Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(298,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.dl (of order \(6\), 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: | \(6.53974792554\) |
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: | \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 298.2 | ||
Root | \(1.84073 + 1.06275i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.298 |
Dual form | 819.2.dl.e.415.2 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84073 | + | 1.06275i | −1.30159 | + | 0.751474i | −0.980677 | − | 0.195634i | \(-0.937324\pi\) |
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.25885 | − | 2.18040i | 0.629427 | − | 1.09020i | ||||
\(5\) | 3.12291 | − | 1.80301i | 1.39661 | − | 0.806332i | 0.402572 | − | 0.915388i | \(-0.368116\pi\) |
0.994036 | + | 0.109056i | \(0.0347828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.20931 | − | 2.35320i | 0.457076 | − | 0.889428i | ||||
\(8\) | 1.10038i | 0.389044i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.83229 | + | 6.63772i | −1.21188 | + | 2.09903i | ||||
\(11\) | 3.45748 | + | 1.99618i | 1.04247 | + | 0.601871i | 0.920532 | − | 0.390667i | \(-0.127756\pi\) |
0.121939 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.51771 | + | 2.58092i | −0.698287 | + | 0.715818i | ||||
\(14\) | 0.274848 | + | 5.61680i | 0.0734563 | + | 1.50115i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.34828 | + | 2.33529i | 0.337070 | + | 0.583823i | ||||
\(17\) | −2.39458 | + | 4.14753i | −0.580771 | + | 1.00592i | 0.414618 | + | 0.909996i | \(0.363915\pi\) |
−0.995388 | + | 0.0959284i | \(0.969418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.72850 | − | 1.57530i | 0.625960 | − | 0.361398i | −0.153226 | − | 0.988191i | \(-0.548966\pi\) |
0.779186 | + | 0.626793i | \(0.215633\pi\) | |||||||
\(20\) | − | 9.07892i | − | 2.03011i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.48572 | −1.80916 | ||||||||
\(23\) | 1.08943 | + | 1.88694i | 0.227161 | + | 0.393455i | 0.956966 | − | 0.290201i | \(-0.0937222\pi\) |
−0.729804 | + | 0.683656i | \(0.760389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00171 | − | 6.93117i | 0.800343 | − | 1.38623i | ||||
\(26\) | 1.89156 | − | 7.42645i | 0.370965 | − | 1.45645i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.60858 | − | 5.59912i | −0.681958 | − | 1.05813i | ||||
\(29\) | 6.57198 | 1.22039 | 0.610193 | − | 0.792253i | \(-0.291092\pi\) | ||||
0.610193 | + | 0.792253i | \(0.291092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.28753 | + | 0.743358i | 0.231248 | + | 0.133511i | 0.611148 | − | 0.791517i | \(-0.290708\pi\) |
−0.379900 | + | 0.925028i | \(0.624042\pi\) | |||||||
\(32\) | −6.86956 | − | 3.96614i | −1.21438 | − | 0.701121i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 10.1793i | − | 1.74574i | ||||||
\(35\) | −0.466298 | − | 9.52925i | −0.0788187 | − | 1.61074i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.29984 | − | 2.48252i | 0.706890 | − | 0.408123i | −0.103019 | − | 0.994679i | \(-0.532850\pi\) |
0.809908 | + | 0.586556i | \(0.199517\pi\) | |||||||
\(38\) | −3.34828 | + | 5.79939i | −0.543163 | + | 0.940786i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.98401 | + | 3.43640i | 0.313699 | + | 0.543342i | ||||
\(41\) | − | 2.11931i | − | 0.330981i | −0.986211 | − | 0.165490i | \(-0.947079\pi\) | ||
0.986211 | − | 0.165490i | \(-0.0529207\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.43145 | −0.218294 | −0.109147 | − | 0.994026i | \(-0.534812\pi\) | ||||
−0.109147 | + | 0.994026i | \(0.534812\pi\) | |||||||
\(44\) | 8.70494 | − | 5.02580i | 1.31232 | − | 0.757667i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.01068 | − | 2.31557i | −0.591342 | − | 0.341412i | ||||
\(47\) | −0.882417 | + | 0.509464i | −0.128714 | + | 0.0743129i | −0.562974 | − | 0.826474i | \(-0.690343\pi\) |
0.434261 | + | 0.900787i | \(0.357010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.07515 | − | 5.69150i | −0.582164 | − | 0.813072i | ||||
\(50\) | 17.0112i | 2.40575i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.45801 | + | 8.73861i | 0.340864 | + | 1.21183i | ||||
\(53\) | 3.01771 | − | 5.22682i | 0.414514 | − | 0.717959i | −0.580863 | − | 0.814001i | \(-0.697285\pi\) |
0.995377 | + | 0.0960417i | \(0.0306182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.3966 | 1.94123 | ||||||||
\(56\) | 2.58943 | + | 1.33070i | 0.346027 | + | 0.177823i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.0972 | + | 6.98434i | −1.58844 | + | 0.917089i | ||||
\(59\) | −4.24631 | − | 2.45161i | −0.552823 | − | 0.319172i | 0.197437 | − | 0.980316i | \(-0.436738\pi\) |
−0.750260 | + | 0.661143i | \(0.770072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.01771 | + | 1.76272i | 0.130304 | + | 0.225693i | 0.923794 | − | 0.382890i | \(-0.125071\pi\) |
−0.793490 | + | 0.608584i | \(0.791738\pi\) | |||||||
\(62\) | −3.16000 | −0.401320 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.4669 | 1.43336 | ||||||||
\(65\) | −3.20914 | + | 12.5994i | −0.398045 | + | 1.56277i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.38694 | + | 1.95545i | 0.413781 | + | 0.238896i | 0.692413 | − | 0.721501i | \(-0.256548\pi\) |
−0.278632 | + | 0.960398i | \(0.589881\pi\) | |||||||
\(68\) | 6.02885 | + | 10.4423i | 0.731105 | + | 1.26631i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.9855 | + | 17.0452i | 1.31302 | + | 2.03729i | ||||
\(71\) | − | 8.80684i | − | 1.04518i | −0.852584 | − | 0.522590i | \(-0.824966\pi\) | ||
0.852584 | − | 0.522590i | \(-0.175034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.67497 | − | 1.54439i | −0.313081 | − | 0.180757i | 0.335223 | − | 0.942139i | \(-0.391188\pi\) |
−0.648304 | + | 0.761381i | \(0.724522\pi\) | |||||||
\(74\) | −5.27656 | + | 9.13927i | −0.613388 | + | 1.06242i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.93228i | − | 0.909895i | ||||||
\(77\) | 8.87858 | − | 5.72217i | 1.01181 | − | 0.652102i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.984006 | − | 1.70435i | −0.110709 | − | 0.191754i | 0.805347 | − | 0.592803i | \(-0.201979\pi\) |
−0.916056 | + | 0.401049i | \(0.868646\pi\) | |||||||
\(80\) | 8.42112 | + | 4.86194i | 0.941510 | + | 0.543581i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.25229 | + | 3.90108i | 0.248724 | + | 0.430802i | ||||
\(83\) | 7.66020i | 0.840816i | 0.907335 | + | 0.420408i | \(0.138113\pi\) | ||||
−0.907335 | + | 0.420408i | \(0.861887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.2698i | 1.87318i | ||||||||
\(86\) | 2.63491 | − | 1.52126i | 0.284129 | − | 0.164042i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.19656 | + | 3.80456i | −0.234154 | + | 0.405567i | ||||
\(89\) | 11.0844 | − | 6.39960i | 1.17495 | − | 0.678356i | 0.220107 | − | 0.975476i | \(-0.429359\pi\) |
0.954840 | + | 0.297120i | \(0.0960261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02875 | + | 9.04581i | 0.317499 | + | 0.948259i | ||||
\(92\) | 5.48572 | 0.571926 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.08286 | − | 1.87557i | 0.111689 | − | 0.193450i | ||||
\(95\) | 5.68057 | − | 9.83903i | 0.582814 | − | 1.00946i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.35900i | − | 0.137986i | −0.997617 | − | 0.0689930i | \(-0.978021\pi\) | ||
0.997617 | − | 0.0689930i | \(-0.0219786\pi\) | |||||||
\(98\) | 13.5499 | + | 6.14567i | 1.36874 | + | 0.620806i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0751 | − | 17.4507i | −1.00751 | − | 1.74507i | ||||
\(101\) | −2.14400 | + | 3.71353i | −0.213336 | + | 0.369510i | −0.952757 | − | 0.303735i | \(-0.901766\pi\) |
0.739420 | + | 0.673244i | \(0.235100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.21744 | + | 12.5010i | 0.711155 | + | 1.23176i | 0.964424 | + | 0.264361i | \(0.0851610\pi\) |
−0.253269 | + | 0.967396i | \(0.581506\pi\) | |||||||
\(104\) | −2.84000 | − | 2.77044i | −0.278485 | − | 0.271664i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.8282i | 1.24599i | ||||||||
\(107\) | −4.85942 | − | 8.41677i | −0.469778 | − | 0.813680i | 0.529625 | − | 0.848232i | \(-0.322333\pi\) |
−0.999403 | + | 0.0345525i | \(0.988999\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.75782 | − | 3.32428i | −0.551499 | − | 0.318408i | 0.198227 | − | 0.980156i | \(-0.436482\pi\) |
−0.749726 | + | 0.661748i | \(0.769815\pi\) | |||||||
\(110\) | −26.5001 | + | 15.2999i | −2.52669 | + | 1.45878i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.12591 | − | 0.348694i | 0.673335 | − | 0.0329485i | ||||
\(113\) | −17.5434 | −1.65035 | −0.825173 | − | 0.564880i | \(-0.808922\pi\) | ||||
