Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(26,475)]
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([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.4601315889.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(1.07988 + 1.87040i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.26 |
Dual form | 475.2.e.e.201.1 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.832272 | − | 1.44154i | −0.588506 | − | 1.01932i | −0.994428 | − | 0.105414i | \(-0.966383\pi\) |
0.405923 | − | 0.913907i | \(-0.366950\pi\) | |||||||
\(3\) | −0.579878 | − | 1.00438i | −0.334793 | − | 0.579878i | 0.648652 | − | 0.761085i | \(-0.275333\pi\) |
−0.983445 | + | 0.181207i | \(0.942000\pi\) | |||||||
\(4\) | −0.385355 | + | 0.667454i | −0.192677 | + | 0.333727i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.965233 | + | 1.67183i | −0.394055 | + | 0.682523i | ||||
\(7\) | 2.43525 | 0.920440 | 0.460220 | − | 0.887805i | \(-0.347771\pi\) | ||||
0.460220 | + | 0.887805i | \(0.347771\pi\) | |||||||
\(8\) | −2.04621 | −0.723444 | ||||||||
\(9\) | 0.827483 | − | 1.43324i | 0.275828 | − | 0.477748i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.75477 | −1.73513 | −0.867564 | − | 0.497326i | \(-0.834315\pi\) | ||||
−0.867564 | + | 0.497326i | \(0.834315\pi\) | |||||||
\(12\) | 0.893835 | 0.258028 | ||||||||
\(13\) | −0.797505 | + | 1.38132i | −0.221188 | + | 0.383109i | −0.955169 | − | 0.296061i | \(-0.904327\pi\) |
0.733981 | + | 0.679170i | \(0.237660\pi\) | |||||||
\(14\) | −2.02680 | − | 3.51051i | −0.541684 | − | 0.938224i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.47371 | + | 4.28460i | 0.618428 | + | 1.07115i | ||||
\(17\) | −2.99203 | − | 5.18234i | −0.725673 | − | 1.25690i | −0.958696 | − | 0.284432i | \(-0.908195\pi\) |
0.233023 | − | 0.972471i | \(-0.425138\pi\) | |||||||
\(18\) | −2.75477 | −0.649305 | ||||||||
\(19\) | 0.149412 | − | 4.35634i | 0.0342775 | − | 0.999412i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41215 | − | 2.44592i | −0.308156 | − | 0.533743i | ||||
\(22\) | 4.78953 | + | 8.29572i | 1.02113 | + | 1.76865i | ||||
\(23\) | −0.470022 | + | 0.814102i | −0.0980064 | + | 0.169752i | −0.910859 | − | 0.412717i | \(-0.864580\pi\) |
0.812853 | + | 0.582469i | \(0.197913\pi\) | |||||||
\(24\) | 1.18655 | + | 2.05517i | 0.242204 | + | 0.419509i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.65497 | 0.520682 | ||||||||
\(27\) | −5.39862 | −1.03897 | ||||||||
\(28\) | −0.938437 | + | 1.62542i | −0.177348 | + | 0.307176i | ||||
\(29\) | −1.30917 | + | 2.26755i | −0.243106 | + | 0.421073i | −0.961598 | − | 0.274463i | \(-0.911500\pi\) |
0.718491 | + | 0.695536i | \(0.244833\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.26913 | −0.946364 | −0.473182 | − | 0.880965i | \(-0.656895\pi\) | ||||
−0.473182 | + | 0.880965i | \(0.656895\pi\) | |||||||
\(32\) | 2.07140 | − | 3.58777i | 0.366175 | − | 0.634233i | ||||
\(33\) | 3.33706 | + | 5.77996i | 0.580908 | + | 1.00616i | ||||
\(34\) | −4.98037 | + | 8.62625i | −0.854126 | + | 1.47939i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.637749 | + | 1.10461i | 0.106292 | + | 0.184102i | ||||
\(37\) | 2.89384 | 0.475744 | 0.237872 | − | 0.971297i | \(-0.423550\pi\) | ||||
0.237872 | + | 0.971297i | \(0.423550\pi\) | |||||||
\(38\) | −6.40418 | + | 3.41028i | −1.03889 | + | 0.553220i | ||||
\(39\) | 1.84982 | 0.296209 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.15767 | + | 5.46925i | 0.493145 | + | 0.854153i | 0.999969 | − | 0.00789701i | \(-0.00251372\pi\) |
−0.506823 | + | 0.862050i | \(0.669180\pi\) | |||||||
\(42\) | −2.35059 | + | 4.07134i | −0.362704 | + | 0.628221i | ||||
\(43\) | 2.26961 | + | 3.93108i | 0.346113 | + | 0.599485i | 0.985555 | − | 0.169354i | \(-0.0541682\pi\) |
−0.639443 | + | 0.768839i | \(0.720835\pi\) | |||||||
\(44\) | 2.21763 | − | 3.84104i | 0.334320 | − | 0.579059i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.56475 | 0.230709 | ||||||||
\(47\) | 4.47718 | − | 7.75471i | 0.653064 | − | 1.13114i | −0.329311 | − | 0.944221i | \(-0.606816\pi\) |
0.982375 | − | 0.186919i | \(-0.0598502\pi\) | |||||||
\(48\) | 2.86890 | − | 4.96909i | 0.414090 | − | 0.717226i | ||||
\(49\) | −1.06953 | −0.152791 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.47002 | + | 6.01025i | −0.485900 | + | 0.841604i | ||||
\(52\) | −0.614645 | − | 1.06460i | −0.0852359 | − | 0.147633i | ||||
\(53\) | −1.09819 | + | 1.90213i | −0.150848 | + | 0.261277i | −0.931540 | − | 0.363640i | \(-0.881534\pi\) |
0.780691 | + | 0.624917i | \(0.214867\pi\) | |||||||
\(54\) | 4.49313 | + | 7.78232i | 0.611437 | + | 1.05904i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.98304 | −0.665887 | ||||||||
\(57\) | −4.46205 | + | 2.37608i | −0.591013 | + | 0.314719i | ||||
\(58\) | 4.35834 | 0.572278 | ||||||||
\(59\) | 5.39939 | + | 9.35202i | 0.702941 | + | 1.21753i | 0.967430 | + | 0.253140i | \(0.0814634\pi\) |
−0.264489 | + | 0.964389i | \(0.585203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26434 | − | 9.11811i | 0.674030 | − | 1.16745i | −0.302721 | − | 0.953079i | \(-0.597895\pi\) |
0.976751 | − | 0.214375i | \(-0.0687716\pi\) | |||||||
\(62\) | 4.38535 | + | 7.59566i | 0.556941 | + | 0.964649i | ||||
\(63\) | 2.01513 | − | 3.49031i | 0.253883 | − | 0.439738i | ||||
\(64\) | 2.99898 | 0.374873 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.55469 | − | 9.62100i | 0.683735 | − | 1.18426i | ||||
\(67\) | 0.504789 | − | 0.874320i | 0.0616698 | − | 0.106815i | −0.833542 | − | 0.552456i | \(-0.813691\pi\) |
0.895212 | + | 0.445641i | \(0.147024\pi\) | |||||||
\(68\) | 4.61197 | 0.559284 | ||||||||
\(69\) | 1.09022 | 0.131247 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41694 | − | 7.65036i | −0.524194 | − | 0.907931i | −0.999603 | − | 0.0281662i | \(-0.991033\pi\) |
0.475409 | − | 0.879765i | \(-0.342300\pi\) | |||||||
\(72\) | −1.69320 | + | 2.93271i | −0.199546 | + | 0.345624i | ||||
\(73\) | −5.12499 | − | 8.87674i | −0.599835 | − | 1.03894i | −0.992845 | − | 0.119410i | \(-0.961900\pi\) |
0.393011 | − | 0.919534i | \(-0.371434\pi\) | |||||||
\(74\) | −2.40846 | − | 4.17157i | −0.279978 | − | 0.484936i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.85008 | + | 1.77846i | 0.326927 | + | 0.204004i | ||||
\(77\) | −14.0143 | −1.59708 | ||||||||
\(78\) | −1.53956 | − | 2.66659i | −0.174320 | − | 0.301932i | ||||
\(79\) | −3.80229 | − | 6.58577i | −0.427792 | − | 0.740957i | 0.568885 | − | 0.822417i | \(-0.307375\pi\) |
−0.996677 | + | 0.0814604i | \(0.974042\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.648093 | + | 1.12253i | 0.0720103 | + | 0.124726i | ||||
\(82\) | 5.25609 | − | 9.10381i | 0.580438 | − | 1.00535i | ||||
\(83\) | −3.11355 | −0.341756 | −0.170878 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170878 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(84\) | 2.17672 | 0.237499 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.77787 | − | 6.54346i | 0.407378 | − | 0.705600i | ||||
\(87\) | 3.03663 | 0.325561 | ||||||||
\(88\) | 11.7755 | 1.25527 | ||||||||
\(89\) | 5.55706 | − | 9.62511i | 0.589047 | − | 1.02026i | −0.405310 | − | 0.914179i | \(-0.632837\pi\) |
0.994358 | − | 0.106081i | \(-0.0338302\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.94213 | + | 3.36387i | −0.203590 | + | 0.352629i | ||||
\(92\) | −0.362251 | − | 0.627436i | −0.0377672 | − | 0.0654148i | ||||
\(93\) | 3.05545 | + | 5.29220i | 0.316836 | + | 0.548776i | ||||
\(94\) | −14.9049 | −1.53733 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.80463 | −0.490371 | ||||||||
\(97\) | 2.02888 | + | 3.51412i | 0.206002 | + | 0.356805i | 0.950451 | − | 0.310873i | \(-0.100621\pi\) |
−0.744450 | + | 0.667678i | \(0.767288\pi\) | |||||||
\(98\) | 0.890144 | + | 1.54177i | 0.0899181 | + | 0.155743i | ||||
\(99\) | −4.76197 | + | 8.24798i | −0.478596 | + | 0.828953i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56503 | − | 9.63892i | 0.553741 | − | 0.959108i | −0.444259 | − | 0.895898i | \(-0.646533\pi\) |
0.998000 | − | 0.0632098i | \(-0.0201337\pi\) | |||||||
\(102\) | 11.5520 | 1.14382 | ||||||||
\(103\) | −11.5791 | −1.14092 | −0.570460 | − | 0.821326i | \(-0.693235\pi\) | ||||
−0.570460 | + | 0.821326i | \(0.693235\pi\) | |||||||
\(104\) | 1.63186 | − | 2.82647i | 0.160017 | − | 0.277158i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.65598 | 0.355101 | ||||||||
\(107\) | −17.9177 | −1.73217 | −0.866086 | − | 0.499894i | \(-0.833372\pi\) | ||||
−0.866086 | + | 0.499894i | \(0.833372\pi\) | |||||||
\(108\) | 2.08039 | − | 3.60333i | 0.200185 | − | 0.346731i | ||||
\(109\) | −2.81235 | − | 4.87113i | −0.269374 | − | 0.466570i | 0.699326 | − | 0.714803i | \(-0.253484\pi\) |
−0.968700 | + | 0.248233i | \(0.920150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.67807 | − | 2.90650i | −0.159275 | − | 0.275873i | ||||
\(112\) | 6.02412 | + | 10.4341i | 0.569226 | + | 0.985928i | ||||
