Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-1.30089 - 0.554694i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.i.30.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82678 | − | 1.05469i | −1.29173 | − | 0.745781i | −0.312770 | − | 0.949829i | \(-0.601257\pi\) |
−0.978961 | + | 0.204047i | \(0.934590\pi\) | |||||||
\(3\) | −2.26165 | −1.30576 | −0.652882 | − | 0.757460i | \(-0.726440\pi\) | ||||
−0.652882 | + | 0.757460i | \(0.726440\pi\) | |||||||
\(4\) | 1.22476 | + | 2.12135i | 0.612380 | + | 1.06067i | ||||
\(5\) | −3.11923 | + | 1.80089i | −1.39496 | + | 0.805382i | −0.993859 | − | 0.110650i | \(-0.964707\pi\) |
−0.401104 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(6\) | 4.13154 | + | 2.38535i | 1.68670 | + | 0.973814i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.948212i | − | 0.335243i | ||||||
\(9\) | 2.11505 | 0.705018 | ||||||||
\(10\) | 7.59755 | 2.40256 | ||||||||
\(11\) | 0.886384i | 0.267255i | 0.991032 | + | 0.133627i | \(0.0426626\pi\) | ||||
−0.991032 | + | 0.133627i | \(0.957337\pi\) | |||||||
\(12\) | −2.76998 | − | 4.79774i | −0.799623 | − | 1.38499i | ||||
\(13\) | 1.17349 | + | 3.40924i | 0.325467 | + | 0.945553i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.05461 | − | 4.07298i | 1.82149 | − | 1.05164i | ||||
\(16\) | 1.44945 | − | 2.51051i | 0.362362 | − | 0.627629i | ||||
\(17\) | 2.48008 | + | 4.29563i | 0.601508 | + | 1.04184i | 0.992593 | + | 0.121488i | \(0.0387665\pi\) |
−0.391085 | + | 0.920355i | \(0.627900\pi\) | |||||||
\(18\) | −3.86375 | − | 2.23073i | −0.910694 | − | 0.525789i | ||||
\(19\) | 2.37878i | 0.545729i | 0.962053 | + | 0.272864i | \(0.0879710\pi\) | ||||
−0.962053 | + | 0.272864i | \(0.912029\pi\) | |||||||
\(20\) | −7.64062 | − | 4.41132i | −1.70849 | − | 0.986400i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.934864 | − | 1.61923i | 0.199314 | − | 0.345222i | ||||
\(23\) | −1.92926 | + | 3.34157i | −0.402278 | + | 0.696765i | −0.994000 | − | 0.109376i | \(-0.965115\pi\) |
0.591723 | + | 0.806142i | \(0.298448\pi\) | |||||||
\(24\) | 2.14452i | 0.437749i | ||||||||
\(25\) | 3.98641 | − | 6.90466i | 0.797282 | − | 1.38093i | ||||
\(26\) | 1.45200 | − | 7.46562i | 0.284761 | − | 1.46413i | ||||
\(27\) | 2.00144 | 0.385177 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.640986 | − | 1.11022i | −0.119028 | − | 0.206163i | 0.800355 | − | 0.599527i | \(-0.204645\pi\) |
−0.919383 | + | 0.393364i | \(0.871311\pi\) | |||||||
\(30\) | −17.1830 | −3.13717 | ||||||||
\(31\) | −7.33455 | − | 4.23460i | −1.31732 | − | 0.760557i | −0.334027 | − | 0.942564i | \(-0.608408\pi\) |
−0.983297 | + | 0.182006i | \(0.941741\pi\) | |||||||
\(32\) | −6.93800 | + | 4.00566i | −1.22648 | + | 0.708107i | ||||
\(33\) | − | 2.00469i | − | 0.348972i | ||||||
\(34\) | − | 10.4629i | − | 1.79437i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.59043 | + | 4.48676i | 0.431739 | + | 0.747793i | ||||