−0.825173 | + | 0.564880i | \(0.808922\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.80437 | + | 3.92850i | 0.634511 | + | 0.366335i | ||||
\(116\) | 8.27316 | − | 14.3295i | 0.768144 | − | 1.33046i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4217 | 0.959399 | ||||||||
\(119\) | 6.86421 | + | 10.6506i | 0.629241 | + | 0.976337i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.46946 | + | 4.27724i | 0.224497 | + | 0.388840i | ||||
\(122\) | −3.74665 | − | 2.16313i | −0.339206 | − | 0.195840i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.24163 | − | 1.87156i | 0.291107 | − | 0.168071i | ||||
\(125\) | − | 10.8304i | − | 0.968704i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.5143 | −1.73162 | −0.865809 | − | 0.500375i | \(-0.833195\pi\) | ||||
−0.865809 | + | 0.500375i | \(0.833195\pi\) | |||||||
\(128\) | −7.36826 | + | 4.25407i | −0.651269 | + | 0.376010i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.48283 | − | 26.6027i | −0.656288 | − | 2.33321i | ||||
\(131\) | 9.53713 | + | 16.5188i | 0.833263 | + | 1.44325i | 0.895437 | + | 0.445188i | \(0.146863\pi\) |
−0.0621741 | + | 0.998065i | \(0.519803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.407406 | − | 8.32573i | −0.0353266 | − | 0.721933i | ||||
\(134\) | −8.31259 | −0.718098 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.56387 | − | 2.63495i | −0.391349 | − | 0.225945i | ||||
\(137\) | −5.56759 | − | 3.21445i | −0.475672 | − | 0.274629i | 0.242939 | − | 0.970042i | \(-0.421888\pi\) |
−0.718611 | + | 0.695412i | \(0.755222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.42854 | −0.205986 | −0.102993 | − | 0.994682i | \(-0.532842\pi\) | ||||
−0.102993 | + | 0.994682i | \(0.532842\pi\) | |||||||
\(140\) | −21.3646 | − | 10.9792i | −1.80564 | − | 0.927913i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.35942 | + | 16.2110i | 0.785425 | + | 1.36040i | ||||
\(143\) | −13.8569 | + | 3.89769i | −1.15877 | + | 0.325941i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.5237 | − | 11.8494i | 1.70440 | − | 0.984036i | ||||
\(146\) | 6.56518 | 0.543338 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 12.5005i | − | 1.02753i | ||||||
\(149\) | −0.0998984 | + | 0.0576764i | −0.00818400 | + | 0.00472503i | −0.504086 | − | 0.863653i | \(-0.668171\pi\) |
0.495902 | + | 0.868378i | \(0.334837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2218 | − | 5.90155i | −0.831838 | − | 0.480262i | 0.0226438 | − | 0.999744i | \(-0.492792\pi\) |
−0.854481 | + | 0.519482i | \(0.826125\pi\) | |||||||
\(152\) | 1.73343 | + | 3.00239i | 0.140600 | + | 0.243526i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.2619 | + | 19.9686i | −0.826924 | + | 1.60912i | ||||
\(155\) | 5.36114 | 0.430617 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.57343 | − | 11.3855i | 0.524617 | − | 0.908663i | −0.474972 | − | 0.880001i | \(-0.657542\pi\) |
0.999589 | − | 0.0286625i | \(-0.00912481\pi\) | |||||||
\(158\) | 3.62257 | + | 2.09149i | 0.288197 | + | 0.166390i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −28.6040 | −2.26135 | ||||||||
\(161\) | 5.75782 | − | 0.281749i | 0.453780 | − | 0.0222049i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1501 | − | 9.32424i | 1.26497 | − | 0.730331i | 0.290938 | − | 0.956742i | \(-0.406033\pi\) |
0.974032 | + | 0.226411i | \(0.0726994\pi\) | |||||||
\(164\) | −4.62094 | − | 2.66790i | −0.360835 | − | 0.208328i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.14084 | − | 14.1003i | −0.631852 | − | 1.09440i | ||||
\(167\) | − | 0.972672i | − | 0.0752676i | −0.999292 | − | 0.0376338i | \(-0.988018\pi\) | ||
0.999292 | − | 0.0376338i | \(-0.0119820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.322293 | − | 12.9960i | −0.0247917 | − | 0.999693i | ||||
\(170\) | −18.3534 | − | 31.7891i | −1.40764 | − | 2.43811i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.80198 | + | 3.12113i | −0.137400 | + | 0.237984i | ||||
\(173\) | −1.22855 | − | 2.12791i | −0.0934050 | − | 0.161782i | 0.815537 | − | 0.578705i | \(-0.196442\pi\) |
−0.908942 | + | 0.416923i | \(0.863108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4712 | − | 17.7988i | −0.867138 | − | 1.34546i | ||||
\(176\) | 10.7656i | 0.811491i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.6023 | + | 23.5598i | −1.01953 | + | 1.76588i | ||||
\(179\) | −7.23629 | + | 12.5336i | −0.540866 | + | 0.936807i | 0.457989 | + | 0.888958i | \(0.348570\pi\) |
−0.998855 | + | 0.0478492i | \(0.984763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.17885 | −0.682259 | −0.341129 | − | 0.940016i | \(-0.610809\pi\) | ||||
−0.341129 | + | 0.940016i | \(0.610809\pi\) | |||||||
\(182\) | −15.1885 | − | 13.4321i | −1.12585 | − | 0.995653i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.07636 | + | 1.19879i | −0.153071 | + | 0.0883758i | ||||
\(185\) | 8.95202 | − | 15.5053i | 0.658165 | − | 1.13998i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.5584 | + | 9.56002i | −1.21087 | + | 0.699098i | ||||
\(188\) | 2.56536i | 0.187098i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.1480i | 1.75188i | ||||||||
\(191\) | 8.79202 | + | 15.2282i | 0.636168 | + | 1.10188i | 0.986266 | + | 0.165162i | \(0.0528148\pi\) |
−0.350098 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.1090 | − | 9.87791i | −1.23154 | − | 0.711028i | −0.264186 | − | 0.964472i | \(-0.585103\pi\) |
−0.967350 | + | 0.253444i | \(0.918437\pi\) | |||||||
\(194\) | 1.44428 | + | 2.50156i | 0.103693 | + | 0.179601i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.5398 | + | 1.72068i | −1.25284 | + | 0.122905i | ||||
\(197\) | − | 7.66020i | − | 0.545767i | −0.962047 | − | 0.272883i | \(-0.912023\pi\) | ||
0.962047 | − | 0.272883i | \(-0.0879773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.27171 | + | 5.66677i | −0.231925 | + | 0.401706i | −0.958375 | − | 0.285514i | \(-0.907836\pi\) |
0.726449 | + | 0.687220i | \(0.241169\pi\) | |||||||
\(200\) | 7.62694 | + | 4.40342i | 0.539306 | + | 0.311369i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 9.11412i | − | 0.641267i | ||||||
\(203\) | 7.94755 | − | 15.4652i | 0.557809 | − | 1.08545i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.82115 | − | 6.61842i | −0.266880 | − | 0.462250i | ||||
\(206\) | −26.5707 | − | 15.3406i | −1.85127 | − | 1.06883i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.42178 | − | 2.39978i | −0.653283 | − | 0.166395i | ||||
\(209\) | 12.5783 | 0.870060 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0452 | 1.37997 | 0.689983 | − | 0.723825i | \(-0.257618\pi\) | ||||
0.689983 | + | 0.723825i | \(0.257618\pi\) | |||||||
\(212\) | −7.59771 | − | 13.1596i | −0.521813 | − | 0.903806i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.8898 | + | 10.3287i | 1.22292 | + | 0.706052i | ||||
\(215\) | −4.47028 | + | 2.58092i | −0.304871 | + | 0.176017i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.30630 | − | 2.13088i | 0.224446 | − | 0.144654i | ||||
\(218\) | 14.1314 | 0.957102 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18.1232 | − | 31.3902i | 1.22186 | − | 2.11633i | ||||
\(221\) | −4.67560 | − | 16.6225i | −0.314515 | − | 1.11815i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.7139i | 1.85586i | 0.372752 | + | 0.927931i | \(0.378414\pi\) | ||||
−0.372752 | + | 0.927931i | \(0.621586\pi\) | |||||||
\(224\) | −17.6406 | + | 11.3692i | −1.17866 | + | 0.759636i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.2927 | − | 18.6442i | 2.14808 | − | 1.24019i | ||||
\(227\) | 9.84766 | + | 5.68555i | 0.653612 | + | 0.377363i | 0.789839 | − | 0.613315i | \(-0.210164\pi\) |
−0.136227 | + | 0.990678i | \(0.543498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.54406 | − | 4.35556i | 0.498525 | − | 0.287824i | −0.229579 | − | 0.973290i | \(-0.573735\pi\) |
0.728104 | + | 0.685466i | \(0.240402\pi\) | |||||||
\(230\) | −16.7000 | −1.10116 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.23170i | 0.474784i | ||||||||
\(233\) | 1.68228 | + | 2.91380i | 0.110210 | + | 0.190889i | 0.915855 | − | 0.401510i | \(-0.131514\pi\) |
−0.805645 | + | 0.592399i | \(0.798181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.83714 | + | 3.18202i | −0.119842 | + | 0.207572i | ||||
\(236\) | −10.6910 | + | 6.17244i | −0.695923 | + | 0.401791i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −23.9540 | − | 12.3099i | −1.55271 | − | 0.797934i | ||||
\(239\) | 19.8798i | 1.28592i | 0.765902 | + | 0.642958i | \(0.222293\pi\) | ||||
−0.765902 | + | 0.642958i | \(0.777707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3435 | − | 9.43595i | −1.05278 | − | 0.607823i | −0.129354 | − | 0.991599i | \(-0.541290\pi\) |
−0.923426 | + | 0.383776i | \(0.874624\pi\) | |||||||