\(113\) | 15.6789 | 1.47494 | 0.737472 | − | 0.675378i | \(-0.236019\pi\) | ||||
0.737472 | + | 0.675378i | \(0.236019\pi\) | |||||||
\(114\) | 7.13885 | + | 4.45467i | 0.668614 | + | 0.417218i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00899 | − | 1.74762i | −0.0936822 | − | 0.162262i | ||||
\(117\) | 1.31984 | + | 2.28604i | 0.122020 | + | 0.211344i | ||||
\(118\) | 8.98753 | − | 15.5669i | 0.827369 | − | 1.43304i | ||||
\(119\) | −7.28635 | − | 12.6203i | −0.667939 | − | 1.15690i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.1173 | 2.01067 | ||||||||
\(122\) | −17.5255 | −1.58668 | ||||||||
\(123\) | 3.66213 | − | 6.34299i | 0.330203 | − | 0.571928i | ||||
\(124\) | 2.03049 | − | 3.51691i | 0.182343 | − | 0.315827i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.70856 | −0.597646 | ||||||||
\(127\) | 3.05996 | − | 5.30000i | 0.271527 | − | 0.470299i | −0.697726 | − | 0.716365i | \(-0.745805\pi\) |
0.969253 | + | 0.246066i | \(0.0791380\pi\) | |||||||
\(128\) | −6.63877 | − | 11.4987i | −0.586790 | − | 1.01635i | ||||
\(129\) | 2.63220 | − | 4.55910i | 0.231752 | − | 0.401406i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.44055 | + | 12.8874i | 0.650084 | + | 1.12598i | 0.983102 | + | 0.183058i | \(0.0585997\pi\) |
−0.333018 | + | 0.942920i | \(0.608067\pi\) | |||||||
\(132\) | −5.14381 | −0.447711 | ||||||||
\(133\) | 0.363857 | − | 10.6088i | 0.0315504 | − | 0.919899i | ||||
\(134\) | −1.68049 | −0.145172 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.12231 | + | 10.6042i | 0.524984 | + | 0.909299i | ||||
\(137\) | 8.67518 | − | 15.0258i | 0.741170 | − | 1.28374i | −0.210793 | − | 0.977531i | \(-0.567604\pi\) |
0.951963 | − | 0.306214i | \(-0.0990622\pi\) | |||||||
\(138\) | −0.907361 | − | 1.57160i | −0.0772397 | − | 0.133783i | ||||
\(139\) | 3.35267 | − | 5.80700i | 0.284370 | − | 0.492543i | −0.688086 | − | 0.725629i | \(-0.741549\pi\) |
0.972456 | + | 0.233086i | \(0.0748823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3849 | −0.874564 | ||||||||
\(142\) | −7.35219 | + | 12.7344i | −0.616982 | + | 1.06864i | ||||
\(143\) | 4.58946 | − | 7.94917i | 0.383790 | − | 0.664743i | ||||
\(144\) | 8.18782 | 0.682319 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.53077 | + | 14.7757i | −0.706012 | + | 1.22285i | ||||
\(147\) | 0.620199 | + | 1.07422i | 0.0511532 | + | 0.0885999i | ||||
\(148\) | −1.11515 | + | 1.93150i | −0.0916651 | + | 0.158769i | ||||
\(149\) | −7.19642 | − | 12.4646i | −0.589553 | − | 1.02114i | −0.994291 | − | 0.106704i | \(-0.965970\pi\) |
0.404737 | − | 0.914433i | \(-0.367363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7219 | 1.03529 | 0.517645 | − | 0.855595i | \(-0.326809\pi\) | ||||
0.517645 | + | 0.855595i | \(0.326809\pi\) | |||||||
\(152\) | −0.305729 | + | 8.91398i | −0.0247979 | + | 0.723019i | ||||
\(153\) | −9.90341 | −0.800644 | ||||||||
\(154\) | 11.6637 | + | 20.2022i | 0.939890 | + | 1.62794i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.712838 | + | 1.23467i | −0.0570727 | + | 0.0988529i | ||||
\(157\) | −1.68765 | − | 2.92309i | −0.134689 | − | 0.233288i | 0.790790 | − | 0.612088i | \(-0.209670\pi\) |
−0.925479 | + | 0.378800i | \(0.876337\pi\) | |||||||
\(158\) | −6.32909 | + | 10.9623i | −0.503515 | + | 0.872114i | ||||
\(159\) | 2.54727 | 0.202012 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.14462 | + | 1.98255i | −0.0902089 | + | 0.156246i | ||||
\(162\) | 1.07878 | − | 1.86850i | 0.0847569 | − | 0.146803i | ||||
\(163\) | −0.307960 | −0.0241213 | −0.0120607 | − | 0.999927i | \(-0.503839\pi\) | ||||
−0.0120607 | + | 0.999927i | \(0.503839\pi\) | |||||||
\(164\) | −4.86730 | −0.380072 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.59132 | + | 4.48830i | 0.201125 | + | 0.348359i | ||||
\(167\) | 7.13215 | − | 12.3532i | 0.551902 | − | 0.955923i | −0.446235 | − | 0.894916i | \(-0.647235\pi\) |
0.998137 | − | 0.0610070i | \(-0.0194312\pi\) | |||||||
\(168\) | 2.88955 | + | 5.00486i | 0.222934 | + | 0.386133i | ||||
\(169\) | 5.22797 | + | 9.05511i | 0.402152 | + | 0.696547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.12005 | − | 3.81894i | −0.468012 | − | 0.292042i | ||||
\(172\) | −3.49842 | −0.266752 | ||||||||
\(173\) | 6.67357 | + | 11.5590i | 0.507382 | + | 0.878811i | 0.999963 | + | 0.00854514i | \(0.00272003\pi\) |
−0.492581 | + | 0.870266i | \(0.663947\pi\) | |||||||
\(174\) | −2.52730 | − | 4.37742i | −0.191594 | − | 0.331851i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.2356 | − | 24.6569i | −1.07305 | − | 1.85858i | ||||
\(177\) | 6.26197 | − | 10.8461i | 0.470679 | − | 0.815239i | ||||
\(178\) | −18.5000 | −1.38663 | ||||||||
\(179\) | −14.2207 | −1.06291 | −0.531454 | − | 0.847087i | \(-0.678354\pi\) | ||||
−0.531454 | + | 0.847087i | \(0.678354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.94132 | + | 8.55861i | −0.367285 | + | 0.636157i | −0.989140 | − | 0.146976i | \(-0.953046\pi\) |
0.621855 | + | 0.783133i | \(0.286379\pi\) | |||||||
\(182\) | 6.46552 | 0.479256 | ||||||||
\(183\) | −12.2107 | −0.902641 | ||||||||
\(184\) | 0.961763 | − | 1.66582i | 0.0709021 | − | 0.122806i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.08594 | − | 8.80911i | 0.372919 | − | 0.645915i | ||||
\(187\) | 17.2184 | + | 29.8232i | 1.25914 | + | 2.18089i | ||||
\(188\) | 3.45061 | + | 5.97663i | 0.251661 | + | 0.435891i | ||||
\(189\) | −13.1470 | −0.956305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9942 | −0.940228 | −0.470114 | − | 0.882606i | \(-0.655787\pi\) | ||||
−0.470114 | + | 0.882606i | \(0.655787\pi\) | |||||||
\(192\) | −1.73904 | − | 3.01211i | −0.125505 | − | 0.217380i | ||||
\(193\) | 7.25795 | + | 12.5711i | 0.522439 | + | 0.904890i | 0.999659 | + | 0.0261066i | \(0.00831094\pi\) |
−0.477221 | + | 0.878784i | \(0.658356\pi\) | |||||||
\(194\) | 3.37716 | − | 5.84942i | 0.242466 | − | 0.419964i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.412150 | − | 0.713865i | 0.0294393 | − | 0.0509904i | ||||
\(197\) | 25.0010 | 1.78125 | 0.890624 | − | 0.454740i | \(-0.150268\pi\) | ||||
0.890624 | + | 0.454740i | \(0.150268\pi\) | |||||||
\(198\) | 15.8530 | 1.12663 | ||||||||
\(199\) | 1.12769 | − | 1.95322i | 0.0799401 | − | 0.138460i | −0.823284 | − | 0.567630i | \(-0.807860\pi\) |
0.903224 | + | 0.429170i | \(0.141194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.17086 | −0.0825864 | ||||||||
\(202\) | −18.5265 | −1.30352 | ||||||||
\(203\) | −3.18816 | + | 5.52205i | −0.223765 | + | 0.387572i | ||||
\(204\) | −2.67438 | − | 4.63216i | −0.187244 | − | 0.324316i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.63694 | + | 16.6917i | 0.671437 | + | 1.16296i | ||||
\(207\) | 0.777871 | + | 1.34731i | 0.0540657 | + | 0.0936446i | ||||
\(208\) | −7.89120 | −0.547156 | ||||||||
\(209\) | −0.859833 | + | 25.0697i | −0.0594759 | + | 1.73411i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1081 | − | 19.2397i | −0.764710 | − | 1.32452i | −0.940400 | − | 0.340071i | \(-0.889549\pi\) |
0.175689 | − | 0.984446i | \(-0.443785\pi\) | |||||||
\(212\) | −0.846388 | − | 1.46599i | −0.0581302 | − | 0.100684i | ||||
\(213\) | −5.12257 | + | 8.87255i | −0.350993 | + | 0.607937i | ||||
\(214\) | 14.9124 | + | 25.8291i | 1.01939 | + | 1.76564i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.0467 | 0.751634 | ||||||||
\(217\) | −12.8317 | −0.871071 | ||||||||
\(218\) | −4.68128 | + | 8.10822i | −0.317057 | + | 0.549158i | ||||
\(219\) | −5.94373 | + | 10.2949i | −0.401640 | + | 0.695662i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.54463 | 0.642041 | ||||||||
\(222\) | −2.79322 | + | 4.83801i | −0.187469 | + | 0.324706i | ||||
\(223\) | 5.10799 | + | 8.84730i | 0.342056 | + | 0.592459i | 0.984814 | − | 0.173610i | \(-0.0555432\pi\) |
−0.642758 | + | 0.766069i | \(0.722210\pi\) | |||||||
\(224\) | 5.04438 | − | 8.73712i | 0.337042 | − | 0.583774i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0491 | − | 22.6017i | −0.868012 | − | 1.50344i | ||||
\(227\) | −4.15180 | −0.275565 | −0.137782 | − | 0.990463i | \(-0.543997\pi\) | ||||
−0.137782 | + | 0.990463i | \(0.543997\pi\) | |||||||
\(228\) | 0.133550 | − | 3.89385i | 0.00884456 | − | 0.257876i | ||||
\(229\) | 6.53286 | 0.431703 | 0.215852 | − | 0.976426i | \(-0.430747\pi\) | ||||
0.215852 | + | 0.976426i | \(0.430747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.12660 | + | 14.0757i | 0.534691 | + | 0.926111i | ||||
\(232\) | 2.67883 | − | 4.63987i | 0.175874 | − | 0.304623i | ||||
\(233\) | 2.57410 | + | 4.45848i | 0.168635 | + | 0.292084i | 0.937940 | − | 0.346797i | \(-0.112731\pi\) |
−0.769305 | + | 0.638882i | \(0.779397\pi\) | |||||||
\(234\) | 2.19694 | − | 3.80521i | 0.143618 | − | 0.248755i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.32272 | −0.541763 | ||||||||
\(237\) | −4.40973 | + | 7.63788i | −0.286443 | + | 0.496134i | ||||
\(238\) | −12.1285 | + | 21.0071i | −0.786171 | + | 1.36169i | ||||
