.68 | odd | 12 | 9025.2.a.bg.1.2 | 4 | |||
95.83 | odd | 12 | 475.2.e.e.26.3 | 8 | |||
95.87 | odd | 12 | 1805.2.a.o.1.3 | 4 | |||
285.197 | even | 12 | 855.2.k.h.406.3 | 8 | |||
380.7 | 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 | 5.2 | odd | 4 | ||
95.2.e.c.26.2 | yes | 8 | 95.7 | odd | 12 | ||
475.2.e.e.26.3 | 8 | 95.83 | odd | 12 | |||
475.2.e.e.201.3 | 8 | 5.3 | odd | 4 | |||
475.2.j.c.49.4 | 16 | 5.4 | even | 2 | inner | ||
475.2.j.c.49.5 | 16 | 1.1 | even | 1 | trivial | ||
475.2.j.c.349.4 | 16 | 19.7 | even | 3 | inner | ||
475.2.j.c.349.5 | 16 | 95.64 | even | 6 | inner | ||
855.2.k.h.406.3 | 8 | 285.197 | even | 12 | |||
855.2.k.h.676.3 | 8 | 15.2 | even | 4 | |||
1520.2.q.o.881.2 | 8 | 380.7 | even | 12 | |||
1520.2.q.o.961.2 | 8 | 20.7 | even | 4 | |||
1805.2.a.i.1.2 | 4 | 95.27 | even | 12 | |||
1805.2.a.o.1.3 | 4 | 95.87 | odd | 12 | |||
9025.2.a.bg.1.2 | 4 | 95.68 | odd | 12 | |||
9025.2.a.bp.1.3 | 4 | 95.8 | even | 12 |