\(242\) | −9.09123 | − | 5.24882i | −0.584406 | − | 0.337407i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.12458 | 0.328068 | ||||||||
\(245\) | −22.9882 | − | 10.4265i | −1.46866 | − | 0.666125i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.80384 | + | 11.0082i | −0.178404 | + | 0.700433i | ||||
\(248\) | −0.817978 | + | 1.41678i | −0.0519417 | + | 0.0899656i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.5100 | + | 19.9359i | 0.727956 | + | 1.26086i | ||||
\(251\) | −9.79601 | −0.618319 | −0.309159 | − | 0.951010i | \(-0.600048\pi\) | ||||
−0.309159 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.69877i | 0.546887i | ||||||||
\(254\) | 35.9206 | − | 20.7388i | 2.25386 | − | 1.30127i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.42488 | + | 4.20002i | −0.151555 | + | 0.262501i | ||||
\(257\) | −10.4697 | − | 18.1341i | −0.653083 | − | 1.13117i | −0.982371 | − | 0.186944i | \(-0.940142\pi\) |
0.329287 | − | 0.944230i | \(-0.393192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.642031 | − | 13.1205i | −0.0398939 | − | 0.815271i | ||||
\(260\) | 23.4320 | + | 22.8581i | 1.45319 | + | 1.41760i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −35.1105 | − | 20.2711i | −2.16914 | − | 1.25235i | ||||
\(263\) | −3.69340 | + | 6.39715i | −0.227745 | + | 0.394465i | −0.957139 | − | 0.289628i | \(-0.906468\pi\) |
0.729395 | + | 0.684093i | \(0.239802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 21.7639i | − | 1.33694i | ||||||
\(266\) | 9.59806 | + | 14.8924i | 0.588495 | + | 0.913114i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.52733 | − | 4.92326i | 0.520890 | − | 0.300736i | ||||
\(269\) | 11.3946 | − | 19.7360i | 0.694740 | − | 1.20332i | −0.275529 | − | 0.961293i | \(-0.588853\pi\) |
0.970268 | − | 0.242032i | \(-0.0778138\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.60814 | − | 2.08316i | 0.219179 | − | 0.126543i | −0.386391 | − | 0.922335i | \(-0.626278\pi\) |
0.605570 | + | 0.795792i | \(0.292945\pi\) | |||||||
\(272\) | −12.9143 | −0.783042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.6646 | 0.825507 | ||||||||
\(275\) | 27.6717 | − | 15.9763i | 1.66867 | − | 0.963406i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.388551 | − | 0.672989i | 0.0233457 | − | 0.0404360i | −0.854116 | − | 0.520082i | \(-0.825901\pi\) |
0.877462 | + | 0.479646i | \(0.159235\pi\) | |||||||
\(278\) | 4.47028 | − | 2.58092i | 0.268110 | − | 0.154793i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.4858 | − | 0.513106i | 0.626648 | − | 0.0306639i | ||||
\(281\) | 11.8988i | 0.709824i | 0.934900 | + | 0.354912i | \(0.115489\pi\) | ||||
−0.934900 | + | 0.354912i | \(0.884511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.95202 | + | 13.7733i | −0.472698 | + | 0.818738i | −0.999512 | − | 0.0312434i | \(-0.990053\pi\) |
0.526813 | + | 0.849981i | \(0.323387\pi\) | |||||||
\(284\) | −19.2024 | − | 11.0865i | −1.13945 | − | 0.657864i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.3646 | − | 21.9010i | 1.26331 | − | 1.29503i | ||||
\(287\) | −4.98717 | − | 2.56290i | −0.294383 | − | 0.151283i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.96801 | − | 5.14075i | −0.174589 | − | 0.302397i | ||||
\(290\) | −25.1857 | + | 43.6229i | −1.47896 | + | 2.56163i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.73478 | + | 3.88833i | −0.394123 | + | 0.227547i | ||||
\(293\) | 6.73698i | 0.393579i | 0.980446 | + | 0.196789i | \(0.0630515\pi\) | ||||
−0.980446 | + | 0.196789i | \(0.936949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.6811 | −1.02944 | ||||||||
\(296\) | 2.73172 | + | 4.73148i | 0.158778 | + | 0.275011i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.122591 | − | 0.212333i | 0.00710148 | − | 0.0123001i | ||||
\(299\) | −7.61291 | − | 1.93905i | −0.440266 | − | 0.112138i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.73106 | + | 3.36849i | −0.0997768 | + | 0.194157i | ||||
\(302\) | 25.0874 | 1.44362 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.35756 | + | 4.24789i | 0.421985 | + | 0.243633i | ||||
\(305\) | 6.35642 | + | 3.66988i | 0.363968 | + | 0.210137i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7179i | 0.839996i | 0.907525 | + | 0.419998i | \(0.137969\pi\) | ||||
−0.907525 | + | 0.419998i | \(0.862031\pi\) | |||||||
\(308\) | −1.29978 | − | 26.5622i | −0.0740617 | − | 1.51352i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.86840 | + | 5.69752i | −0.560487 | + | 0.323597i | ||||
\(311\) | −14.3289 | + | 24.8184i | −0.812517 | + | 1.40732i | 0.0985808 | + | 0.995129i | \(0.468570\pi\) |
−0.911097 | + | 0.412191i | \(0.864764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4125 | + | 28.4274i | 0.927692 | + | 1.60681i | 0.787174 | + | 0.616732i | \(0.211544\pi\) |
0.140518 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(314\) | 27.9435i | 1.57694i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.95488 | −0.278734 | ||||||||
\(317\) | −9.01715 | + | 5.20605i | −0.506453 | + | 0.292401i | −0.731375 | − | 0.681976i | \(-0.761121\pi\) |
0.224921 | + | 0.974377i | \(0.427788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.7225 | + | 13.1188i | 1.27222 | + | 0.734515i | ||||
\(320\) | 35.8100 | − | 20.6749i | 2.00184 | − | 1.15576i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.2992 | + | 6.63772i | −0.573949 | + | 0.369905i | ||||
\(323\) | 15.0887i | 0.839558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.81365 | + | 27.7788i | 0.433423 | + | 1.54089i | ||||
\(326\) | −19.8186 | + | 34.3268i | −1.09765 | + | 1.90118i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.33205 | 0.128766 | ||||||||
\(329\) | 0.131758 | + | 2.69261i | 0.00726406 | + | 0.148448i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.86260 | + | 2.23007i | −0.212308 | + | 0.122576i | −0.602383 | − | 0.798207i | \(-0.705782\pi\) |
0.390076 | + | 0.920783i | \(0.372449\pi\) | |||||||
\(332\) | 16.7023 | + | 9.64307i | 0.916657 | + | 0.529232i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.03370 | + | 1.79043i | 0.0565617 | + | 0.0979677i | ||||
\(335\) | 14.1028 | 0.770519 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7949 | 0.588034 | 0.294017 | − | 0.955800i | \(-0.405008\pi\) | ||||
0.294017 | + | 0.955800i | \(0.405008\pi\) | |||||||
\(338\) | 14.4047 | + | 23.5796i | 0.783512 | + | 1.28256i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 37.6551 | + | 21.7402i | 2.04214 | + | 1.17903i | ||||
\(341\) | 2.96775 | + | 5.14030i | 0.160713 | + | 0.278363i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3214 | + | 2.70687i | −0.989261 | + | 0.146157i | ||||
\(344\) | − | 1.57514i | − | 0.0849259i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.52286 | + | 2.61127i | 0.243150 | + | 0.140383i | ||||
\(347\) | −2.03516 | + | 3.52499i | −0.109253 | + | 0.189232i | −0.915468 | − | 0.402391i | \(-0.868179\pi\) |
0.806215 | + | 0.591623i | \(0.201513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8727i | 1.27788i | 0.769258 | + | 0.638938i | \(0.220626\pi\) | ||||
−0.769258 | + | 0.638938i | \(0.779374\pi\) | |||||||
\(350\) | 40.0309 | + | 20.5718i | 2.13974 | + | 1.09961i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.8343 | − | 27.4257i | −0.843969 | − | 1.46180i | ||||
\(353\) | −22.5894 | − | 13.0420i | −1.20231 | − | 0.694154i | −0.241242 | − | 0.970465i | \(-0.577555\pi\) |
−0.961068 | + | 0.276311i | \(0.910888\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.8788 | − | 27.5030i | −0.842762 | − | 1.45971i | ||||
\(356\) | − | 32.2246i | − | 1.70790i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 30.7613i | − | 1.62579i | ||||||
\(359\) | 19.8271 | − | 11.4472i | 1.04644 | − | 0.604160i | 0.124786 | − | 0.992184i | \(-0.460176\pi\) |
0.921649 | + | 0.388024i | \(0.126842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.53687 | + | 7.85809i | −0.238783 | + | 0.413584i | ||||
\(362\) | 16.8958 | − | 9.75478i | 0.888022 | − | 0.512700i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.5362 | + | 4.78348i | 1.23363 | + | 0.250722i | ||||
\(365\) | −11.1382 | −0.583002 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.08003 | − | 15.7271i | 0.473974 | − | 0.820946i | −0.525582 | − | 0.850743i | \(-0.676153\pi\) |
0.999556 | + | 0.0297964i | \(0.00948589\pi\) | |||||||
\(368\) | −2.93771 | + | 5.08826i | −0.153139 | + | 0.265244i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 38.0548i | 1.97838i | ||||||||
\(371\) | −8.65045 | − | 13.4221i | −0.449109 | − | 0.696842i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.93457 | + | 13.7431i | 0.410836 | + | 0.711590i | 0.994981 | − | 0.100060i | \(-0.0319034\pi\) |