\(239\) | 13.9962 | 0.905338 | 0.452669 | − | 0.891679i | \(-0.350472\pi\) | ||||
0.452669 | + | 0.891679i | \(0.350472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.61285 | + | 13.1858i | −0.490387 | + | 0.849375i | −0.999939 | − | 0.0110652i | \(-0.996478\pi\) |
0.509552 | + | 0.860440i | \(0.329811\pi\) | |||||||
\(242\) | −18.4076 | − | 31.8830i | −1.18329 | − | 2.04952i | ||||
\(243\) | −7.34631 | + | 12.7242i | −0.471266 | + | 0.816256i | ||||
\(244\) | 4.05728 | + | 7.02742i | 0.259741 | + | 0.449884i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.1916 | −0.777305 | ||||||||
\(247\) | 5.89834 | + | 3.68059i | 0.375302 | + | 0.234190i | ||||
\(248\) | 10.7817 | 0.684642 | ||||||||
\(249\) | 1.80548 | + | 3.12718i | 0.114417 | + | 0.198177i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.05630 | − | 5.29366i | 0.192912 | − | 0.334133i | −0.753302 | − | 0.657674i | \(-0.771540\pi\) |
0.946214 | + | 0.323542i | \(0.104874\pi\) | |||||||
\(252\) | 1.55308 | + | 2.69002i | 0.0978350 | + | 0.169455i | ||||
\(253\) | 2.70487 | − | 4.68497i | 0.170053 | − | 0.294541i | ||||
\(254\) | −10.1869 | −0.639181 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.05154 | + | 13.9457i | −0.503221 | + | 0.871605i | ||||
\(257\) | 0.0613414 | − | 0.106246i | 0.00382637 | − | 0.00662747i | −0.864106 | − | 0.503310i | \(-0.832115\pi\) |
0.867932 | + | 0.496683i | \(0.165449\pi\) | |||||||
\(258\) | −8.76281 | −0.545549 | ||||||||
\(259\) | 7.04723 | 0.437893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.16663 | + | 3.75271i | 0.134111 | + | 0.232287i | ||||
\(262\) | 12.3851 | − | 21.4517i | 0.765156 | − | 1.32529i | ||||
\(263\) | −5.03027 | − | 8.71267i | −0.310179 | − | 0.537247i | 0.668222 | − | 0.743962i | \(-0.267056\pi\) |
−0.978401 | + | 0.206716i | \(0.933722\pi\) | |||||||
\(264\) | −6.82832 | − | 11.8270i | −0.420254 | − | 0.727902i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.5958 | + | 8.30489i | −0.956240 | + | 0.509206i | ||||
\(267\) | −12.8897 | −0.788835 | ||||||||
\(268\) | 0.389046 | + | 0.673847i | 0.0237648 | + | 0.0411618i | ||||
\(269\) | −2.85614 | − | 4.94698i | −0.174142 | − | 0.301623i | 0.765722 | − | 0.643172i | \(-0.222382\pi\) |
−0.939864 | + | 0.341549i | \(0.889049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.35560 | + | 11.0082i | 0.386075 | + | 0.668702i | 0.991918 | − | 0.126883i | \(-0.0404972\pi\) |
−0.605843 | + | 0.795585i | \(0.707164\pi\) | |||||||
\(272\) | 14.8028 | − | 25.6393i | 0.897554 | − | 1.55461i | ||||
\(273\) | 4.50479 | 0.272642 | ||||||||
\(274\) | −28.8804 | −1.74473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.420122 | + | 0.727673i | −0.0252884 | + | 0.0438008i | ||||
\(277\) | −17.6019 | −1.05760 | −0.528799 | − | 0.848747i | \(-0.677358\pi\) | ||||
−0.528799 | + | 0.848747i | \(0.677358\pi\) | |||||||
\(278\) | −11.1613 | −0.669413 | ||||||||
\(279\) | −4.36012 | + | 7.55195i | −0.261034 | + | 0.452123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2502 | − | 17.7539i | 0.611476 | − | 1.05911i | −0.379516 | − | 0.925185i | \(-0.623910\pi\) |
0.990992 | − | 0.133922i | \(-0.0427571\pi\) | |||||||
\(282\) | 8.64305 | + | 14.9702i | 0.514686 | + | 0.891462i | ||||
\(283\) | −5.92805 | − | 10.2677i | −0.352386 | − | 0.610350i | 0.634281 | − | 0.773103i | \(-0.281296\pi\) |
−0.986667 | + | 0.162752i | \(0.947963\pi\) | |||||||
\(284\) | 6.80836 | 0.404002 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.2787 | −0.903449 | ||||||||
\(287\) | 7.68973 | + | 13.3190i | 0.453911 | + | 0.786196i | ||||
\(288\) | −3.42809 | − | 5.93763i | −0.202002 | − | 0.349878i | ||||
\(289\) | −9.40447 | + | 16.2890i | −0.553204 | + | 0.958177i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.35301 | − | 4.07552i | 0.137936 | − | 0.238911i | ||||
\(292\) | 7.89976 | 0.462298 | ||||||||
\(293\) | 24.9814 | 1.45943 | 0.729715 | − | 0.683751i | \(-0.239653\pi\) | ||||
0.729715 | + | 0.683751i | \(0.239653\pi\) | |||||||
\(294\) | 1.03235 | − | 1.78808i | 0.0602079 | − | 0.104283i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.92139 | −0.344174 | ||||||||
\(297\) | 31.0678 | 1.80274 | ||||||||
\(298\) | −11.9788 | + | 20.7478i | −0.693911 | + | 1.20189i | ||||
\(299\) | −0.749690 | − | 1.29850i | −0.0433557 | − | 0.0750943i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.52708 | + | 9.57319i | 0.318576 | + | 0.551789i | ||||
\(302\) | −10.5881 | − | 18.3391i | −0.609274 | − | 1.05529i | ||||
\(303\) | −12.9082 | −0.741554 | ||||||||
\(304\) | 19.0348 | − | 10.1362i | 1.09172 | − | 0.581348i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.24234 | + | 14.2761i | 0.471183 | + | 0.816113i | ||||
\(307\) | 8.45997 | + | 14.6531i | 0.482836 | + | 0.836296i | 0.999806 | − | 0.0197074i | \(-0.00627348\pi\) |
−0.516970 | + | 0.856003i | \(0.672940\pi\) | |||||||
\(308\) | 5.40049 | − | 9.35392i | 0.307721 | − | 0.532989i | ||||
\(309\) | 6.71444 | + | 11.6298i | 0.381971 | + | 0.661594i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2133 | −0.862670 | −0.431335 | − | 0.902192i | \(-0.641957\pi\) | ||||
−0.431335 | + | 0.902192i | \(0.641957\pi\) | |||||||
\(312\) | −3.78512 | −0.214290 | ||||||||
\(313\) | 12.4637 | − | 21.5877i | 0.704488 | − | 1.22021i | −0.262389 | − | 0.964962i | \(-0.584510\pi\) |
0.966876 | − | 0.255246i | \(-0.0821564\pi\) | |||||||
\(314\) | −2.80917 | + | 4.86562i | −0.158531 | + | 0.274583i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.86093 | 0.329703 | ||||||||
\(317\) | −12.6152 | + | 21.8502i | −0.708541 | + | 1.22723i | 0.256857 | + | 0.966449i | \(0.417313\pi\) |
−0.965398 | + | 0.260780i | \(0.916020\pi\) | |||||||
\(318\) | −2.12002 | − | 3.67199i | −0.118885 | − | 0.205915i | ||||
\(319\) | 7.53396 | − | 13.0492i | 0.421821 | − | 0.730615i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3901 | + | 17.9962i | 0.579919 | + | 1.00445i | ||||
\(322\) | 3.81055 | 0.212354 | ||||||||
\(323\) | −23.0231 | + | 12.2600i | −1.28104 | + | 0.682163i | ||||
\(324\) | −0.998983 | −0.0554991 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.256307 | + | 0.443937i | 0.0141955 | + | 0.0245874i | ||||
\(327\) | −3.26164 | + | 5.64933i | −0.180369 | + | 0.312408i | ||||
\(328\) | −6.46125 | − | 11.1912i | −0.356763 | − | 0.617932i | ||||
\(329\) | 10.9031 | − | 18.8847i | 0.601106 | − | 1.04115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2063 | −1.11064 | −0.555320 | − | 0.831637i | \(-0.687404\pi\) | ||||
−0.555320 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(332\) | 1.19982 | − | 2.07815i | 0.0658487 | − | 0.114053i | ||||
\(333\) | 2.39460 | − | 4.14757i | 0.131223 | − | 0.227285i | ||||
\(334\) | −23.7436 | −1.29919 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.98651 | − | 12.1010i | 0.381145 | − | 0.660163i | ||||
\(337\) | −15.9123 | − | 27.5610i | −0.866800 | − | 1.50134i | −0.865249 | − | 0.501342i | \(-0.832840\pi\) |
−0.00155051 | − | 0.999999i | \(-0.500494\pi\) | |||||||
\(338\) | 8.70219 | − | 15.0726i | 0.473337 | − | 0.819843i | ||||
\(339\) | −9.09183 | − | 15.7475i | −0.493800 | − | 0.855287i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.3226 | 1.64206 | ||||||||
\(342\) | −0.411596 | + | 12.0007i | −0.0222566 | + | 0.648923i | ||||
\(343\) | −19.6514 | −1.06107 | ||||||||
\(344\) | −4.64410 | − | 8.04382i | −0.250393 | − | 0.433693i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1085 | − | 19.2404i | 0.597194 | − | 1.03437i | ||||
\(347\) | −1.65128 | − | 2.86009i | −0.0886451 | − | 0.153538i | 0.818294 | − | 0.574801i | \(-0.194920\pi\) |
−0.906939 | + | 0.421263i | \(0.861587\pi\) | |||||||
\(348\) | −1.17018 | + | 2.02681i | −0.0627283 | + | 0.108649i | ||||
\(349\) | 17.8486 | 0.955416 | 0.477708 | − | 0.878519i | \(-0.341468\pi\) | ||||
0.477708 | + | 0.878519i | \(0.341468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.30543 | − | 7.45723i | 0.229807 | − | 0.398037i | ||||
\(352\) | −11.9204 | + | 20.6468i | −0.635360 | + | 1.10048i | ||||
\(353\) | 8.29523 | 0.441511 | 0.220755 | − | 0.975329i | \(-0.429148\pi\) | ||||
0.220755 | + | 0.975329i | \(0.429148\pi\) | |||||||
\(354\) | −20.8467 | −1.10799 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.28288 | + | 7.41817i | 0.226992 | + | 0.393162i | ||||
\(357\) | −8.45039 | + | 14.6365i | −0.447242 | + | 0.774646i | ||||
\(358\) | 11.8355 | + | 20.4997i | 0.625527 | + | 1.08344i | ||||
\(359\) | −4.17511 | − | 7.23150i | −0.220354 | − | 0.381664i | 0.734562 | − | 0.678542i | \(-0.237388\pi\) |
−0.954915 | + | 0.296878i | \(0.904055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9554 | − | 1.30178i | −0.997650 | − | 0.0685148i | ||||
\(362\) | 16.4501 | 0.864598 | ||||||||
\(363\) | −12.8254 | − | 22.2142i | −0.673156 | − | 1.16594i | ||||
\(364\) | −1.49682 | − | 2.59256i | −0.0784545 | − | 0.135887i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.1626 | + | 17.6022i | 0.531209 | + | 0.920082i | ||||