\(37\) | 8.34686 | + | 4.81906i | 1.37222 | + | 0.792249i | 0.991207 | − | 0.132323i | \(-0.0422435\pi\) |
0.381009 | + | 0.924571i | \(0.375577\pi\) | |||||||
\(38\) | 2.50888 | − | 4.34551i | 0.406994 | − | 0.704935i | ||||
\(39\) | −2.65402 | − | 7.71051i | −0.424983 | − | 1.23467i | ||||
\(40\) | 1.70762 | + | 2.95769i | 0.269999 | + | 0.467652i | ||||
\(41\) | −10.4652 | + | 6.04207i | −1.63438 | + | 0.943612i | −0.651666 | + | 0.758506i | \(0.725929\pi\) |
−0.982719 | + | 0.185106i | \(0.940737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82125 | + | 3.15450i | −0.277738 | + | 0.481056i | −0.970822 | − | 0.239800i | \(-0.922918\pi\) |
0.693084 | + | 0.720856i | \(0.256251\pi\) | |||||||
\(44\) | −1.88033 | + | 1.08561i | −0.283470 | + | 0.163662i | ||||
\(45\) | −6.59734 | + | 3.80898i | −0.983474 | + | 0.567809i | ||||
\(46\) | 7.04867 | − | 4.06955i | 1.03927 | − | 0.600022i | ||||
\(47\) | −2.58274 | + | 1.49115i | −0.376731 | + | 0.217506i | −0.676395 | − | 0.736539i | \(-0.736459\pi\) |
0.299664 | + | 0.954045i | \(0.403126\pi\) | |||||||
\(48\) | −3.27814 | + | 5.67790i | −0.473158 | + | 0.819535i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.5646 | + | 8.40888i | −2.05975 | + | 1.18920i | ||||
\(51\) | −5.60907 | − | 9.71520i | −0.785427 | − | 1.36040i | ||||
\(52\) | −5.79494 | + | 6.66487i | −0.803614 | + | 0.924252i | ||||
\(53\) | −2.46016 | + | 4.26112i | −0.337929 | + | 0.585310i | −0.984043 | − | 0.177931i | \(-0.943060\pi\) |
0.646114 | + | 0.763241i | \(0.276393\pi\) | |||||||
\(54\) | −3.65619 | − | 2.11090i | −0.497545 | − | 0.287258i | ||||
\(55\) | −1.59628 | − | 2.76484i | −0.215242 | − | 0.372811i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.37995i | − | 0.712592i | ||||||
\(58\) | 2.70418i | 0.355076i | ||||||||
\(59\) | 6.34577 | − | 3.66373i | 0.826148 | − | 0.476977i | −0.0263837 | − | 0.999652i | \(-0.508399\pi\) |
0.852532 | + | 0.522675i | \(0.175066\pi\) | |||||||
\(60\) | 17.2804 | + | 9.97684i | 2.23089 | + | 1.28800i | ||||
\(61\) | 1.53926 | 0.197082 | 0.0985412 | − | 0.995133i | \(-0.468582\pi\) | ||||
0.0985412 | + | 0.995133i | \(0.468582\pi\) | |||||||
\(62\) | 8.93242 | + | 15.4714i | 1.13442 | + | 1.96487i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.1012 | 1.38765 | ||||||||
\(65\) | −9.80005 | − | 8.52090i | −1.21555 | − | 1.05689i | ||||
\(66\) | −2.11433 | + | 3.66213i | −0.260257 | + | 0.450778i | ||||
\(67\) | 8.42649i | 1.02946i | 0.857352 | + | 0.514730i | \(0.172108\pi\) | ||||
−0.857352 | + | 0.514730i | \(0.827892\pi\) | |||||||
\(68\) | −6.07501 | + | 10.5222i | −0.736703 | + | 1.27601i | ||||
\(69\) | 4.36330 | − | 7.55745i | 0.525279 | − | 0.909811i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.58490 | − | 3.22444i | −0.662805 | − | 0.382671i | 0.130540 | − | 0.991443i | \(-0.458329\pi\) |