−0.584145 | + | 0.811649i | \(0.698570\pi\) | |||||||
\(374\) | 20.3197 | − | 35.1948i | 1.05071 | − | 1.81988i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.560605 | − | 0.970997i | −0.0289110 | − | 0.0500754i | ||||
\(377\) | −16.5463 | + | 16.9618i | −0.852179 | + | 0.873575i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.7634i | − | 1.42611i | −0.701108 | − | 0.713055i | \(-0.747311\pi\) | ||
0.701108 | − | 0.713055i | \(-0.252689\pi\) | |||||||
\(380\) | −14.3020 | − | 24.7718i | −0.733678 | − | 1.27077i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.3674 | − | 18.6873i | −1.65606 | − | 0.956128i | ||||
\(383\) | −22.7304 | + | 13.1234i | −1.16147 | + | 0.670576i | −0.951656 | − | 0.307165i | \(-0.900620\pi\) |
−0.209815 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.4099 | − | 33.8780i | 0.887289 | − | 1.72658i | ||||
\(386\) | 41.9908 | 2.13728 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.96317 | − | 1.71079i | −0.150432 | − | 0.0868521i | ||||
\(389\) | 12.6277 | − | 21.8718i | 0.640250 | − | 1.10895i | −0.345127 | − | 0.938556i | \(-0.612164\pi\) |
0.985377 | − | 0.170389i | \(-0.0545026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4349 | −0.527714 | ||||||||
\(392\) | 6.26283 | − | 4.48422i | 0.316321 | − | 0.226487i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.14084 | + | 14.1003i | 0.410129 | + | 0.710365i | ||||
\(395\) | −6.14592 | − | 3.54835i | −0.309235 | − | 0.178537i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.9701 | + | 7.48827i | −0.650949 | + | 0.375826i | −0.788820 | − | 0.614625i | \(-0.789308\pi\) |
0.137871 | + | 0.990450i | \(0.455974\pi\) | |||||||
\(398\) | − | 13.9080i | − | 0.697143i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5817 | 1.07909 | ||||||||
\(401\) | 4.62811 | − | 2.67204i | 0.231117 | − | 0.133435i | −0.379970 | − | 0.924999i | \(-0.624066\pi\) |
0.611087 | + | 0.791563i | \(0.290733\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.16018 | + | 1.45146i | −0.257047 | + | 0.0723025i | ||||
\(404\) | 5.39798 | + | 9.34957i | 0.268559 | + | 0.465159i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.80630 | + | 36.9135i | 0.0896451 | + | 1.83199i | ||||
\(407\) | 19.8222 | 0.982549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.91433 | − | 1.68259i | −0.144104 | − | 0.0831985i | 0.426214 | − | 0.904622i | \(-0.359847\pi\) |
−0.570319 | + | 0.821424i | \(0.693180\pi\) | |||||||
\(410\) | 14.0674 | + | 8.12181i | 0.694739 | + | 0.401107i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 36.3428 | 1.79048 | ||||||||
\(413\) | −10.9042 | + | 7.02769i | −0.536562 | + | 0.345810i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8114 | + | 23.9221i | 0.677977 | + | 1.17429i | ||||
\(416\) | 27.5318 | − | 7.74419i | 1.34986 | − | 0.379690i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.1533 | + | 13.3675i | −1.13246 | + | 0.653828i | ||||
\(419\) | 28.8639 | 1.41010 | 0.705048 | − | 0.709160i | \(-0.250926\pi\) | ||||
0.705048 | + | 0.709160i | \(0.250926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6125i | 0.809644i | 0.914395 | + | 0.404822i | \(0.132667\pi\) | ||||
−0.914395 | + | 0.404822i | \(0.867333\pi\) | |||||||
\(422\) | −36.8977 | + | 21.3029i | −1.79615 | + | 1.03701i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.75151 | + | 3.32064i | 0.279318 | + | 0.161264i | ||||
\(425\) | 19.1648 | + | 33.1945i | 0.929631 | + | 1.61017i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.37877 | − | 0.263201i | 0.260297 | − | 0.0127372i | ||||
\(428\) | −24.4692 | −1.18276 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.48572 | − | 9.50154i | 0.264545 | − | 0.458205i | ||||
\(431\) | −17.8015 | − | 10.2777i | −0.857469 | − | 0.495060i | 0.00569505 | − | 0.999984i | \(-0.498187\pi\) |
−0.863164 | + | 0.504924i | \(0.831521\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.4092 | −0.932748 | −0.466374 | − | 0.884588i | \(-0.654440\pi\) | ||||
−0.466374 | + | 0.884588i | \(0.654440\pi\) | |||||||
\(434\) | −3.82141 | + | 7.43613i | −0.183434 | + | 0.356945i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.4965 | + | 8.36956i | −0.694257 | + | 0.400829i | ||||
\(437\) | 5.94500 | + | 3.43235i | 0.284388 | + | 0.164191i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.71256 | + | 11.6265i | 0.320373 | + | 0.554902i | 0.980565 | − | 0.196195i | \(-0.0628585\pi\) |
−0.660192 | + | 0.751097i | \(0.729525\pi\) | |||||||
\(440\) | 15.8417i | 0.755225i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.2720 | + | 25.6285i | 1.24963 | + | 1.21902i | ||||
\(443\) | −16.7766 | − | 29.0579i | −0.797080 | − | 1.38058i | −0.921510 | − | 0.388354i | \(-0.873044\pi\) |
0.124430 | − | 0.992228i | \(-0.460290\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.0771 | − | 39.9707i | 1.09396 | − | 1.89479i | ||||
\(446\) | −29.4528 | − | 51.0138i | −1.39463 | − | 2.41557i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.8670 | − | 26.9839i | 0.655153 | − | 1.27487i | ||||
\(449\) | − | 34.4284i | − | 1.62478i | −0.583117 | − | 0.812388i | \(-0.698167\pi\) | ||
0.583117 | − | 0.812388i | \(-0.301833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.23052 | − | 7.32748i | 0.199208 | − | 0.345038i | ||||
\(452\) | −22.0846 | + | 38.2517i | −1.03877 | + | 1.79921i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.1691 | −1.13431 | ||||||||
\(455\) | 25.7682 | + | 22.7884i | 1.20803 | + | 1.06834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.6735 | − | 6.73967i | 0.546061 | − | 0.315269i | −0.201471 | − | 0.979495i | \(-0.564572\pi\) |
0.747532 | + | 0.664226i | \(0.231239\pi\) | |||||||
\(458\) | −9.25771 | + | 16.0348i | −0.432584 | + | 0.749258i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.1314 | − | 9.89082i | 0.798756 | − | 0.461162i | ||||
\(461\) | − | 1.35900i | − | 0.0632951i | −0.999499 | − | 0.0316476i | \(-0.989925\pi\) | ||
0.999499 | − | 0.0316476i | \(-0.0100754\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.49836i | 0.116109i | 0.998313 | + | 0.0580543i | \(0.0184897\pi\) | ||||
−0.998313 | + | 0.0580543i | \(0.981510\pi\) | |||||||
\(464\) | 8.86088 | + | 15.3475i | 0.411356 | + | 0.712489i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.19325 | − | 3.57567i | −0.286897 | − | 0.165640i | ||||
\(467\) | 13.1091 | + | 22.7056i | 0.606617 | + | 1.05069i | 0.991794 | + | 0.127849i | \(0.0408072\pi\) |
−0.385176 | + | 0.922843i | \(0.625859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.69744 | − | 5.60542i | 0.401610 | − | 0.258834i | ||||
\(470\) | − | 7.80965i | − | 0.360232i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.69771 | − | 4.67257i | 0.124172 | − | 0.215072i | ||||
\(473\) | −4.94921 | − | 2.85743i | −0.227565 | − | 0.131385i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25.2156i | − | 1.15697i | ||||||
\(476\) | 31.8635 | − | 1.55919i | 1.46046 | − | 0.0714653i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.1271 | − | 36.5933i | −0.966332 | − | 1.67374i | ||||
\(479\) | 20.6513 | + | 11.9230i | 0.943583 | + | 0.544778i | 0.891082 | − | 0.453843i | \(-0.149947\pi\) |
0.0525011 | + | 0.998621i | \(0.483281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.41858 | + | 17.3478i | −0.201470 | + | 0.790992i | ||||
\(482\) | 40.1120 | 1.82705 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.4348 | 0.565217 | ||||||||
\(485\) | −2.45030 | − | 4.24405i | −0.111263 | − | 0.192712i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.17524 | + | 5.29733i | 0.415770 | + | 0.240045i | 0.693266 | − | 0.720682i | \(-0.256171\pi\) |
−0.277496 | + | 0.960727i | \(0.589504\pi\) | |||||||
\(488\) | −1.93967 | + | 1.11987i | −0.0878047 | + | 0.0506941i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 53.3957 | − | 5.23820i | 2.41217 | − | 0.236638i | ||||
\(491\) | −19.7704 | −0.892224 | −0.446112 | − | 0.894977i | \(-0.647192\pi\) | ||||
−0.446112 | + | 0.894977i | \(0.647192\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.7371 | + | 27.2575i | −0.708764 | + | 1.22762i | ||||
\(494\) | −6.53777 | − | 23.2428i | −0.294148 | − | 1.04574i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00902i | 0.180010i | ||||||||
\(497\) | −20.7243 | − | 10.6502i | −0.929612 | − | 0.477726i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4234 | − | 6.59530i | 0.511381 | − | 0.295246i | −0.222020 | − | 0.975042i | \(-0.571265\pi\) |
0.733401 | + | 0.679796i | \(0.237932\pi\) | |||||||
\(500\) | −23.6147 | − | 13.6339i | −1.05608 | − | 0.609728i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.0318 | − | 10.4107i | 0.804798 | − | 0.464651i | ||||