\(367\) | 7.20988 | − | 12.4879i | 0.376353 | − | 0.651862i | −0.614176 | − | 0.789169i | \(-0.710511\pi\) |
0.990528 | + | 0.137307i | \(0.0438448\pi\) | |||||||
\(368\) | −4.65080 | −0.242440 | ||||||||
\(369\) | 10.4517 | 0.544093 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.67438 | + | 4.63216i | −0.138847 | + | 0.240490i | ||||
\(372\) | −4.70974 | −0.244188 | ||||||||
\(373\) | 24.1157 | 1.24866 | 0.624332 | − | 0.781159i | \(-0.285371\pi\) | ||||
0.624332 | + | 0.781159i | \(0.285371\pi\) | |||||||
\(374\) | 28.6608 | − | 49.6420i | 1.48202 | − | 2.56693i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.16125 | + | 15.8678i | −0.472455 | + | 0.818317i | ||||
\(377\) | −2.08814 | − | 3.61676i | −0.107545 | − | 0.186273i | ||||
\(378\) | 10.9419 | + | 18.9519i | 0.562791 | + | 0.974783i | ||||
\(379\) | 16.6757 | 0.856571 | 0.428285 | − | 0.903644i | \(-0.359118\pi\) | ||||
0.428285 | + | 0.903644i | \(0.359118\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.09760 | −0.363621 | ||||||||
\(382\) | 10.8147 | + | 18.7316i | 0.553329 | + | 0.958395i | ||||
\(383\) | −5.43895 | − | 9.42053i | −0.277917 | − | 0.481367i | 0.692950 | − | 0.720986i | \(-0.256311\pi\) |
−0.970867 | + | 0.239619i | \(0.922977\pi\) | |||||||
\(384\) | −7.69935 | + | 13.3357i | −0.392906 | + | 0.680533i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0812 | − | 20.9252i | 0.614916 | − | 1.06507i | ||||
\(387\) | 7.51226 | 0.381870 | ||||||||
\(388\) | −3.12736 | −0.158767 | ||||||||
\(389\) | −18.2272 | + | 31.5704i | −0.924154 | + | 1.60068i | −0.131237 | + | 0.991351i | \(0.541895\pi\) |
−0.792917 | + | 0.609330i | \(0.791438\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62528 | 0.284482 | ||||||||
\(392\) | 2.18849 | 0.110535 | ||||||||
\(393\) | 8.62922 | − | 14.9463i | 0.435287 | − | 0.753939i | ||||
\(394\) | −20.8077 | − | 36.0399i | −1.04827 | − | 1.81566i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.67010 | − | 6.35680i | −0.184429 | − | 0.319441i | ||||
\(397\) | 4.29191 | + | 7.43380i | 0.215405 | + | 0.373092i | 0.953398 | − | 0.301717i | \(-0.0975597\pi\) |
−0.737993 | + | 0.674808i | \(0.764226\pi\) | |||||||
\(398\) | −3.75419 | −0.188181 | ||||||||
\(399\) | −10.8662 | + | 5.78635i | −0.543992 | + | 0.289680i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.52785 | + | 14.7707i | 0.425860 | + | 0.737612i | 0.996500 | − | 0.0835885i | \(-0.0266381\pi\) |
−0.570640 | + | 0.821200i | \(0.693305\pi\) | |||||||
\(402\) | 0.974478 | + | 1.68785i | 0.0486026 | + | 0.0841821i | ||||
\(403\) | 4.20216 | − | 7.27836i | 0.209325 | − | 0.362561i | ||||
\(404\) | 4.28903 | + | 7.42881i | 0.213387 | + | 0.369597i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.6137 | 0.526747 | ||||||||
\(407\) | −16.6533 | −0.825476 | ||||||||
\(408\) | 7.10039 | − | 12.2982i | 0.351522 | − | 0.608853i | ||||
\(409\) | 5.89702 | − | 10.2139i | 0.291589 | − | 0.505047i | −0.682597 | − | 0.730795i | \(-0.739149\pi\) |
0.974186 | + | 0.225749i | \(0.0724828\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.1222 | −0.992553 | ||||||||
\(412\) | 4.46205 | − | 7.72850i | 0.219829 | − | 0.380756i | ||||
\(413\) | 13.1489 | + | 22.7745i | 0.647015 | + | 1.12066i | ||||
\(414\) | 1.29480 | − | 2.24266i | 0.0636360 | − | 0.110221i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.30390 | + | 5.72252i | 0.161987 | + | 0.280570i | ||||
\(417\) | −7.77656 | −0.380820 | ||||||||
\(418\) | 36.8546 | − | 19.6253i | 1.80261 | − | 0.959907i | ||||
\(419\) | 1.14280 | 0.0558292 | 0.0279146 | − | 0.999610i | \(-0.491113\pi\) | ||||
0.0279146 | + | 0.999610i | \(0.491113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.75944 | − | 16.9039i | −0.475646 | − | 0.823843i | 0.523965 | − | 0.851740i | \(-0.324452\pi\) |
−0.999611 | + | 0.0278967i | \(0.991119\pi\) | |||||||
\(422\) | −18.4899 | + | 32.0254i | −0.900072 | + | 1.55897i | ||||
\(423\) | −7.40959 | − | 12.8338i | −0.360266 | − | 0.624000i | ||||
\(424\) | 2.24713 | − | 3.89215i | 0.109130 | − | 0.189019i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.0535 | 0.826245 | ||||||||
\(427\) | 12.8200 | − | 22.2049i | 0.620404 | − | 1.07457i | ||||
\(428\) | 6.90469 | − | 11.9593i | 0.333751 | − | 0.578073i | ||||
\(429\) | −10.6453 | −0.513960 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4392 | − | 31.9377i | 0.888187 | − | 1.53838i | 0.0461694 | − | 0.998934i | \(-0.485299\pi\) |
0.842017 | − | 0.539451i | \(-0.181368\pi\) | |||||||
\(432\) | −13.3546 | − | 23.1309i | −0.642526 | − | 1.11289i | ||||
\(433\) | 0.184467 | − | 0.319506i | 0.00886490 | − | 0.0153545i | −0.861559 | − | 0.507658i | \(-0.830512\pi\) |
0.870424 | + | 0.492303i | \(0.163845\pi\) | |||||||
\(434\) | 10.6795 | + | 18.4974i | 0.512630 | + | 0.887902i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.33501 | 0.207609 | ||||||||
\(437\) | 3.47628 | + | 2.16921i | 0.166293 | + | 0.103767i | ||||
\(438\) | 19.7872 | 0.945470 | ||||||||
\(439\) | 1.13220 | + | 1.96102i | 0.0540367 | + | 0.0935944i | 0.891778 | − | 0.452472i | \(-0.149458\pi\) |
−0.837742 | + | 0.546067i | \(0.816125\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.885022 | + | 1.53290i | −0.0421439 | + | 0.0729954i | ||||
\(442\) | −7.94373 | − | 13.7590i | −0.377845 | − | 0.654447i | ||||
\(443\) | −8.23137 | + | 14.2572i | −0.391084 | + | 0.677378i | −0.992593 | − | 0.121488i | \(-0.961233\pi\) |
0.601508 | + | 0.798866i | \(0.294567\pi\) | |||||||
\(444\) | 2.58661 | 0.122755 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.50248 | − | 14.7267i | 0.402604 | − | 0.697331i | ||||
\(447\) | −8.34609 | + | 14.4558i | −0.394756 | + | 0.683738i | ||||
\(448\) | 7.30329 | 0.345048 | ||||||||
\(449\) | 14.1613 | 0.668315 | 0.334158 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334158 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.1717 | − | 31.4742i | −0.855670 | − | 1.48206i | ||||
\(452\) | −6.04193 | + | 10.4649i | −0.284188 | + | 0.492229i | ||||
\(453\) | −7.37713 | − | 12.7776i | −0.346608 | − | 0.600342i | ||||
\(454\) | 3.45543 | + | 5.98498i | 0.162171 | + | 0.280889i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.13029 | − | 4.86195i | 0.427565 | − | 0.227682i | ||||
\(457\) | −1.22073 | −0.0571033 | −0.0285516 | − | 0.999592i | \(-0.509090\pi\) | ||||
−0.0285516 | + | 0.999592i | \(0.509090\pi\) | |||||||
\(458\) | −5.43712 | − | 9.41736i | −0.254060 | − | 0.440045i | ||||
\(459\) | 16.1528 | + | 27.9775i | 0.753950 | + | 1.30588i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.34580 | + | 7.52714i | 0.202404 | + | 0.350574i | 0.949303 | − | 0.314364i | \(-0.101791\pi\) |
−0.746898 | + | 0.664938i | \(0.768458\pi\) | |||||||
\(462\) | 13.5271 | − | 23.4296i | 0.629337 | − | 1.09004i | ||||
\(463\) | 19.7149 | 0.916229 | 0.458114 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458114 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(464\) | −12.9540 | −0.601375 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.28471 | − | 7.42133i | 0.198485 | − | 0.343787i | ||||
\(467\) | 11.4795 | 0.531207 | 0.265604 | − | 0.964082i | \(-0.414429\pi\) | ||||
0.265604 | + | 0.964082i | \(0.414429\pi\) | |||||||
\(468\) | −2.03443 | −0.0940418 | ||||||||
\(469\) | 1.22929 | − | 2.12919i | 0.0567633 | − | 0.0983170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.95726 | + | 3.39008i | −0.0901858 | + | 0.156206i | ||||
\(472\) | −11.0483 | − | 19.1362i | −0.508538 | − | 0.880814i | ||||
\(473\) | −13.0611 | − | 22.6225i | −0.600549 | − | 1.04018i | ||||
\(474\) | 14.6804 | 0.674293 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.2313 | 0.514787 | ||||||||
\(477\) | 1.81747 | + | 3.14796i | 0.0832164 | + | 0.144135i | ||||
\(478\) | −11.6486 | − | 20.1760i | −0.532796 | − | 0.922830i | ||||
\(479\) | −19.6316 | + | 34.0029i | −0.896989 | + | 1.55363i | −0.0656652 | + | 0.997842i | \(0.520917\pi\) |
−0.831324 | + | 0.555789i | \(0.812416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.30785 | + | 3.99731i | −0.105229 | + | 0.182262i | ||||
\(482\) | 25.3439 | 1.15438 | ||||||||
\(483\) | 2.65497 | 0.120805 | ||||||||
\(484\) | −8.52302 | + | 14.7623i | −0.387410 | + | 0.671014i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.4565 | 1.10937 | ||||||||
\(487\) | −31.5943 | −1.43168 | −0.715838 | − | 0.698266i | \(-0.753955\pi\) | ||||
−0.715838 | + | 0.698266i | \(0.753955\pi\) | |||||||
\(488\) | −10.7719 | + | 18.6576i | −0.487623 | + | 0.844588i | ||||
\(489\) | 0.178579 | + | 0.309309i | 0.00807564 | + | 0.0139874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.53187 | + | 9.58148i | 0.249650 | + | 0.432406i | 0.963429 | − | 0.267965i | \(-0.0863511\pi\) |
−0.713779 | + | 0.700371i | \(0.753018\pi\) | |||||||
\(492\) | 2.82244 | + | 4.88861i | 0.127245 | + | 0.220395i | ||||
\(493\) | 15.6683 | 0.705663 | ||||||||
\(494\) | 0.396685 | − | 11.5659i | 0.0178477 | − | 0.520376i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.0343 | − | 22.5761i | −0.585258 | − | 1.01370i | ||||