−0.793345 | + | 0.608772i | \(0.791662\pi\) | |||||||
\(72\) | − | 2.00552i | − | 0.236353i | ||||||
\(73\) | −6.19086 | − | 3.57430i | −0.724586 | − | 0.418340i | 0.0918526 | − | 0.995773i | \(-0.470721\pi\) |
−0.816438 | + | 0.577433i | \(0.804054\pi\) | |||||||
\(74\) | −10.1653 | − | 17.6068i | −1.18169 | − | 2.04675i | ||||
\(75\) | −9.01585 | + | 15.6159i | −1.04106 | + | 1.80317i | ||||
\(76\) | −5.04621 | + | 2.91343i | −0.578840 | + | 0.334193i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.28391 | + | 16.8846i | −0.371830 | + | 1.91180i | ||||
\(79\) | −0.378775 | − | 0.656058i | −0.0426156 | − | 0.0738123i | 0.843931 | − | 0.536452i | \(-0.180236\pi\) |
−0.886546 | + | 0.462640i | \(0.846902\pi\) | |||||||
\(80\) | 10.4412i | 1.16736i | ||||||||
\(81\) | −10.8717 | −1.20797 | ||||||||
\(82\) | 25.4901 | 2.81491 | ||||||||
\(83\) | − | 4.76766i | − | 0.523319i | −0.965160 | − | 0.261659i | \(-0.915730\pi\) | ||
0.965160 | − | 0.261659i | \(-0.0842697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.4719 | − | 8.93270i | −1.67816 | − | 0.968888i | ||||
\(86\) | 6.65406 | − | 3.84172i | 0.717525 | − | 0.414263i | ||||
\(87\) | 1.44969 | + | 2.51093i | 0.155423 | + | 0.269200i | ||||
\(88\) | 0.840480 | 0.0895955 | ||||||||
\(89\) | 3.13400 | + | 1.80942i | 0.332204 | + | 0.191798i | 0.656819 | − | 0.754048i | \(-0.271902\pi\) |
−0.324615 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(90\) | 16.0692 | 1.69385 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.45150 | −0.985387 | ||||||||
\(93\) | 16.5882 | + | 9.57719i | 1.72011 | + | 0.993108i | ||||
\(94\) | 6.29081 | 0.648848 | ||||||||
\(95\) | −4.28391 | − | 7.41995i | −0.439520 | − | 0.761271i | ||||
\(96\) | 15.6913 | − | 9.05939i | 1.60149 | − | 0.924620i | ||||
\(97\) | 0.401229 | + | 0.231650i | 0.0407386 | + | 0.0235205i | 0.520231 | − | 0.854026i | \(-0.325846\pi\) |
−0.479492 | + | 0.877546i | \(0.659179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.87475i | 0.188419i | ||||||||
\(100\) | 19.5296 | 1.95296 | ||||||||
\(101\) | 5.82303 | 0.579413 | 0.289707 | − | 0.957115i | \(-0.406442\pi\) | ||||
0.289707 | + | 0.957115i | \(0.406442\pi\) | |||||||
\(102\) | 23.6634i | 2.34303i | ||||||||
\(103\) | −4.11944 | − | 7.13508i | −0.405901 | − | 0.703040i | 0.588525 | − | 0.808479i | \(-0.299709\pi\) |
−0.994426 | + | 0.105438i | \(0.966375\pi\) | |||||||
\(104\) | 3.23268 | − | 1.11271i | 0.316991 | − | 0.109111i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.98837 | − | 5.18944i | 0.873027 | − | 0.504043i | ||||
\(107\) | 1.91630 | − | 3.31913i | 0.185256 | − | 0.320872i | −0.758407 | − | 0.651781i | \(-0.774022\pi\) |
0.943663 | + | 0.330909i | \(0.107355\pi\) | |||||||
\(108\) | 2.45128 | + | 4.24574i | 0.235875 | + | 0.408547i | ||||
\(109\) | −9.02229 | − | 5.20902i | −0.864178 | − | 0.498934i | 0.00123094 | − | 0.999999i | \(-0.499608\pi\) |