\(503\) | −37.9046 | −1.69008 | −0.845040 | − | 0.534703i | \(-0.820424\pi\) | ||||
−0.845040 | + | 0.534703i | \(0.820424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4627i | 0.688080i | ||||||||
\(506\) | −9.24457 | − | 16.0121i | −0.410971 | − | 0.711823i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.5657 | + | 42.5490i | −1.08993 | + | 1.88781i | ||||
\(509\) | −23.9565 | + | 13.8313i | −1.06185 | + | 0.613062i | −0.925944 | − | 0.377660i | \(-0.876729\pi\) |
−0.135909 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.86913 | + | 4.42710i | −0.303872 | + | 0.195843i | ||||
\(512\) | − | 27.3244i | − | 1.20758i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 38.5438 | + | 22.2533i | 1.70010 | + | 0.981551i | ||||
\(515\) | 45.0788 | + | 26.0263i | 1.98641 | + | 1.14685i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.06792 | −0.178907 | ||||||||
\(518\) | 15.1256 | + | 23.4690i | 0.664580 | + | 1.03117i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.8642 | − | 3.53129i | −0.607986 | − | 0.154857i | ||||
\(521\) | 7.78339 | − | 13.4812i | 0.340996 | − | 0.590623i | −0.643622 | − | 0.765344i | \(-0.722569\pi\) |
0.984618 | + | 0.174721i | \(0.0559022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6169 | − | 23.5852i | −0.595425 | − | 1.03131i | −0.993487 | − | 0.113948i | \(-0.963650\pi\) |
0.398061 | − | 0.917359i | \(-0.369683\pi\) | |||||||
\(524\) | 48.0234 | 2.09791 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 15.7005i | − | 0.684577i | ||||||
\(527\) | −6.16620 | + | 3.56006i | −0.268604 | + | 0.155079i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.12630 | − | 15.8072i | 0.396796 | − | 0.687270i | ||||
\(530\) | 23.1294 | + | 40.0614i | 1.00468 | + | 1.74015i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.6663 | − | 9.59258i | −0.809286 | − | 0.415891i | ||||
\(533\) | 5.46977 | + | 5.33581i | 0.236922 | + | 0.231119i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.3511 | − | 17.5232i | −1.31219 | − | 0.757594i | ||||
\(536\) | −2.15175 | + | 3.72693i | −0.0929413 | + | 0.160979i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 48.4381i | 2.08832i | ||||||||
\(539\) | −2.72850 | − | 27.8130i | −0.117525 | − | 1.19799i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.9626 | + | 12.1027i | −0.901251 | + | 0.520338i | −0.877606 | − | 0.479383i | \(-0.840861\pi\) |
−0.0236453 | + | 0.999720i | \(0.507527\pi\) | |||||||
\(542\) | −4.42774 | + | 7.66907i | −0.190188 | + | 0.329415i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.8994 | − | 18.9945i | 1.41055 | − | 0.814381i | ||||
\(545\) | −23.9749 | −1.02697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2177 | −0.949960 | −0.474980 | − | 0.879997i | \(-0.657545\pi\) | ||||
−0.474980 | + | 0.879997i | \(0.657545\pi\) | |||||||
\(548\) | −14.0176 | + | 8.09305i | −0.598801 | + | 0.345718i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −33.9574 | + | 58.8160i | −1.44795 | + | 2.50792i | ||||
\(551\) | 17.9316 | − | 10.3528i | 0.763913 | − | 0.441045i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.20065 | + | 0.254485i | −0.221154 | + | 0.0108218i | ||||
\(554\) | 1.65172i | 0.0701749i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.05718 | + | 5.29519i | −0.129653 | + | 0.224566i | ||||
\(557\) | 19.3300 | + | 11.1602i | 0.819040 | + | 0.472873i | 0.850085 | − | 0.526645i | \(-0.176550\pi\) |
−0.0310455 | + | 0.999518i | \(0.509884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.60397 | − | 3.69445i | 0.152432 | − | 0.156259i | ||||
\(560\) | 21.6249 | − | 13.9370i | 0.913818 | − | 0.588948i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.6454 | − | 21.9025i | −0.533415 | − | 0.923901i | ||||
\(563\) | −13.3519 | + | 23.1262i | −0.562717 | + | 0.974655i | 0.434541 | + | 0.900652i | \(0.356911\pi\) |
−0.997258 | + | 0.0740027i | \(0.976423\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.7865 | + | 31.6310i | −2.30489 | + | 1.33073i | ||||
\(566\) | − | 33.8039i | − | 1.42088i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.69090 | 0.406621 | ||||||||
\(569\) | −3.30510 | − | 5.72461i | −0.138557 | − | 0.239988i | 0.788393 | − | 0.615171i | \(-0.210913\pi\) |
−0.926951 | + | 0.375183i | \(0.877580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0643 | + | 36.4844i | −0.881513 | + | 1.52683i | −0.0318546 | + | 0.999493i | \(0.510141\pi\) |
−0.849659 | + | 0.527333i | \(0.823192\pi\) | |||||||
\(572\) | −8.94531 | + | 35.1202i | −0.374022 | + | 1.46845i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.9037 | − | 0.582489i | 0.496853 | − | 0.0243126i | ||||
\(575\) | 17.4383 | 0.727227 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7559 | − | 7.94195i | −0.572664 | − | 0.330628i | 0.185549 | − | 0.982635i | \(-0.440594\pi\) |
−0.758213 | + | 0.652007i | \(0.773927\pi\) | |||||||
\(578\) | 10.9266 | + | 6.30848i | 0.454487 | + | 0.262398i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 59.6665i | − | 2.47752i | ||||||
\(581\) | 18.0260 | + | 9.26354i | 0.747845 | + | 0.384316i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.8674 | − | 12.0478i | 0.864238 | − | 0.498968i | ||||
\(584\) | 1.69942 | − | 2.94349i | 0.0703226 | − | 0.121802i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.15969 | − | 12.4010i | −0.295764 | − | 0.512279i | ||||
\(587\) | − | 18.5676i | − | 0.766366i | −0.923672 | − | 0.383183i | \(-0.874828\pi\) | ||
0.923672 | − | 0.383183i | \(-0.125172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.68404 | 0.193003 | ||||||||
\(590\) | 32.5462 | − | 18.7905i | 1.33990 | − | 0.773594i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.5948 | + | 6.69426i | 0.476543 | + | 0.275132i | ||||
\(593\) | −17.8487 | + | 10.3050i | −0.732960 | + | 0.423175i | −0.819504 | − | 0.573073i | \(-0.805751\pi\) |
0.0865442 | + | 0.996248i | \(0.472418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.6394 | + | 20.8845i | 1.66605 | + | 0.856183i | ||||
\(596\) | 0.290425i | 0.0118963i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.0740 | − | 4.52132i | 0.657315 | − | 0.184891i | ||||
\(599\) | −6.80224 | + | 11.7818i | −0.277932 | + | 0.481393i | −0.970871 | − | 0.239604i | \(-0.922982\pi\) |
0.692939 | + | 0.720997i | \(0.256316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1503 | −0.495621 | −0.247810 | − | 0.968809i | \(-0.579711\pi\) | ||||
−0.247810 | + | 0.968809i | \(0.579711\pi\) | |||||||
\(602\) | −0.393431 | − | 8.04015i | −0.0160351 | − | 0.327692i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.7355 | + | 14.8584i | −1.04716 | + | 0.604579i | ||||
\(605\) | 15.4238 | + | 8.90496i | 0.627068 | + | 0.362038i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6166 | − | 30.5128i | −0.715035 | − | 1.23848i | −0.962946 | − | 0.269695i | \(-0.913077\pi\) |
0.247911 | − | 0.968783i | \(-0.420256\pi\) | |||||||
\(608\) | −24.9914 | −1.01354 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.6006 | −0.631650 | ||||||||
\(611\) | 0.906784 | − | 3.56013i | 0.0366845 | − | 0.144027i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0345 | − | 15.0310i | −1.05152 | − | 0.607097i | −0.128448 | − | 0.991716i | \(-0.541000\pi\) |
−0.923075 | + | 0.384619i | \(0.874333\pi\) | |||||||
\(614\) | −15.6414 | − | 27.0917i | −0.631236 | − | 1.09333i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.29658 | + | 9.76984i | 0.253697 | + | 0.393638i | ||||
\(617\) | 7.01712i | 0.282499i | 0.989974 | + | 0.141249i | \(0.0451119\pi\) | ||||
−0.989974 | + | 0.141249i | \(0.954888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.9736 | + | 21.9241i | 1.52629 | + | 0.881203i | 0.999513 | + | 0.0311993i | \(0.00993266\pi\) |
0.526776 | + | 0.850004i | \(0.323401\pi\) | |||||||
\(620\) | 6.74889 | − | 11.6894i | 0.271042 | − | 0.469458i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 60.9118i | − | 2.44234i | ||||||
\(623\) | −1.65507 | − | 33.8230i | −0.0663091 | − | 1.35509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.481145 | + | 0.833367i | 0.0192458 | + | 0.0333347i | ||||
\(626\) | −60.4221 | − | 34.8847i | −2.41495 | − | 1.39427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.5500 | − | 28.6654i | −0.660416 | − | 1.14387i | ||||
\(629\) | 23.7783i | 0.948103i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 23.4936i | − | 0.935267i | −0.883922 | − | 0.467634i | \(-0.845107\pi\) | ||
0.883922 | − | 0.467634i | \(-0.154893\pi\) | |||||||
\(632\) | 1.87544 | − | 1.08278i | 0.0746008 | − | 0.0430708i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.0654 | − | 19.1659i | 0.439464 | − | 0.761173i | ||||