\(497\) | −10.7564 | − | 18.6306i | −0.482489 | − | 0.835696i | ||||
\(498\) | 3.00530 | − | 5.20533i | 0.134671 | − | 0.233256i | ||||
\(499\) | 10.1868 | + | 17.6440i | 0.456023 | + | 0.789854i | 0.998746 | − | 0.0500570i | \(-0.0159403\pi\) |
−0.542724 | + | 0.839911i | \(0.682607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.5431 | −0.739091 | ||||||||
\(502\) | −10.1747 | −0.454118 | ||||||||
\(503\) | −6.83622 | + | 11.8407i | −0.304812 | + | 0.527950i | −0.977219 | − | 0.212231i | \(-0.931927\pi\) |
0.672407 | + | 0.740181i | \(0.265260\pi\) | |||||||
\(504\) | −4.12338 | + | 7.14191i | −0.183670 | + | 0.318126i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00474 | −0.400310 | ||||||||
\(507\) | 6.06317 | − | 10.5017i | 0.269275 | − | 0.466398i | ||||
\(508\) | 2.35834 | + | 4.08476i | 0.104634 | + | 0.181232i | ||||
\(509\) | 3.86196 | − | 6.68912i | 0.171179 | − | 0.296490i | −0.767654 | − | 0.640865i | \(-0.778576\pi\) |
0.938832 | + | 0.344375i | \(0.111909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4807 | − | 21.6171i | −0.552112 | − | 0.956285i | ||||
\(512\) | 0.249240 | 0.0110150 | ||||||||
\(513\) | −0.806621 | + | 23.5182i | −0.0356132 | + | 1.03836i | ||||
\(514\) | −0.204211 | −0.00900736 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.02866 | + | 3.51374i | 0.0893067 | + | 0.154684i | ||||
\(517\) | −25.7651 | + | 44.6265i | −1.13315 | + | 1.96267i | ||||
\(518\) | −5.86521 | − | 10.1588i | −0.257703 | − | 0.446354i | ||||
\(519\) | 7.73971 | − | 13.4056i | 0.339736 | − | 0.588439i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.16876 | −0.0950151 | −0.0475075 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475075 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(522\) | 3.60645 | − | 6.24656i | 0.157850 | − | 0.273404i | ||||
\(523\) | −11.9466 | + | 20.6921i | −0.522389 | + | 0.904804i | 0.477272 | + | 0.878756i | \(0.341626\pi\) |
−0.999661 | + | 0.0260485i | \(0.991708\pi\) | |||||||
\(524\) | −11.4690 | −0.501026 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.37310 | + | 14.5026i | −0.365085 | + | 0.632345i | ||||
\(527\) | 15.7654 | + | 27.3065i | 0.686751 | + | 1.18949i | ||||
\(528\) | −16.5099 | + | 28.5959i | −0.718500 | + | 1.24448i | ||||
\(529\) | 11.0582 | + | 19.1533i | 0.480790 | + | 0.832752i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.8716 | 0.775562 | ||||||||
\(532\) | 6.94067 | + | 4.33101i | 0.300916 | + | 0.187773i | ||||
\(533\) | −10.0730 | −0.436312 | ||||||||
\(534\) | 10.7277 | + | 18.5809i | 0.464234 | + | 0.804076i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.03290 | + | 1.78904i | −0.0446147 | + | 0.0772749i | ||||
\(537\) | 8.24629 | + | 14.2830i | 0.355854 | + | 0.616356i | ||||
\(538\) | −4.75418 | + | 8.23448i | −0.204967 | + | 0.355013i | ||||
\(539\) | 6.15492 | 0.265111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.2275 | + | 36.7671i | −0.912641 | + | 1.58074i | −0.102323 | + | 0.994751i | \(0.532627\pi\) |
−0.810319 | + | 0.585990i | \(0.800706\pi\) | |||||||
\(542\) | 10.5792 | − | 18.3237i | 0.454415 | − | 0.787069i | ||||
\(543\) | 11.4614 | 0.491858 | ||||||||
\(544\) | −24.7907 | −1.06289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.74921 | − | 6.49383i | −0.160451 | − | 0.277910i | ||||
\(547\) | 6.01535 | − | 10.4189i | 0.257198 | − | 0.445480i | −0.708292 | − | 0.705919i | \(-0.750534\pi\) |
0.965490 | + | 0.260439i | \(0.0838674\pi\) | |||||||
\(548\) | 6.68604 | + | 11.5806i | 0.285614 | + | 0.494697i | ||||
\(549\) | −8.71231 | − | 15.0902i | −0.371833 | − | 0.644033i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.68259 | + | 6.04198i | 0.412492 | + | 0.257397i | ||||
\(552\) | −2.23082 | −0.0949500 | ||||||||
\(553\) | −9.25956 | − | 16.0380i | −0.393756 | − | 0.682006i | ||||
\(554\) | 14.6496 | + | 25.3739i | 0.622403 | + | 1.07803i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.58394 | + | 4.47551i | 0.109583 | + | 0.189804i | ||||
\(557\) | −4.37635 | + | 7.58006i | −0.185432 | + | 0.321178i | −0.943722 | − | 0.330740i | \(-0.892702\pi\) |
0.758290 | + | 0.651917i | \(0.226035\pi\) | |||||||
\(558\) | 14.5152 | 0.614479 | ||||||||
\(559\) | −7.24011 | −0.306224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.9692 | − | 34.5876i | 0.843099 | − | 1.46029i | ||||
\(562\) | −34.1238 | −1.43943 | ||||||||
\(563\) | 35.9707 | 1.51598 | 0.757991 | − | 0.652265i | \(-0.226181\pi\) | ||||
0.757991 | + | 0.652265i | \(0.226181\pi\) | |||||||
\(564\) | 4.00186 | − | 6.93143i | 0.168509 | − | 0.291866i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.86750 | + | 17.0910i | −0.414762 | + | 0.718389i | ||||
\(567\) | 1.57827 | + | 2.73365i | 0.0662812 | + | 0.114802i | ||||
\(568\) | 9.03798 | + | 15.6542i | 0.379225 | + | 0.656837i | ||||
\(569\) | −20.3125 | −0.851543 | −0.425772 | − | 0.904831i | \(-0.639997\pi\) | ||||
−0.425772 | + | 0.904831i | \(0.639997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1773 | 0.425906 | 0.212953 | − | 0.977062i | \(-0.431692\pi\) | ||||
0.212953 | + | 0.977062i | \(0.431692\pi\) | |||||||
\(572\) | 3.53714 | + | 6.12650i | 0.147895 | + | 0.256162i | ||||
\(573\) | 7.53505 | + | 13.0511i | 0.314781 | + | 0.545217i | ||||
\(574\) | 12.7999 | − | 22.1701i | 0.534258 | − | 0.925362i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.48161 | − | 4.29827i | 0.103400 | − | 0.179095i | ||||
\(577\) | 32.7441 | 1.36316 | 0.681578 | − | 0.731745i | \(-0.261294\pi\) | ||||
0.681578 | + | 0.731745i | \(0.261294\pi\) | |||||||
\(578\) | 31.3083 | 1.30225 | ||||||||
\(579\) | 8.41745 | − | 14.5794i | 0.349817 | − | 0.605901i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.58228 | −0.314566 | ||||||||
\(582\) | −7.83337 | −0.324703 | ||||||||
\(583\) | 6.31984 | − | 10.9463i | 0.261741 | − | 0.453349i | ||||
\(584\) | 10.4868 | + | 18.1637i | 0.433947 | + | 0.751618i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.7913 | − | 36.0117i | −0.858883 | − | 1.48763i | ||||
\(587\) | 4.38663 | + | 7.59786i | 0.181056 | + | 0.313597i | 0.942240 | − | 0.334938i | \(-0.108715\pi\) |
−0.761185 | + | 0.648535i | \(0.775382\pi\) | |||||||
\(588\) | −0.955987 | −0.0394243 | ||||||||
\(589\) | −0.787274 | + | 22.9541i | −0.0324390 | + | 0.945808i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4975 | − | 25.1105i | −0.596349 | − | 1.03291i | ||||
\(592\) | 7.15852 | + | 12.3989i | 0.294213 | + | 0.509592i | ||||
\(593\) | −16.1603 | + | 27.9905i | −0.663625 | + | 1.14943i | 0.316031 | + | 0.948749i | \(0.397650\pi\) |
−0.979656 | + | 0.200684i | \(0.935684\pi\) | |||||||
\(594\) | −25.8569 | − | 44.7855i | −1.06092 | − | 1.83757i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.0927 | 0.454375 | ||||||||
\(597\) | −2.61570 | −0.107053 | ||||||||
\(598\) | −1.24789 | + | 2.16141i | −0.0510301 | + | 0.0883868i | ||||
\(599\) | 9.77520 | − | 16.9311i | 0.399404 | − | 0.691787i | −0.594249 | − | 0.804281i | \(-0.702551\pi\) |
0.993652 | + | 0.112494i | \(0.0358839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.401837 | −0.0163913 | −0.00819564 | − | 0.999966i | \(-0.502609\pi\) | ||||
−0.00819564 | + | 0.999966i | \(0.502609\pi\) | |||||||
\(602\) | 9.20008 | − | 15.9350i | 0.374967 | − | 0.649462i | ||||
\(603\) | −0.835409 | − | 1.44697i | −0.0340205 | − | 0.0589252i | ||||
\(604\) | −4.90243 | + | 8.49126i | −0.199477 | + | 0.345505i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.7431 | + | 18.6076i | 0.436409 | + | 0.755882i | ||||
\(607\) | −13.4453 | −0.545727 | −0.272863 | − | 0.962053i | \(-0.587971\pi\) | ||||
−0.272863 | + | 0.962053i | \(0.587971\pi\) | |||||||
\(608\) | −15.3200 | − | 9.55976i | −0.621309 | − | 0.387700i | ||||
\(609\) | 7.39497 | 0.299659 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.14115 | + | 12.3688i | 0.288900 | + | 0.500390i | ||||
\(612\) | 3.81633 | − | 6.61008i | 0.154266 | − | 0.267196i | ||||
\(613\) | −10.3527 | − | 17.9313i | −0.418140 | − | 0.724239i | 0.577613 | − | 0.816311i | \(-0.303984\pi\) |
−0.995752 | + | 0.0920716i | \(0.970651\pi\) | |||||||
\(614\) | 14.0820 | − | 24.3907i | 0.568303 | − | 0.984330i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6762 | 1.15540 | ||||||||
\(617\) | −4.63936 | + | 8.03560i | −0.186773 | + | 0.323501i | −0.944173 | − | 0.329451i | \(-0.893136\pi\) |
0.757399 | + | 0.652952i | \(0.226470\pi\) | |||||||
\(618\) | 11.1765 | − | 19.3583i | 0.449585 | − | 0.778703i | ||||
\(619\) | −2.89129 | −0.116211 | −0.0581053 | − | 0.998310i | \(-0.518506\pi\) | ||||
−0.0581053 | + | 0.998310i | \(0.518506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.53747 | − | 4.39503i | 0.101825 | − | 0.176366i | ||||
\(622\) | 12.6616 | + | 21.9306i | 0.507686 | + | 0.879338i | ||||
\(623\) | 13.5329 | − | 23.4396i | 0.542183 | − | 0.939088i | ||||
\(624\) | 4.57593 | + | 7.92574i | 0.183184 | + | 0.317284i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −41.4926 | −1.65838 | ||||||||