−0.865409 | + | 0.501066i | \(0.832942\pi\) | |||||||
\(110\) | 6.73435i | 0.642095i | ||||||||
\(111\) | −18.8777 | − | 10.8990i | −1.79179 | − | 1.03449i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.45505 | − | 4.25228i | 0.230952 | − | 0.400021i | −0.727136 | − | 0.686493i | \(-0.759149\pi\) |
0.958089 | + | 0.286472i | \(0.0924826\pi\) | |||||||
\(114\) | −5.67421 | + | 9.82801i | −0.531438 | + | 0.920478i | ||||
\(115\) | − | 13.8975i | − | 1.29595i | ||||||
\(116\) | 1.57011 | − | 2.71951i | 0.145781 | − | 0.252500i | ||||
\(117\) | 2.48199 | + | 7.21073i | 0.229460 | + | 0.666632i | ||||
\(118\) | −15.4565 | −1.42288 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.86205 | − | 6.68926i | −0.352555 | − | 0.610643i | ||||
\(121\) | 10.2143 | 0.928575 | ||||||||
\(122\) | −2.81190 | − | 1.62345i | −0.254578 | − | 0.146980i | ||||
\(123\) | 23.6685 | − | 13.6650i | 2.13412 | − | 1.23213i | ||||
\(124\) | − | 20.7455i | − | 1.86300i | ||||||
\(125\) | 10.7074i | 0.957702i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.15508 | − | 10.6609i | −0.546175 | − | 0.946003i | −0.998532 | − | 0.0541658i | \(-0.982750\pi\) |
0.452357 | − | 0.891837i | \(-0.350583\pi\) | |||||||
\(128\) | −6.40347 | − | 3.69704i | −0.565992 | − | 0.326776i | ||||
\(129\) | 4.11902 | − | 7.13436i | 0.362660 | − | 0.628145i | ||||
\(130\) | 8.91563 | + | 25.9019i | 0.781953 | + | 2.27175i | ||||
\(131\) | −4.10133 | − | 7.10371i | −0.358335 | − | 0.620654i | 0.629348 | − | 0.777123i | \(-0.283322\pi\) |
−0.987683 | + | 0.156470i | \(0.949989\pi\) | |||||||
\(132\) | 4.25264 | − | 2.45526i | 0.370145 | − | 0.213703i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.88737 | − | 15.3934i | 0.767752 | − | 1.32979i | ||||
\(135\) | −6.24295 | + | 3.60437i | −0.537308 | + | 0.310215i | ||||
\(136\) | 4.07316 | − | 2.35164i | 0.349271 | − | 0.201652i | ||||
\(137\) | −6.45670 | + | 3.72778i | −0.551633 | + | 0.318485i | −0.749780 | − | 0.661687i | \(-0.769841\pi\) |
0.198147 | + | 0.980172i | \(0.436508\pi\) | |||||||
\(138\) | −15.9416 | + | 9.20389i | −1.35704 | + | 0.783487i | ||||
\(139\) | 8.34028 | − | 14.4458i | 0.707413 | − | 1.22528i | −0.258400 | − | 0.966038i | \(-0.583195\pi\) |
0.965813 | − | 0.259238i | \(-0.0834714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.84125 | − | 3.37245i | 0.491922 | − | 0.284011i | ||||
\(142\) | 6.80160 | + | 11.7807i | 0.570778 | + | 0.988616i | ||||
\(143\) | −3.02190 | + | 1.04016i | −0.252704 | + | 0.0869826i | ||||
\(144\) | 3.06566 | − | 5.30987i | 0.255471 | − | 0.442489i | ||||
\(145\) | 3.99877 | + | 2.30869i | 0.332080 | + | 0.191726i | ||||
\(146\) | 7.53958 | + | 13.0589i | 0.623980 | + | 1.08076i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.6088i | 1.94063i | ||||||||
\(149\) | 2.52163i | 0.206580i | 0.994651 | + | 0.103290i | \(0.0329370\pi\) | ||||