\(635\) | −60.9415 | + | 35.1846i | −2.41839 | + | 1.39626i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.9493 | + | 3.81191i | 0.988529 | + | 0.151033i | ||||
\(638\) | −55.7680 | −2.20788 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.3403 | + | 26.5702i | −0.606378 | + | 1.05028i | ||||
\(641\) | −3.70233 | + | 6.41262i | −0.146233 | + | 0.253283i | −0.929832 | − | 0.367983i | \(-0.880048\pi\) |
0.783599 | + | 0.621267i | \(0.213382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.9607i | − | 1.57590i | −0.615742 | − | 0.787948i | \(-0.711144\pi\) | ||
0.615742 | − | 0.787948i | \(-0.288856\pi\) | |||||||
\(644\) | 6.63393 | − | 12.9090i | 0.261413 | − | 0.508687i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0354 | − | 27.7742i | −0.630906 | − | 1.09276i | ||||
\(647\) | −13.6234 | + | 23.5964i | −0.535591 | + | 0.927670i | 0.463544 | + | 0.886074i | \(0.346578\pi\) |
−0.999134 | + | 0.0415963i | \(0.986756\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.78770 | − | 16.9528i | −0.384201 | − | 0.665456i | ||||
\(650\) | −43.9046 | − | 42.8292i | −1.72208 | − | 1.67990i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 46.9514i | − | 1.83876i | ||||||
\(653\) | 9.57255 | + | 16.5801i | 0.374603 | + | 0.648831i | 0.990267 | − | 0.139177i | \(-0.0444458\pi\) |
−0.615665 | + | 0.788008i | \(0.711112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 59.5672 | + | 34.3911i | 2.32748 | + | 1.34377i | ||||
\(656\) | 4.94921 | − | 2.85743i | 0.193234 | − | 0.111564i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.10409 | − | 4.81633i | −0.121010 | − | 0.187760i | ||||
\(659\) | −41.5725 | −1.61943 | −0.809717 | − | 0.586820i | \(-0.800380\pi\) | ||||
−0.809717 | + | 0.586820i | \(0.800380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.6221 | − | 17.1023i | −1.15217 | − | 0.665203i | −0.202752 | − | 0.979230i | \(-0.564988\pi\) |
−0.949414 | + | 0.314027i | \(0.898322\pi\) | |||||||
\(662\) | 4.74000 | − | 8.20992i | 0.184225 | − | 0.319088i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.42915 | −0.327115 | ||||||||
\(665\) | −16.2837 | − | 25.2660i | −0.631455 | − | 0.979772i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.15969 | + | 12.4010i | 0.277224 | + | 0.480167i | ||||
\(668\) | −2.12081 | − | 1.22445i | −0.0820567 | − | 0.0473755i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.9595 | + | 14.9877i | −1.00290 | + | 0.579025i | ||||
\(671\) | 8.12611i | 0.313705i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.4308 | −0.826098 | −0.413049 | − | 0.910709i | \(-0.635536\pi\) | ||||
−0.413049 | + | 0.910709i | \(0.635536\pi\) | |||||||
\(674\) | −19.8704 | + | 11.4722i | −0.765381 | + | 0.441893i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.7422 | − | 15.6573i | −1.10547 | − | 0.602206i | ||||
\(677\) | 4.89083 | + | 8.47117i | 0.187970 | + | 0.325573i | 0.944573 | − | 0.328301i | \(-0.106476\pi\) |
−0.756603 | + | 0.653874i | \(0.773143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.19802 | − | 1.64346i | −0.122729 | − | 0.0630700i | ||||
\(680\) | −19.0034 | −0.728748 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.9256 | − | 6.30793i | −0.418365 | − | 0.241543i | ||||
\(683\) | 13.2297 | + | 7.63818i | 0.506221 | + | 0.292267i | 0.731279 | − | 0.682079i | \(-0.238924\pi\) |
−0.225058 | + | 0.974345i | \(0.572257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.1828 | −0.885769 | ||||||||
\(686\) | 30.8480 | − | 24.4536i | 1.17778 | − | 0.933642i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.92999 | − | 3.34285i | −0.0735803 | − | 0.127445i | ||||
\(689\) | 5.89230 | + | 20.9481i | 0.224479 | + | 0.798058i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.7690 | + | 21.2286i | −1.39876 | + | 0.807573i | −0.994263 | − | 0.106967i | \(-0.965886\pi\) |
−0.404496 | + | 0.914540i | \(0.632553\pi\) | |||||||
\(692\) | −6.18627 | −0.235167 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 8.65141i | − | 0.328403i | ||||||
\(695\) | −7.58412 | + | 4.37869i | −0.287682 | + | 0.166093i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.78991 | + | 5.07486i | 0.332942 | + | 0.192224i | ||||
\(698\) | −25.3706 | − | 43.9432i | −0.960291 | − | 1.66327i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −53.2489 | + | 2.60565i | −2.01262 | + | 0.0984842i | ||||
\(701\) | −2.79985 | −0.105749 | −0.0528744 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528744 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.82141 | − | 13.5471i | 0.294990 | − | 0.510937i | ||||
\(704\) | 39.6465 | + | 22.8899i | 1.49423 | + | 0.862696i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 55.4412 | 2.08656 | ||||||||
\(707\) | 6.14592 | + | 9.53608i | 0.231141 | + | 0.358641i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6149 | + | 7.28319i | −0.473761 | + | 0.273526i | −0.717813 | − | 0.696236i | \(-0.754857\pi\) |
0.244052 | + | 0.969762i | \(0.421523\pi\) | |||||||
\(710\) | 58.4573 | + | 33.7503i | 2.19386 | + | 1.26663i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.04201 | + | 12.1971i | 0.263910 | + | 0.457106i | ||||
\(713\) | 3.23934i | 0.121314i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.2463 | + | 37.1563i | −1.35554 | + | 1.38957i | ||||
\(716\) | 18.2189 | + | 31.5560i | 0.680871 | + | 1.17930i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.3309 | + | 42.1423i | −0.908021 | + | 1.57274i | ||||
\(719\) | −17.2529 | − | 29.8828i | −0.643423 | − | 1.11444i | −0.984663 | − | 0.174465i | \(-0.944180\pi\) |
0.341240 | − | 0.939976i | \(-0.389153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.1454 | − | 1.86658i | 1.42061 | − | 0.0695152i | ||||
\(722\) | − | 19.2861i | − | 0.717756i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.5548 | + | 20.0136i | −0.429432 | + | 0.743798i | ||||
\(725\) | 26.2992 | − | 45.5515i | 0.976727 | − | 1.69174i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.7571 | −1.32616 | −0.663078 | − | 0.748550i | \(-0.730750\pi\) | ||||
−0.663078 | + | 0.748550i | \(0.730750\pi\) | |||||||
\(728\) | −9.95386 | + | 3.33278i | −0.368915 | + | 0.123521i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.5025 | − | 11.8371i | 0.758830 | − | 0.438111i | ||||
\(731\) | 3.42771 | − | 5.93698i | 0.126779 | − | 0.219587i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.5504 | − | 20.5250i | 1.31308 | − | 0.758108i | 0.330477 | − | 0.943814i | \(-0.392790\pi\) |
0.982605 | + | 0.185706i | \(0.0594571\pi\) | |||||||
\(734\) | 38.5990i | 1.42472i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 17.2833i | − | 0.637071i | ||||||
\(737\) | 7.80686 | + | 13.5219i | 0.287570 | + | 0.498085i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.629089 | + | 0.363205i | 0.0231414 | + | 0.0133607i | 0.511526 | − | 0.859268i | \(-0.329080\pi\) |
−0.488385 | + | 0.872628i | \(0.662414\pi\) | |||||||
\(740\) | −22.5386 | − | 39.0379i | −0.828534 | − | 1.43506i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.1874 | + | 15.5133i | 1.10822 | + | 0.569510i | ||||
\(743\) | 16.4547i | 0.603664i | 0.953361 | + | 0.301832i | \(0.0975981\pi\) | ||||
−0.953361 | + | 0.301832i | \(0.902402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.207983 | + | 0.360236i | −0.00761989 | + | 0.0131980i | ||||
\(746\) | −29.2108 | − | 16.8648i | −1.06948 | − | 0.617466i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 48.1387i | 1.76012i | ||||||||
\(749\) | −25.6829 | + | 1.25675i | −0.938433 | + | 0.0459206i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5854 | + | 21.7985i | 0.459247 | + | 0.795439i | 0.998921 | − | 0.0464350i | \(-0.0147860\pi\) |
−0.539675 | + | 0.841874i | \(0.681453\pi\) | |||||||
\(752\) | −2.37949 | − | 1.37380i | −0.0867712 | − | 0.0500974i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.4313 | − | 48.8065i | 0.452720 | − | 1.77743i | ||||
\(755\) | −42.5623 | −1.54900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.0743 | 1.60191 | 0.800953 | − | 0.598727i | \(-0.204327\pi\) | ||||
0.800953 | + | 0.598727i | \(0.204327\pi\) | |||||||
\(758\) | 29.5054 | + | 51.1049i | 1.07168 | + | 1.85621i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.8267 | + | 6.25080i | 0.392726 | + | 0.226740i | ||||
\(761\) | 33.5171 | − | 19.3511i | 1.21499 | − | 0.701477i | 0.251151 | − | 0.967948i | \(-0.419191\pi\) |
0.963843 | + | 0.266471i | \(0.0858577\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.7857 | + | 9.52925i | −0.535278 | + | 0.344982i | ||||
\(764\) | 44.2715 | 1.60169 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.8937 | − | 48.3133i | 1.00784 | − | 1.74563i | ||||