\(627\) | 25.6781 | − | 13.6738i | 1.02548 | − | 0.546078i | ||||
\(628\) | 2.60138 | 0.103806 | ||||||||
\(629\) | −8.65844 | − | 14.9969i | −0.345234 | − | 0.597964i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2270 | + | 26.3740i | −0.606178 | + | 1.04993i | 0.385686 | + | 0.922630i | \(0.373965\pi\) |
−0.991864 | + | 0.127301i | \(0.959369\pi\) | |||||||
\(632\) | 7.78029 | + | 13.4759i | 0.309483 | + | 0.536041i | ||||
\(633\) | −12.8826 | + | 22.3134i | −0.512039 | + | 0.886877i | ||||
\(634\) | 41.9972 | 1.66792 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.981604 | + | 1.70019i | −0.0389231 | + | 0.0674168i | ||||
\(637\) | 0.852959 | − | 1.47737i | 0.0337955 | − | 0.0585355i | ||||
\(638\) | −25.0812 | −0.992975 | ||||||||
\(639\) | −14.6198 | −0.578349 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0369 | + | 17.3845i | 0.396434 | + | 0.686645i | 0.993283 | − | 0.115709i | \(-0.0369141\pi\) |
−0.596849 | + | 0.802354i | \(0.703581\pi\) | |||||||
\(642\) | 17.2948 | − | 29.9554i | 0.682571 | − | 1.18225i | ||||
\(643\) | −1.04457 | − | 1.80924i | −0.0411937 | − | 0.0713496i | 0.844693 | − | 0.535250i | \(-0.179783\pi\) |
−0.885887 | + | 0.463901i | \(0.846449\pi\) | |||||||
\(644\) | −0.882172 | − | 1.52797i | −0.0347625 | − | 0.0602103i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.8347 | + | 22.9850i | 1.44924 | + | 0.904334i | ||||
\(647\) | 2.10623 | 0.0828043 | 0.0414021 | − | 0.999143i | \(-0.486818\pi\) | ||||
0.0414021 | + | 0.999143i | \(0.486818\pi\) | |||||||
\(648\) | −1.32613 | − | 2.29693i | −0.0520954 | − | 0.0902319i | ||||
\(649\) | −31.0722 | − | 53.8187i | −1.21969 | − | 2.11257i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.44081 | + | 12.8879i | 0.291628 | + | 0.505115i | ||||
\(652\) | 0.118674 | − | 0.205549i | 0.00464763 | − | 0.00804994i | ||||
\(653\) | −1.83067 | −0.0716395 | −0.0358197 | − | 0.999358i | \(-0.511404\pi\) | ||||
−0.0358197 | + | 0.999358i | \(0.511404\pi\) | |||||||
\(654\) | 10.8583 | 0.424593 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.6223 | + | 27.0587i | −0.609950 | + | 1.05646i | ||||
\(657\) | −16.9634 | −0.661804 | ||||||||
\(658\) | −36.2973 | −1.41502 | ||||||||
\(659\) | −12.0268 | + | 20.8310i | −0.468497 | + | 0.811460i | −0.999352 | − | 0.0360024i | \(-0.988538\pi\) |
0.530855 | + | 0.847463i | \(0.321871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.72110 | − | 15.1054i | 0.339211 | − | 0.587531i | −0.645073 | − | 0.764121i | \(-0.723173\pi\) |
0.984285 | + | 0.176589i | \(0.0565065\pi\) | |||||||
\(662\) | 16.8172 | + | 29.1282i | 0.653617 | + | 1.13210i | ||||
\(663\) | −5.53472 | − | 9.58642i | −0.214951 | − | 0.372306i | ||||
\(664\) | 6.37097 | 0.247241 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.97184 | −0.308902 | ||||||||
\(667\) | −1.23068 | − | 2.13159i | −0.0476519 | − | 0.0825356i | ||||
\(668\) | 5.49682 | + | 9.52077i | 0.212678 | + | 0.368370i | ||||
\(669\) | 5.92402 | − | 10.2607i | 0.229036 | − | 0.396702i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.2951 | + | 52.4726i | −1.16953 | + | 2.02568i | ||||
\(672\) | −11.7005 | −0.451357 | ||||||||
\(673\) | −47.5187 | −1.83171 | −0.915856 | − | 0.401506i | \(-0.868487\pi\) | ||||
−0.915856 | + | 0.401506i | \(0.868487\pi\) | |||||||
\(674\) | −26.4868 | + | 45.8765i | −1.02023 | + | 1.76709i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.05850 | −0.309942 | ||||||||
\(677\) | −14.5531 | −0.559321 | −0.279661 | − | 0.960099i | \(-0.590222\pi\) | ||||
−0.279661 | + | 0.960099i | \(0.590222\pi\) | |||||||
\(678\) | −15.1338 | + | 26.2124i | −0.581208 | + | 1.00668i | ||||
\(679\) | 4.94084 | + | 8.55778i | 0.189612 | + | 0.328418i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.40754 | + | 4.16998i | 0.0922570 | + | 0.159794i | ||||
\(682\) | −25.2367 | − | 43.7112i | −0.966363 | − | 1.67379i | ||||
\(683\) | −3.33714 | −0.127692 | −0.0638460 | − | 0.997960i | \(-0.520337\pi\) | ||||
−0.0638460 | + | 0.997960i | \(0.520337\pi\) | |||||||
\(684\) | 4.90736 | − | 2.61321i | 0.187638 | − | 0.0999185i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.3553 | + | 28.3282i | 0.624448 | + | 1.08158i | ||||
\(687\) | −3.78826 | − | 6.56146i | −0.144531 | − | 0.250335i | ||||
\(688\) | −11.2287 | + | 19.4487i | −0.428092 | + | 0.741476i | ||||
\(689\) | −1.75163 | − | 3.03391i | −0.0667318 | − | 0.115583i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3318 | −0.735415 | −0.367708 | − | 0.929941i | \(-0.619857\pi\) | ||||
−0.367708 | + | 0.929941i | \(0.619857\pi\) | |||||||
\(692\) | −10.2868 | −0.391044 | ||||||||
\(693\) | −11.5966 | + | 20.0859i | −0.440519 | + | 0.763001i | ||||
\(694\) | −2.74862 | + | 4.76075i | −0.104336 | + | 0.180716i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.21358 | −0.235525 | ||||||||
\(697\) | 18.8957 | − | 32.7283i | 0.715725 | − | 1.23967i | ||||
\(698\) | −14.8549 | − | 25.7295i | −0.562268 | − | 0.973876i | ||||
\(699\) | 2.98533 | − | 5.17074i | 0.112916 | − | 0.195575i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.96892 | − | 8.60643i | −0.187674 | − | 0.325060i | 0.756801 | − | 0.653646i | \(-0.226761\pi\) |
−0.944474 | + | 0.328586i | \(0.893428\pi\) | |||||||
\(702\) | −14.3332 | −0.540971 | ||||||||
\(703\) | 0.432375 | − | 12.6065i | 0.0163073 | − | 0.475464i | ||||
\(704\) | −17.2584 | −0.650452 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.90389 | − | 11.9579i | −0.259831 | − | 0.450041i | ||||
\(707\) | 13.5523 | − | 23.4732i | 0.509686 | − | 0.882801i | ||||
\(708\) | 4.82616 | + | 8.35916i | 0.181378 | + | 0.314157i | ||||
\(709\) | −18.6059 | + | 32.2264i | −0.698760 | + | 1.21029i | 0.270136 | + | 0.962822i | \(0.412931\pi\) |
−0.968897 | + | 0.247466i | \(0.920402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.5853 | −0.471987 | ||||||||
\(712\) | −11.3709 | + | 19.6950i | −0.426143 | + | 0.738101i | ||||
\(713\) | 2.47661 | − | 4.28961i | 0.0927497 | − | 0.160647i | ||||
\(714\) | 28.1321 | 1.05282 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.48003 | − | 9.49169i | 0.204798 | − | 0.354721i | ||||
\(717\) | −8.11608 | − | 14.0575i | −0.303100 | − | 0.524985i | ||||
\(718\) | −6.94966 | + | 12.0372i | −0.259359 | + | 0.449223i | ||||
\(719\) | 1.32109 | + | 2.28819i | 0.0492683 | + | 0.0853351i | 0.889608 | − | 0.456725i | \(-0.150978\pi\) |
−0.840340 | + | 0.542060i | \(0.817644\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.1980 | −1.05015 | ||||||||
\(722\) | 13.8995 | + | 28.4083i | 0.517284 | + | 1.05725i | ||||
\(723\) | 17.6581 | 0.656711 | ||||||||
\(724\) | −3.80832 | − | 6.59621i | −0.141535 | − | 0.245146i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.3484 | + | 36.9765i | −0.792313 | + | 1.37233i | ||||
\(727\) | −5.08653 | − | 8.81013i | −0.188649 | − | 0.326750i | 0.756151 | − | 0.654397i | \(-0.227077\pi\) |
−0.944800 | + | 0.327647i | \(0.893744\pi\) | |||||||
\(728\) | 3.97400 | − | 6.88317i | 0.147286 | − | 0.255107i | ||||
\(729\) | 20.9284 | 0.775126 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5815 | − | 23.5238i | 0.502329 | − | 0.870060i | ||||
\(732\) | 4.70546 | − | 8.15009i | 0.173919 | − | 0.301236i | ||||
\(733\) | −14.8222 | −0.547472 | −0.273736 | − | 0.961805i | \(-0.588259\pi\) | ||||
−0.273736 | + | 0.961805i | \(0.588259\pi\) | |||||||
\(734\) | −24.0023 | −0.885942 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.94720 | + | 3.37266i | 0.0717749 | + | 0.124318i | ||||
\(737\) | −2.90494 | + | 5.03151i | −0.107005 | + | 0.185338i | ||||
\(738\) | −8.69865 | − | 15.0665i | −0.320202 | − | 0.554605i | ||||
\(739\) | −17.7433 | − | 30.7323i | −0.652697 | − | 1.13050i | −0.982466 | − | 0.186443i | \(-0.940304\pi\) |
0.329769 | − | 0.944062i | \(-0.393029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.276386 | − | 8.05845i | 0.0101533 | − | 0.296035i | ||||
\(742\) | 8.90325 | 0.326849 | ||||||||
\(743\) | −4.36941 | − | 7.56804i | −0.160298 | − | 0.277645i | 0.774677 | − | 0.632357i | \(-0.217912\pi\) |
−0.934976 | + | 0.354712i | \(0.884579\pi\) | |||||||
\(744\) | −6.25210 | − | 10.8289i | −0.229213 | − | 0.397009i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.0708 | − | 34.7637i | −0.734846 | − | 1.27279i | ||||
\(747\) | −2.57641 | + | 4.46247i | −0.0942658 | + | 0.163273i | ||||
\(748\) | −26.5408 | −0.970428 | ||||||||
\(749\) | −43.6342 | −1.59436 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.54957 | + | 11.3442i | −0.238997 | + | 0.413955i | −0.960427 | − | 0.278533i | \(-0.910152\pi\) |
0.721430 | + | 0.692488i | \(0.243485\pi\) | |||||||
\(752\) | 44.3011 | 1.61549 | ||||||||
\(753\) | −7.08911 | −0.258342 | ||||||||
\(754\) | −3.47580 | + | 6.02026i | −0.126581 | + | 0.219245i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.06627 | − | 8.77504i | 0.184258 | − | 0.319145i | ||||