−0.994651 | + | 0.103290i | \(0.967063\pi\) | |||||||
\(150\) | 32.9400 | − | 19.0179i | 2.68954 | − | 1.55281i | ||||
\(151\) | 13.7674 | + | 7.94862i | 1.12038 | + | 0.646849i | 0.941497 | − | 0.337022i | \(-0.109420\pi\) |
0.178879 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(152\) | 2.25558 | 0.182952 | ||||||||
\(153\) | 5.24550 | + | 9.08548i | 0.424074 | + | 0.734517i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.5042 | 2.45016 | ||||||||
\(156\) | 13.1061 | − | 15.0736i | 1.04933 | − | 1.20685i | ||||
\(157\) | 6.49155 | − | 11.2437i | 0.518082 | − | 0.897344i | −0.481697 | − | 0.876338i | \(-0.659980\pi\) |
0.999779 | − | 0.0210065i | \(-0.00668708\pi\) | |||||||
\(158\) | 1.59797i | 0.127128i | ||||||||
\(159\) | 5.56402 | − | 9.63717i | 0.441256 | − | 0.764277i | ||||
\(160\) | 14.4275 | − | 24.9892i | 1.14059 | − | 1.97557i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 19.8603 | + | 11.4663i | 1.56037 | + | 0.900880i | ||||
\(163\) | 2.31948i | 0.181676i | 0.995866 | + | 0.0908378i | \(0.0289545\pi\) | ||||
−0.995866 | + | 0.0908378i | \(0.971046\pi\) | |||||||
\(164\) | −25.6346 | − | 14.8002i | −2.00173 | − | 1.15570i | ||||
\(165\) | 3.61023 | + | 6.25309i | 0.281056 | + | 0.486803i | ||||
\(166\) | −5.02843 | + | 8.70949i | −0.390282 | + | 0.675987i | ||||
\(167\) | 11.9441 | − | 6.89591i | 0.924260 | − | 0.533622i | 0.0392682 | − | 0.999229i | \(-0.487497\pi\) |
0.884992 | + | 0.465607i | \(0.154164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2459 | + | 8.00140i | −0.788143 | + | 0.615493i | ||||
\(170\) | 18.8425 | + | 32.6362i | 1.44516 | + | 2.50309i | ||||
\(171\) | 5.03124i | 0.384748i | ||||||||
\(172\) | −8.92237 | −0.680324 | ||||||||
\(173\) | −3.68432 | −0.280113 | −0.140057 | − | 0.990143i | \(-0.544728\pi\) | ||||
−0.140057 | + | 0.990143i | \(0.544728\pi\) | |||||||
\(174\) | − | 6.11590i | − | 0.463645i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.22528 | + | 1.28477i | 0.167737 | + | 0.0968429i | ||||
\(177\) | −14.3519 | + | 8.28607i | −1.07875 | + | 0.622819i | ||||
\(178\) | −3.81677 | − | 6.61083i | −0.286079 | − | 0.495503i | ||||
\(179\) | 5.89277 | 0.440446 | 0.220223 | − | 0.975450i | \(-0.429322\pi\) | ||||
0.220223 | + | 0.975450i | \(0.429322\pi\) | |||||||
\(180\) | −16.1603 | − | 9.33017i | −1.20452 | − | 0.695430i | ||||
\(181\) | 2.11543 | 0.157239 | 0.0786193 | − | 0.996905i | \(-0.474949\pi\) | ||||
0.0786193 | + | 0.996905i | \(0.474949\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.48127 | −0.257343 | ||||||||
\(184\) | 3.16851 | + | 1.82934i | 0.233586 | + | 0.134861i | ||||
\(185\) | −34.7144 | −2.55225 | ||||||||
\(186\) | −20.2020 | − | 34.9909i | −1.48128 | − | 2.56566i | ||||
\(187\) | −3.80758 | + | 2.19830i | −0.278437 | + | 0.160756i | ||||
\(188\) | −6.32647 | − | 3.65259i | −0.461406 | − | 0.266393i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.0729i | 1.31114i | ||||||||