\(767\) | 17.0184 | − | 4.78695i | 0.614498 | − | 0.172847i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.1506i | 1.30362i | 0.758381 | + | 0.651811i | \(0.225991\pi\) | ||||
−0.758381 | + | 0.651811i | \(0.774009\pi\) | |||||||
\(770\) | 3.95687 | + | 80.8625i | 0.142596 | + | 2.91408i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −43.0756 | + | 24.8697i | −1.55032 | + | 0.895080i | ||||
\(773\) | −26.0441 | − | 15.0366i | −0.936740 | − | 0.540827i | −0.0478033 | − | 0.998857i | \(-0.515222\pi\) |
−0.888937 | + | 0.458030i | \(0.848555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3047 | − | 5.94941i | 0.370155 | − | 0.213709i | ||||
\(776\) | 1.49543 | 0.0536827 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 53.6801i | 1.92453i | ||||||||
\(779\) | −3.33855 | − | 5.78253i | −0.119616 | − | 0.207181i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5800 | − | 30.4495i | 0.629063 | − | 1.08957i | ||||
\(782\) | 19.2078 | − | 11.0896i | 0.686868 | − | 0.396564i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.79687 | − | 17.1904i | 0.278460 | − | 0.613943i | ||||
\(785\) | − | 47.4079i | − | 1.69206i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.9106 | + | 18.4236i | 1.13749 | + | 0.656730i | 0.945808 | − | 0.324727i | \(-0.105272\pi\) |
0.191682 | + | 0.981457i | \(0.438606\pi\) | |||||||
\(788\) | −16.7023 | − | 9.64307i | −0.594994 | − | 0.343520i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.0840 | 0.536663 | ||||||||
\(791\) | −21.2154 | + | 41.2833i | −0.754333 | + | 1.46786i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.11174 | − | 1.81140i | −0.252545 | − | 0.0643246i | ||||
\(794\) | 15.9163 | − | 27.5678i | 0.564847 | − | 0.978343i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.23721 | + | 14.2673i | 0.291960 | + | 0.505690i | ||||
\(797\) | 27.5910 | 0.977323 | 0.488661 | − | 0.872474i | \(-0.337485\pi\) | ||||
0.488661 | + | 0.872474i | \(0.337485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.87980i | − | 0.172635i | ||||||
\(800\) | −54.9800 | + | 31.7427i | −1.94384 | + | 1.12227i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.67939 | + | 9.83700i | −0.200546 | + | 0.347356i | ||||
\(803\) | −6.16577 | − | 10.6794i | −0.217585 | − | 0.376869i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.4732 | − | 11.2613i | 0.615848 | − | 0.396909i | ||||
\(806\) | 7.95596 | − | 8.15570i | 0.280237 | − | 0.287272i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.08630 | − | 2.35923i | −0.143756 | − | 0.0829973i | ||||
\(809\) | 17.8551 | − | 30.9260i | 0.627752 | − | 1.08730i | −0.360250 | − | 0.932856i | \(-0.617308\pi\) |
0.988002 | − | 0.154443i | \(-0.0493582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.22418i | − | 0.0781015i | −0.999237 | − | 0.0390508i | \(-0.987567\pi\) | ||
0.999237 | − | 0.0390508i | \(-0.0124334\pi\) | |||||||
\(812\) | −23.7155 | − | 36.7973i | −0.832252 | − | 1.29133i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −36.4873 | + | 21.0659i | −1.27888 | + | 0.738360i | ||||
\(815\) | 33.6234 | − | 58.2375i | 1.17778 | − | 2.03997i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.90570 | + | 2.25496i | −0.136643 | + | 0.0788910i | ||||
\(818\) | 7.15264 | 0.250086 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.2411 | −0.671927 | ||||||||
\(821\) | −46.2192 | + | 26.6847i | −1.61306 | + | 0.931302i | −0.624407 | + | 0.781099i | \(0.714659\pi\) |
−0.988655 | + | 0.150203i | \(0.952007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.6043 | − | 44.3479i | 0.892509 | − | 1.54587i | 0.0556519 | − | 0.998450i | \(-0.482276\pi\) |
0.836857 | − | 0.547421i | \(-0.184390\pi\) | |||||||
\(824\) | −13.7559 | + | 7.94195i | −0.479208 | + | 0.276671i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.6031 | − | 24.5245i | 0.438518 | − | 0.853316i | ||||
\(827\) | − | 8.97196i | − | 0.311986i | −0.987758 | − | 0.155993i | \(-0.950142\pi\) | ||
0.987758 | − | 0.155993i | \(-0.0498577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2858 | − | 35.1360i | 0.704554 | − | 1.22032i | −0.262298 | − | 0.964987i | \(-0.584480\pi\) |
0.966852 | − | 0.255337i | \(-0.0821864\pi\) | |||||||
\(830\) | −50.8462 | − | 29.3561i | −1.76490 | − | 1.01896i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28.8702 | + | 29.5951i | −1.00089 | + | 1.02602i | ||||
\(833\) | 33.3639 | − | 3.27305i | 1.15599 | − | 0.113405i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.75374 | − | 3.03757i | −0.0606907 | − | 0.105119i | ||||
\(836\) | 15.8343 | − | 27.4257i | 0.547639 | − | 0.948539i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −53.1307 | + | 30.6750i | −1.83537 | + | 1.05965i | ||||
\(839\) | 32.3005i | 1.11514i | 0.830131 | + | 0.557568i | \(0.188266\pi\) | ||||
−0.830131 | + | 0.557568i | \(0.811734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1909 | 0.489342 | ||||||||
\(842\) | −17.6549 | − | 30.5791i | −0.608427 | − | 1.05383i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.2340 | − | 43.7065i | 0.868588 | − | 1.50444i | ||||
\(845\) | −24.4385 | − | 40.0043i | −0.840709 | − | 1.37619i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.0516 | − | 0.638656i | 0.448457 | − | 0.0219445i | ||||
\(848\) | 16.2749 | 0.558882 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −70.5545 | − | 40.7347i | −2.42000 | − | 1.39719i | ||||
\(851\) | 9.36873 | + | 5.40904i | 0.321156 | + | 0.185419i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.5887i | 1.21853i | 0.792965 | + | 0.609267i | \(0.208536\pi\) | ||||
−0.792965 | + | 0.609267i | \(0.791464\pi\) | |||||||
\(854\) | −9.62114 | + | 6.20074i | −0.329229 | + | 0.212185i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.26167 | − | 5.34723i | 0.316557 | − | 0.182764i | ||||
\(857\) | −23.0114 | + | 39.8570i | −0.786055 | + | 1.36149i | 0.142311 | + | 0.989822i | \(0.454547\pi\) |
−0.928367 | + | 0.371666i | \(0.878787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6229 | − | 21.8635i | −0.430689 | − | 0.745975i | 0.566244 | − | 0.824238i | \(-0.308396\pi\) |
−0.996933 | + | 0.0782630i | \(0.975063\pi\) | |||||||
\(860\) | 12.9960i | 0.443160i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 43.6903 | 1.48810 | ||||||||
\(863\) | 11.9803 | − | 6.91684i | 0.407815 | − | 0.235452i | −0.282036 | − | 0.959404i | \(-0.591010\pi\) |
0.689850 | + | 0.723952i | \(0.257676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.67331 | − | 4.43019i | −0.260900 | − | 0.150631i | ||||
\(866\) | 35.7271 | − | 20.6271i | 1.21406 | − | 0.700936i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.484025 | − | 9.89152i | −0.0164289 | − | 0.335740i | ||||
\(869\) | − | 7.85701i | − | 0.266531i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.5742 | + | 3.81817i | −0.459944 | + | 0.129374i | ||||
\(872\) | 3.65798 | − | 6.33581i | 0.123875 | − | 0.214557i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.5908 | −0.493542 | ||||||||
\(875\) | −25.4862 | − | 13.0973i | −0.861592 | − | 0.442771i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.16459 | − | 1.82708i | 0.106861 | − | 0.0616961i | −0.445617 | − | 0.895224i | \(-0.647016\pi\) |
0.552478 | + | 0.833528i | \(0.313682\pi\) | |||||||
\(878\) | −24.7120 | − | 14.2675i | −0.833989 | − | 0.481504i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.4106 | + | 33.6201i | 0.654331 | + | 1.13333i | ||||
\(881\) | 36.6320 | 1.23416 | 0.617082 | − | 0.786899i | \(-0.288315\pi\) | ||||
0.617082 | + | 0.786899i | \(0.288315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.11145 | 0.239319 | 0.119660 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119660 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(884\) | −42.1295 | − | 10.7306i | −1.41697 | − | 0.360910i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61.7623 | + | 35.6585i | 2.07494 | + | 1.19797i | ||||
\(887\) | −3.36773 | − | 5.83308i | −0.113077 | − | 0.195856i | 0.803932 | − | 0.594721i | \(-0.202737\pi\) |
−0.917010 | + | 0.398865i | \(0.869404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.5989 | + | 45.9212i | −0.791480 | + | 1.54015i | ||||
\(890\) | 98.1004i | 3.28833i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 60.4274 | + | 34.8878i | 2.02326 | + | 1.16813i | ||||
\(893\) | −1.60512 | + | 2.78014i | −0.0537131 | + | 0.0930339i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.1885i | 1.74447i | ||||||||
\(896\) | 1.10019 | + | 22.4835i | 0.0367549 | + | 0.751122i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.5886 | + | 63.3733i | 1.22098 | + | 2.11479i | ||||
\(899\) | 8.46164 | + | 4.88533i | 0.282212 | + | 0.162935i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.4523 | + | 25.0321i | 0.481475 | + | 0.833939i | ||||