\(757\) | −8.21901 | − | 14.2357i | −0.298725 | − | 0.517407i | 0.677119 | − | 0.735873i | \(-0.263228\pi\) |
−0.975845 | + | 0.218466i | \(0.929895\pi\) | |||||||
\(758\) | −13.8787 | − | 24.0386i | −0.504097 | − | 0.873121i | ||||
\(759\) | −6.27397 | −0.227731 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3918 | 0.594203 | 0.297101 | − | 0.954846i | \(-0.403980\pi\) | ||||
0.297101 | + | 0.954846i | \(0.403980\pi\) | |||||||
\(762\) | 5.90714 | + | 10.2315i | 0.213993 | + | 0.370647i | ||||
\(763\) | −6.84879 | − | 11.8625i | −0.247943 | − | 0.429450i | ||||
\(764\) | 5.00738 | − | 8.67304i | 0.181161 | − | 0.313780i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.05337 | + | 15.6809i | −0.327112 | + | 0.566574i | ||||
\(767\) | −17.2242 | −0.621929 | ||||||||
\(768\) | 18.6756 | 0.673899 | ||||||||
\(769\) | 25.0210 | − | 43.3377i | 0.902282 | − | 1.56280i | 0.0777564 | − | 0.996972i | \(-0.475224\pi\) |
0.824525 | − | 0.565825i | \(-0.191442\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.142282 | −0.00512416 | ||||||||
\(772\) | −11.1875 | −0.402649 | ||||||||
\(773\) | 24.3436 | − | 42.1644i | 0.875580 | − | 1.51655i | 0.0194356 | − | 0.999811i | \(-0.493813\pi\) |
0.856144 | − | 0.516737i | \(-0.172854\pi\) | |||||||
\(774\) | −6.25225 | − | 10.8292i | −0.224732 | − | 0.389248i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.15151 | − | 7.19063i | −0.149031 | − | 0.258129i | ||||
\(777\) | −4.08653 | − | 7.07808i | −0.146603 | − | 0.253925i | ||||
\(778\) | 60.6799 | 2.17548 | ||||||||
\(779\) | 24.2977 | − | 12.9387i | 0.870555 | − | 0.463577i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4185 | + | 44.0261i | 0.909544 | + | 1.57538i | ||||
\(782\) | −4.68176 | − | 8.10905i | −0.167419 | − | 0.289979i | ||||
\(783\) | 7.06771 | − | 12.2416i | 0.252579 | − | 0.437480i | ||||
\(784\) | −2.64572 | − | 4.58252i | −0.0944900 | − | 0.163662i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −28.7275 | −1.02467 | ||||||||
\(787\) | −6.51678 | −0.232298 | −0.116149 | − | 0.993232i | \(-0.537055\pi\) | ||||
−0.116149 | + | 0.993232i | \(0.537055\pi\) | |||||||
\(788\) | −9.63426 | + | 16.6870i | −0.343206 | + | 0.594451i | ||||
\(789\) | −5.83388 | + | 10.1046i | −0.207692 | + | 0.359732i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.1820 | 1.35760 | ||||||||
\(792\) | 9.74399 | − | 16.8771i | 0.346238 | − | 0.599701i | ||||
\(793\) | 8.39668 | + | 14.5435i | 0.298175 | + | 0.516454i | ||||
\(794\) | 7.14407 | − | 12.3739i | 0.253534 | − | 0.439133i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.869124 | + | 1.50537i | 0.0308053 | + | 0.0533563i | ||||
\(797\) | −38.3796 | −1.35947 | −0.679737 | − | 0.733456i | \(-0.737906\pi\) | ||||
−0.679737 | + | 0.733456i | \(0.737906\pi\) | |||||||
\(798\) | 17.3849 | + | 10.8483i | 0.615419 | + | 0.384024i | ||||
\(799\) | −53.5834 | −1.89565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.19675 | − | 15.9292i | −0.324951 | − | 0.562832i | ||||
\(802\) | 14.1950 | − | 24.5864i | 0.501242 | − | 0.868177i | ||||
\(803\) | 29.4931 | + | 51.0836i | 1.04079 | + | 1.80270i | ||||
\(804\) | 0.451198 | − | 0.781498i | 0.0159125 | − | 0.0275613i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.9894 | −0.492755 | ||||||||
\(807\) | −3.31243 | + | 5.73729i | −0.116603 | + | 0.201962i | ||||
\(808\) | −11.3872 | + | 19.7232i | −0.400601 | + | 0.693861i | ||||
\(809\) | 25.1409 | 0.883906 | 0.441953 | − | 0.897038i | \(-0.354286\pi\) | ||||
0.441953 | + | 0.897038i | \(0.354286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.5053 | − | 40.7124i | 0.825383 | − | 1.42961i | −0.0762426 | − | 0.997089i | \(-0.524292\pi\) |
0.901626 | − | 0.432517i | \(-0.142374\pi\) | |||||||
\(812\) | −2.45714 | − | 4.25590i | −0.0862289 | − | 0.149353i | ||||
\(813\) | 7.37094 | − | 12.7668i | 0.258510 | − | 0.447753i | ||||
\(814\) | 13.8601 | + | 24.0064i | 0.485797 | + | 0.841425i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −34.3354 | −1.20198 | ||||||||
\(817\) | 17.4642 | − | 9.29984i | 0.610996 | − | 0.325360i | ||||
\(818\) | −19.6317 | −0.686406 | ||||||||
\(819\) | 3.21416 | + | 5.56708i | 0.112312 | + | 0.194530i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.91021 | − | 17.1650i | 0.345869 | − | 0.599062i | −0.639642 | − | 0.768673i | \(-0.720918\pi\) |
0.985511 | + | 0.169610i | \(0.0542509\pi\) | |||||||
\(822\) | 16.7471 | + | 29.0069i | 0.584123 | + | 1.01173i | ||||
\(823\) | −19.6084 | + | 33.9627i | −0.683505 | + | 1.18387i | 0.290399 | + | 0.956906i | \(0.406212\pi\) |
−0.973904 | + | 0.226960i | \(0.927121\pi\) | |||||||
\(824\) | 23.6932 | 0.825391 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.8869 | − | 37.9092i | 0.761543 | − | 1.31903i | ||||
\(827\) | −5.92176 | + | 10.2568i | −0.205920 | + | 0.356663i | −0.950425 | − | 0.310953i | \(-0.899352\pi\) |
0.744506 | + | 0.667616i | \(0.232685\pi\) | |||||||
\(828\) | −1.19903 | −0.0416690 | ||||||||
\(829\) | 46.9321 | 1.63002 | 0.815010 | − | 0.579447i | \(-0.196731\pi\) | ||||
0.815010 | + | 0.579447i | \(0.196731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2070 | + | 17.6790i | 0.354076 | + | 0.613278i | ||||
\(832\) | −2.39170 | + | 4.14255i | −0.0829174 | + | 0.143617i | ||||
\(833\) | 3.20008 | + | 5.54270i | 0.110876 | + | 0.192043i | ||||
\(834\) | 6.47222 | + | 11.2102i | 0.224115 | + | 0.388178i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.4015 | − | 10.2346i | −0.567259 | − | 0.353972i | ||||
\(837\) | 28.4461 | 0.983240 | ||||||||
\(838\) | −0.951117 | − | 1.64738i | −0.0328558 | − | 0.0569079i | ||||
\(839\) | 26.5669 | + | 46.0153i | 0.917192 | + | 1.58862i | 0.803660 | + | 0.595089i | \(0.202883\pi\) |
0.113532 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0722 | + | 19.1775i | 0.381799 | + | 0.661294i | ||||
\(842\) | −16.2450 | + | 28.1372i | −0.559841 | + | 0.969673i | ||||
\(843\) | −23.7755 | −0.818870 | ||||||||
\(844\) | 17.1222 | 0.589370 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.3336 | + | 21.3624i | −0.424038 | + | 0.734455i | ||||
\(847\) | 53.8613 | 1.85070 | ||||||||
\(848\) | −10.8665 | −0.373156 | ||||||||
\(849\) | −6.87509 | + | 11.9080i | −0.235952 | + | 0.408682i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.36017 | + | 2.35588i | −0.0466259 | + | 0.0807584i | ||||
\(852\) | −3.94802 | − | 6.83816i | −0.135257 | − | 0.234272i | ||||
\(853\) | 21.1499 | + | 36.6327i | 0.724159 | + | 1.25428i | 0.959319 | + | 0.282324i | \(0.0911052\pi\) |
−0.235160 | + | 0.971957i | \(0.575562\pi\) | |||||||
\(854\) | −42.6790 | −1.46045 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.6634 | 1.25313 | ||||||||
\(857\) | 11.7692 | + | 20.3849i | 0.402028 | + | 0.696333i | 0.993971 | − | 0.109647i | \(-0.0349720\pi\) |
−0.591942 | + | 0.805980i | \(0.701639\pi\) | |||||||
\(858\) | 8.85979 | + | 15.3456i | 0.302468 | + | 0.523890i | ||||
\(859\) | −4.74062 | + | 8.21099i | −0.161748 | + | 0.280156i | −0.935496 | − | 0.353338i | \(-0.885046\pi\) |
0.773748 | + | 0.633494i | \(0.218380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.91821 | − | 15.4468i | 0.303932 | − | 0.526425i | ||||
\(862\) | −61.3859 | −2.09081 | ||||||||
\(863\) | −22.8204 | −0.776816 | −0.388408 | − | 0.921487i | \(-0.626975\pi\) | ||||
−0.388408 | + | 0.921487i | \(0.626975\pi\) | |||||||
\(864\) | −11.1827 | + | 19.3690i | −0.380443 | + | 0.658947i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.614106 | −0.0208682 | ||||||||
\(867\) | 21.8138 | 0.740834 | ||||||||
\(868\) | 4.94475 | − | 8.56456i | 0.167836 | − | 0.290700i | ||||
\(869\) | 21.8813 | + | 37.8996i | 0.742273 | + | 1.28565i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.805144 | + | 1.39455i | 0.0272813 | + | 0.0472525i | ||||
\(872\) | 5.75466 | + | 9.96736i | 0.194877 | + | 0.337537i | ||||
\(873\) | 6.71546 | 0.227284 | ||||||||
\(874\) | 0.233792 | − | 6.81656i | 0.00790814 | − | 0.230574i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.58089 | − | 7.93434i | −0.154774 | − | 0.268077i | ||||
\(877\) | −12.6471 | − | 21.9054i | −0.427062 | − | 0.739693i | 0.569549 | − | 0.821958i | \(-0.307118\pi\) |
−0.996611 | + | 0.0822647i | \(0.973785\pi\) | |||||||
\(878\) | 1.88459 | − | 3.26421i | 0.0636018 | − | 0.110162i | ||||
\(879\) | −14.4862 | − | 25.0908i | −0.488606 | − | 0.846291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.2871 | −1.12147 | −0.560736 | − | 0.827995i | \(-0.689482\pi\) | ||||
−0.560736 | + | 0.827995i | \(0.689482\pi\) | |||||||
\(882\) | 2.94632 | 0.0992077 | ||||||||
\(883\) | −7.65544 | + | 13.2596i | −0.257626 | + | 0.446222i | −0.965606 | − | 0.260011i | \(-0.916274\pi\) |
0.707979 | + | 0.706233i | \(0.249607\pi\) | |||||||
\(884\) | −3.67807 | + | 6.37061i | −0.123707 | + | 0.214267i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.4030 | 0.920621 | ||||||||
\(887\) | 21.6027 | − | 37.4171i | 0.725349 | − | 1.25634i | −0.233481 | − | 0.972361i | \(-0.575012\pi\) |
0.958830 | − | 0.283980i | \(-0.0916550\pi\) | |||||||
\(888\) | 3.43368 | + | 5.94731i | 0.115227 | + | 0.199579i | ||||
\(889\) | 7.45177 | − | 12.9068i | 0.249924 | − | 0.432882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.72962 | − | 6.45990i | −0.124947 | − | 0.216415i | ||||
\(892\) | −7.87356 | −0.263626 | ||||||||
\(893\) | −33.1132 | − | 20.6628i | −1.10809 | − | 0.691453i | ||||
\(894\) | 27.7849 | 0.929265 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.1671 | − | 28.0022i | −0.540104 | − | 0.935488i | ||||
\(897\) | −0.869457 | + | 1.50594i | −0.0290303 | + | 0.0502820i | ||||
\(898\) | −11.7861 | − | 20.4141i | −0.393307 | − | 0.681228i | ||||
\(899\) | 6.89818 | − | 11.9480i | 0.230067 | − | 0.398488i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1433 | 0.437867 | ||||||||
\(902\) | −30.2475 | + | 52.3903i | −1.00713 | + | 1.74441i | ||||
\(903\) | 6.41007 | − | 11.1026i | 0.213314 | − | 0.369470i | ||||
\(904\) | −32.0822 | −1.06704 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.2796 | + | 21.2688i | −0.407961 | + | 0.706609i | ||||
\(907\) | 7.16392 | + | 12.4083i | 0.237874 | + | 0.412010i | 0.960104 | − | 0.279643i | \(-0.0902161\pi\) |
−0.722230 | + | 0.691653i | \(0.756883\pi\) | |||||||
\(908\) | 1.59992 | − | 2.77114i | 0.0530951 | − | 0.0919634i | ||||
\(909\) | −9.20994 | − | 15.9521i | −0.305475 | − | 0.529097i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.61162 | −0.152790 | −0.0763949 | − | 0.997078i | \(-0.524341\pi\) | ||||
−0.0763949 | + | 0.997078i | \(0.524341\pi\) | |||||||
\(912\) | −21.2184 | − | 13.2404i | −0.702610 | − | 0.438432i | ||||
\(913\) | 17.9177 | 0.592990 | ||||||||
\(914\) | 1.01598 | + | 1.75973i | 0.0336056 | + | 0.0582066i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.51747 | + | 4.36038i | −0.0831795 | + | 0.144071i | ||||
\(917\) | 18.1196 | + | 31.3841i | 0.598363 | + | 1.03640i | ||||
\(918\) | 26.8871 | − | 46.5699i | 0.887407 | − | 1.53703i | ||||
\(919\) | 26.4921 | 0.873892 | 0.436946 | − | 0.899488i | \(-0.356060\pi\) | ||||
0.436946 | + | 0.899488i | \(0.356060\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.81149 | − | 16.9940i | 0.323300 | − | 0.559972i | ||||
\(922\) | 7.23378 | − | 12.5293i | 0.238232 | − | 0.412630i | ||||
\(923\) | 14.0901 | 0.463782 | ||||||||
\(924\) | −12.5265 | −0.412091 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.4082 | − | 28.4198i | −0.539206 | − | 0.933932i | ||||
\(927\) | −9.58148 | + | 16.5956i | −0.314697 | + | 0.545072i | ||||
\(928\) | 5.42362 | + | 9.39398i | 0.178039 | + | 0.308372i | ||||
\(929\) | 2.37863 | + | 4.11990i | 0.0780402 | + | 0.135170i | 0.902404 | − | 0.430890i | \(-0.141800\pi\) |
−0.824364 | + | 0.566060i | \(0.808467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.159802 | + | 4.65925i | −0.00523729 | + | 0.152701i | ||||
\(932\) | −3.96777 | −0.129969 | ||||||||
\(933\) | 8.82188 | + | 15.2799i | 0.288815 | + | 0.500243i | ||||
\(934\) | −9.55406 | − | 16.5481i | −0.312619 | − | 0.541471i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.70068 | − | 4.67771i | −0.0882744 | − | 0.152896i | ||||
\(937\) | −5.96833 | + | 10.3375i | −0.194977 | + | 0.337710i | −0.946893 | − | 0.321549i | \(-0.895797\pi\) |
0.751916 | + | 0.659259i | \(0.229130\pi\) | |||||||
\(938\) | −4.09242 | −0.133622 | ||||||||
\(939\) | −28.9096 | −0.943429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.99715 | − | 15.5835i | 0.293299 | − | 0.508008i | −0.681289 | − | 0.732015i | \(-0.738580\pi\) |
0.974588 | + | 0.224006i | \(0.0719136\pi\) | |||||||
\(942\) | 6.51590 | 0.212299 | ||||||||
\(943\) | −5.93670 | −0.193326 | ||||||||
\(944\) | −26.7131 | + | 46.2684i | −0.869437 | + | 1.50591i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.7408 | + | 37.6561i | −0.706853 | + | 1.22431i | ||||
\(947\) | −12.6096 | − | 21.8404i | −0.409755 | − | 0.709717i | 0.585107 | − | 0.810956i | \(-0.301053\pi\) |
−0.994862 | + | 0.101239i | \(0.967719\pi\) | |||||||
\(948\) | −3.39862 | − | 5.88659i | −0.110382 | − | 0.191188i | ||||
\(949\) | 16.3488 | 0.530705 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.2611 | 0.948858 | ||||||||
\(952\) | 14.9094 | + | 25.8238i | 0.483216 | + | 0.836955i | ||||
\(953\) | 21.1589 | + | 36.6484i | 0.685405 | + | 1.18716i | 0.973309 | + | 0.229498i | \(0.0737083\pi\) |
−0.287904 | + | 0.957659i | \(0.592958\pi\) | |||||||
\(954\) | 3.02527 | − | 5.23991i | 0.0979466 | − | 0.169648i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.39350 | + | 9.34181i | −0.174438 | + | 0.302136i | ||||
\(957\) | −17.4751 | −0.564890 | ||||||||
\(958\) | 65.3552 | 2.11153 | ||||||||
\(959\) | 21.1263 | − | 36.5918i | 0.682203 | − | 1.18161i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.23623 | −0.104395 | ||||||||
\(962\) | 7.68304 | 0.247711 | ||||||||
\(963\) | −14.8266 | + | 25.6805i | −0.477781 | + | 0.827542i | ||||
\(964\) | −5.86730 | − | 10.1625i | −0.188973 | − | 0.327311i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.20966 | − | 3.82724i | −0.0710945 | − | 0.123139i | ||||
\(967\) | −6.84820 | − | 11.8614i | −0.220223 | − | 0.381438i | 0.734652 | − | 0.678444i | \(-0.237345\pi\) |
−0.954876 | + | 0.297006i | \(0.904012\pi\) | |||||||
\(968\) | −45.2567 | −1.45460 | ||||||||
\(969\) | 25.6642 | + | 16.0146i | 0.824454 | + | 0.514463i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.2906 | + | 33.4123i | 0.619065 | + | 1.07225i | 0.989657 | + | 0.143457i | \(0.0458217\pi\) |
−0.370591 | + | 0.928796i | \(0.620845\pi\) | |||||||
\(972\) | −5.66187 | − | 9.80665i | −0.181605 | − | 0.314548i | ||||
\(973\) | 8.16461 | − | 14.1415i | 0.261745 | − | 0.453356i | ||||
\(974\) | 26.2951 | + | 45.5445i | 0.842549 | + | 1.45934i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.0899 | 1.66736 | ||||||||
\(977\) | 17.4592 | 0.558568 | 0.279284 | − | 0.960209i | \(-0.409903\pi\) | ||||
0.279284 | + | 0.960209i | \(0.409903\pi\) | |||||||
\(978\) | 0.297253 | − | 0.514858i | 0.00950512 | − | 0.0164633i | ||||
\(979\) | −31.9796 | + | 55.3903i | −1.02207 | + | 1.77028i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.30869 | −0.297204 | ||||||||
\(982\) | 9.20805 | − | 15.9488i | 0.293841 | − | 0.508947i | ||||
\(983\) | 21.9581 | + | 38.0325i | 0.700353 | + | 1.21305i | 0.968342 | + | 0.249625i | \(0.0803075\pi\) |
−0.267989 | + | 0.963422i | \(0.586359\pi\) | |||||||
\(984\) | −7.49348 | + | 12.9791i | −0.238883 | + | 0.413758i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.0403 | − | 22.5864i | −0.415287 | − | 0.719298i | ||||
\(987\) | −25.2898 | −0.804984 | ||||||||
\(988\) | −4.72958 | + | 2.51854i | −0.150468 | + | 0.0801254i | ||||
\(989\) | −4.26707 | −0.135685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1731 | − | 40.1370i | −0.736118 | − | 1.27499i | −0.954231 | − | 0.299071i | \(-0.903323\pi\) |
0.218112 | − | 0.975924i | \(-0.430010\pi\) | |||||||
\(992\) | −10.9145 | + | 18.9044i | −0.346535 | + | 0.600216i | ||||
\(993\) | 11.7172 | + | 20.2948i | 0.371834 | + | 0.644035i | ||||
\(994\) | −17.9045 | + | 31.0114i | −0.567895 | + | 0.983623i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.78300 | −0.0881827 | ||||||||
\(997\) | 5.86857 | − | 10.1647i | 0.185859 | − | 0.321918i | −0.758006 | − | 0.652247i | \(-0.773826\pi\) |
0.943866 | + | 0.330329i | \(0.107160\pi\) | |||||||
\(998\) | 16.9563 | − | 29.3692i | 0.536744 | − | 0.929667i | ||||
\(999\) | −15.6227 | −0.494281 |
(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.e.e.26.1 | 8 | ||
5.2 | odd | 4 | 475.2.j.c.349.7 | 16 | |||
5.3 | odd | 4 | 475.2.j.c.349.2 | 16 | |||
5.4 | even | 2 | 95.2.e.c.26.4 | yes | 8 | ||
15.14 | odd | 2 | 855.2.k.h.406.1 | 8 | |||
19.7 | even | 3 | 9025.2.a.bg.1.4 | 4 | |||
19.11 | even | 3 | inner | 475.2.e.e.201.1 | 8 | ||
19.12 | odd | 6 | 9025.2.a.bp.1.1 | 4 | |||
20.19 | odd | 2 | 1520.2.q.o.881.1 | 8 | |||
95.49 | even | 6 | 95.2.e.c.11.4 | ✓ | 8 | ||
95.64 | even | 6 | 1805.2.a.o.1.1 | 4 | |||
95.68 | odd | 12 | 475.2.j.c.49.7 | 16 | |||
95.69 | odd | 6 | 1805.2.a.i.1.4 | 4 | |||
95.87 | odd | 12 | 475.2.j.c.49.2 | 16 | |||
285.239 | odd | 6 | 855.2.k.h.676.1 | 8 | |||
380.239 | odd | 6 | 1520.2.q.o.961.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.c.11.4 | ✓ | 8 | 95.49 | even | 6 | ||
95.2.e.c.26.4 | yes | 8 | 5.4 | even | 2 | ||
475.2.e.e.26.1 | 8 | 1.1 | even | 1 | trivial | ||
475.2.e.e.201.1 | 8 | 19.11 | even | 3 | inner | ||
475.2.j.c.49.2 | 16 | 95.87 | odd | 12 | |||
475.2.j.c.49.7 | 16 | 95.68 | odd | 12 | |||
475.2.j.c.349.2 | 16 | 5.3 | odd | 4 | |||
475.2.j.c.349.7 | 16 | 5.2 | odd | 4 | |||
855.2.k.h.406.1 | 8 | 15.14 | odd | 2 | |||
855.2.k.h.676.1 | 8 | 285.239 | odd | 6 | |||
1520.2.q.o.881.1 | 8 | 20.19 | odd | 2 | |||
1520.2.q.o.961.1 | 8 | 380.239 | odd | 6 | |||
1805.2.a.i.1.4 | 4 | 95.69 | odd | 6 | |||
1805.2.a.o.1.1 | 4 | 95.64 | even | 6 | |||
9025.2.a.bg.1.4 | 4 | 19.7 | even | 3 | |||
9025.2.a.bp.1.1 | 4 | 19.12 | odd | 6 |