\(902\) | 17.9839i | 0.598798i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 19.3045i | − | 0.642058i | ||||||
\(905\) | −28.6647 | + | 16.5496i | −0.952848 | + | 0.550127i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.46630 | + | 4.27175i | −0.0818921 | + | 0.141841i | −0.904063 | − | 0.427400i | \(-0.859430\pi\) |
0.822171 | + | 0.569241i | \(0.192763\pi\) | |||||||
\(908\) | 24.7935 | − | 14.3145i | 0.822802 | − | 0.475045i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −71.6505 | − | 14.5622i | −2.37519 | − | 0.482732i | ||||
\(911\) | 26.6258 | 0.882152 | 0.441076 | − | 0.897470i | \(-0.354597\pi\) | ||||
0.441076 | + | 0.897470i | \(0.354597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.2911 | + | 26.4850i | −0.506063 | + | 0.876526i | ||||
\(914\) | −14.3251 | + | 24.8118i | −0.473833 | + | 0.820702i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 21.9321i | − | 0.724656i | ||||||
\(917\) | 50.4054 | − | 2.46650i | 1.66453 | − | 0.0814512i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.1918 | + | 28.0450i | 0.534118 | + | 0.925119i | 0.999205 | + | 0.0398544i | \(0.0126894\pi\) |
−0.465088 | + | 0.885265i | \(0.653977\pi\) | |||||||
\(920\) | −4.32286 | + | 7.48741i | −0.142520 | + | 0.246853i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.44428 | + | 2.50156i | 0.0475647 | + | 0.0823844i | ||||
\(923\) | 22.7297 | + | 22.1730i | 0.748158 | + | 0.729835i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 39.7373i | − | 1.30655i | ||||||
\(926\) | −2.65512 | − | 4.59880i | −0.0872526 | − | 0.151126i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −45.1466 | − | 26.0654i | −1.48201 | − | 0.855639i | ||||
\(929\) | 24.2722 | − | 14.0135i | 0.796344 | − | 0.459769i | −0.0458472 | − | 0.998948i | \(-0.514599\pi\) |
0.842191 | + | 0.539179i | \(0.181265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0848 | − | 9.10967i | −0.658254 | − | 0.298557i | ||||
\(932\) | 8.47099 | 0.277476 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −48.2606 | − | 27.8633i | −1.57914 | − | 0.911714i | ||||
\(935\) | −34.4737 | + | 59.7102i | −1.12741 | + | 1.95273i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1324 | 0.461686 | 0.230843 | − | 0.972991i | \(-0.425852\pi\) | ||||
0.230843 | + | 0.972991i | \(0.425852\pi\) | |||||||
\(938\) | −10.0525 | + | 19.5612i | −0.328225 | + | 0.638696i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.62538 | + | 8.01140i | 0.150863 | + | 0.261303i | ||||
\(941\) | −7.77080 | − | 4.48647i | −0.253321 | − | 0.146255i | 0.367963 | − | 0.929840i | \(-0.380055\pi\) |
−0.621284 | + | 0.783586i | \(0.713389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.99902 | − | 2.30883i | 0.130226 | − | 0.0751860i | ||||
\(944\) | − | 13.2218i | − | 0.430334i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.1469 | 0.394929 | ||||||||
\(947\) | 40.0933 | − | 23.1479i | 1.30286 | − | 0.752205i | 0.321964 | − | 0.946752i | \(-0.395657\pi\) |
0.980893 | + | 0.194546i | \(0.0623235\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7207 | − | 3.01554i | 0.348010 | − | 0.0978887i | ||||
\(950\) | 26.7977 | + | 46.4150i | 0.869433 | + | 1.50590i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.7197 | + | 7.55326i | −0.379838 | + | 0.244803i | ||||
\(953\) | 19.1097 | 0.619023 | 0.309512 | − | 0.950896i | \(-0.399834\pi\) | ||||
0.309512 | + | 0.950896i | \(0.399834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.9134 | + | 31.7042i | 1.77695 | + | 1.02593i | ||||
\(956\) | 43.3458 | + | 25.0257i | 1.40190 | + | 0.809390i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50.6846 | −1.63755 | ||||||||
\(959\) | −14.2972 | + | 9.21443i | −0.461681 | + | 0.297549i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.3948 | − | 24.9326i | −0.464350 | − | 0.804277i | ||||
\(962\) | −10.3029 | − | 36.6284i | −0.332178 | − | 1.18095i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −41.1483 | + | 23.7570i | −1.32530 | + | 0.765160i | ||||
\(965\) | −71.2400 | −2.29330 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.5432i | − | 0.724942i | −0.931995 | − | 0.362471i | \(-0.881933\pi\) | ||
0.931995 | − | 0.362471i | \(-0.118067\pi\) | |||||||
\(968\) | −4.70660 | + | 2.71736i | −0.151276 | + | 0.0873392i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.02068 | + | 5.20809i | 0.289637 | + | 0.167222i | ||||
\(971\) | 13.6429 | + | 23.6301i | 0.437820 | + | 0.758327i | 0.997521 | − | 0.0703679i | \(-0.0224173\pi\) |
−0.559701 | + | 0.828695i | \(0.689084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.93685 | + | 5.71485i | −0.0941512 | + | 0.183210i | ||||
\(974\) | −22.5188 | −0.721550 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.74431 | + | 4.75329i | −0.0878433 | + | 0.152149i | ||||
\(977\) | 48.6568 | + | 28.0920i | 1.55667 | + | 0.898744i | 0.997572 | + | 0.0696427i | \(0.0221859\pi\) |
0.559098 | + | 0.829101i | \(0.311147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.0990 | 1.63313 | ||||||||
\(980\) | −51.6727 | + | 36.9979i | −1.65062 | + | 1.18186i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.3919 | − | 21.0108i | 1.16131 | − | 0.670483i | ||||
\(983\) | 22.9402 | + | 13.2445i | 0.731678 | + | 0.422435i | 0.819036 | − | 0.573742i | \(-0.194509\pi\) |
−0.0873577 | + | 0.996177i | \(0.527842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.8114 | − | 23.9221i | −0.440069 | − | 0.762222i | ||||
\(986\) | − | 66.8982i | − | 2.13047i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.4726 | + | 19.9712i | 0.651320 | + | 0.635368i | ||||
\(989\) | −1.55946 | − | 2.70106i | −0.0495879 | − | 0.0858887i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.55629 | + | 4.42763i | −0.0812033 | + | 0.140648i | −0.903767 | − | 0.428025i | \(-0.859210\pi\) |
0.822564 | + | 0.568673i | \(0.192543\pi\) | |||||||
\(992\) | −5.89652 | − | 10.2131i | −0.187215 | − | 0.324266i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 49.4662 | − | 2.42055i | 1.56897 | − | 0.0767750i | ||||
\(995\) | 23.5957i | 0.748035i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.01771 | + | 1.76272i | −0.0322311 | + | 0.0558260i | −0.881691 | − | 0.471827i | \(-0.843595\pi\) |
0.849460 | + | 0.527653i | \(0.176928\pi\) | |||||||
\(998\) | −14.0182 | + | 24.2803i | −0.443740 | + | 0.768580i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.dl.e.298.2 | 16 | ||
3.2 | odd | 2 | 91.2.r.a.25.7 | yes | 16 | ||
7.2 | even | 3 | inner | 819.2.dl.e.415.7 | 16 | ||
13.12 | even | 2 | inner | 819.2.dl.e.298.7 | 16 | ||
21.2 | odd | 6 | 91.2.r.a.51.2 | yes | 16 | ||
21.5 | even | 6 | 637.2.r.f.324.2 | 16 | |||
21.11 | odd | 6 | 637.2.c.f.246.7 | 8 | |||
21.17 | even | 6 | 637.2.c.e.246.7 | 8 | |||
21.20 | even | 2 | 637.2.r.f.116.7 | 16 | |||
39.5 | even | 4 | 1183.2.e.i.508.2 | 16 | |||
39.8 | even | 4 | 1183.2.e.i.508.7 | 16 | |||
39.38 | odd | 2 | 91.2.r.a.25.2 | ✓ | 16 | ||
91.51 | even | 6 | inner | 819.2.dl.e.415.2 | 16 | ||
273.38 | even | 6 | 637.2.c.e.246.2 | 8 | |||
273.44 | even | 12 | 1183.2.e.i.170.2 | 16 | |||
273.86 | even | 12 | 1183.2.e.i.170.7 | 16 | |||
273.116 | odd | 6 | 637.2.c.f.246.2 | 8 | |||
273.122 | odd | 12 | 8281.2.a.cj.1.7 | 8 | |||
273.164 | odd | 12 | 8281.2.a.cj.1.2 | 8 | |||
273.194 | even | 6 | 637.2.r.f.324.7 | 16 | |||
273.200 | even | 12 | 8281.2.a.ck.1.7 | 8 | |||
273.233 | odd | 6 | 91.2.r.a.51.7 | yes | 16 | ||
273.242 | even | 12 | 8281.2.a.ck.1.2 | 8 | |||
273.272 | even | 2 | 637.2.r.f.116.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.2 | ✓ | 16 | 39.38 | odd | 2 | ||
91.2.r.a.25.7 | yes | 16 | 3.2 | odd | 2 | ||
91.2.r.a.51.2 | yes | 16 | 21.2 | odd | 6 | ||
91.2.r.a.51.7 | yes | 16 | 273.233 | odd | 6 | ||
637.2.c.e.246.2 | 8 | 273.38 | even | 6 | |||
637.2.c.e.246.7 | 8 | 21.17 | even | 6 | |||
637.2.c.f.246.2 | 8 | 273.116 | odd | 6 | |||
637.2.c.f.246.7 | 8 | 21.11 | odd | 6 | |||
637.2.r.f.116.2 | 16 | 273.272 | even | 2 | |||
637.2.r.f.116.7 | 16 | 21.20 | even | 2 | |||
637.2.r.f.324.2 | 16 | 21.5 | even | 6 | |||
637.2.r.f.324.7 | 16 | 273.194 | even | 6 | |||
819.2.dl.e.298.2 | 16 | 1.1 | even | 1 | trivial | ||
819.2.dl.e.298.7 | 16 | 13.12 | even | 2 | inner | ||
819.2.dl.e.415.2 | 16 | 91.51 | even | 6 | inner | ||
819.2.dl.e.415.7 | 16 | 7.2 | even | 3 | inner | ||
1183.2.e.i.170.2 | 16 | 273.44 | even | 12 | |||
1183.2.e.i.170.7 | 16 | 273.86 | even | 12 | |||
1183.2.e.i.508.2 | 16 | 39.5 | even | 4 | |||
1183.2.e.i.508.7 | 16 | 39.8 | even | 4 | |||
8281.2.a.cj.1.2 | 8 | 273.164 | odd | 12 | |||
8281.2.a.cj.1.7 | 8 | 273.122 | odd | 12 | |||
8281.2.a.ck.1.2 | 8 | 273.242 | even | 12 | |||
8281.2.a.ck.1.7 | 8 | 273.200 | even | 12 |