\(191\) | −11.3667 | −0.822462 | −0.411231 | − | 0.911531i | \(-0.634901\pi\) | ||||
−0.411231 | + | 0.911531i | \(0.634901\pi\) | |||||||
\(192\) | −25.1070 | −1.81194 | ||||||||
\(193\) | 14.0894i | 1.01417i | 0.861895 | + | 0.507087i | \(0.169278\pi\) | ||||
−0.861895 | + | 0.507087i | \(0.830722\pi\) | |||||||
\(194\) | −0.488639 | − | 0.846348i | −0.0350823 | − | 0.0607643i | ||||
\(195\) | 22.1643 | + | 19.2713i | 1.58722 | + | 1.38004i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8815 | + | 11.4786i | −1.41650 | + | 0.817814i | −0.995989 | − | 0.0894753i | \(-0.971481\pi\) |
−0.420507 | + | 0.907289i | \(0.638148\pi\) | |||||||
\(198\) | 1.97729 | − | 3.42476i | 0.140520 | − | 0.243387i | ||||
\(199\) | 1.57492 | + | 2.72785i | 0.111643 | + | 0.193372i | 0.916433 | − | 0.400188i | \(-0.131055\pi\) |
−0.804790 | + | 0.593560i | \(0.797722\pi\) | |||||||
\(200\) | −6.54708 | − | 3.77996i | −0.462949 | − | 0.267283i | ||||
\(201\) | − | 19.0578i | − | 1.34423i | ||||||
\(202\) | −10.6374 | − | 6.14152i | −0.748446 | − | 0.432116i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 13.7395 | − | 23.7976i | 0.961959 | − | 1.66616i | ||||
\(205\) | 21.7622 | − | 37.6932i | 1.51994 | − | 2.63261i | ||||
\(206\) | 17.3790i | 1.21085i | ||||||||
\(207\) | −4.08048 | + | 7.06760i | −0.283613 | + | 0.491232i | ||||
\(208\) | 10.2599 | + | 1.99546i | 0.711393 | + | 0.138360i | ||||
\(209\) | −2.10851 | −0.145849 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43191 | + | 12.8725i | 0.511634 | + | 0.886176i | 0.999909 | + | 0.0134864i | \(0.00429298\pi\) |
−0.488275 | + | 0.872690i | \(0.662374\pi\) | |||||||
\(212\) | −12.0524 | −0.827764 | ||||||||
\(213\) | 12.6311 | + | 7.29255i | 0.865467 | + | 0.499678i | ||||
\(214\) | −7.00133 | + | 4.04222i | −0.478601 | + | 0.276321i | ||||
\(215\) | − | 13.1195i | − | 0.894741i | ||||||
\(216\) | − | 1.89779i | − | 0.129128i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.9878 | + | 19.0315i | 0.744191 | + | 1.28898i | ||||
\(219\) | 14.0016 | + | 8.08380i | 0.946137 | + | 0.546253i | ||||
\(220\) | 3.91012 | − | 6.77253i | 0.263620 | − | 0.456604i | ||||
\(221\) | −11.7345 | + | 13.4961i | −0.789347 | + | 0.907843i | ||||
\(222\) | 22.9903 | + | 39.8203i | 1.54301 | + | 2.67257i | ||||
\(223\) | −3.79396 | + | 2.19044i | −0.254062 | + | 0.146683i | −0.621623 | − | 0.783317i | \(-0.713526\pi\) |
0.367561 | + | 0.930000i | \(0.380193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.43147 | − | 14.6037i | 0.562098 | − | 0.973582i | ||||
\(226\) | −8.96971 | + | 5.17866i | −0.596656 | + | 0.344480i | ||||
\(227\) | 11.7488 | − | 6.78316i | 0.779793 | − | 0.450214i | −0.0565636 | − | 0.998399i | \(-0.518014\pi\) |
0.836357 | + | 0.548185i | \(0.184681\pi\) | |||||||
\(228\) | 11.4127 | − | 6.58915i | 0.755827 | − | 0.436377i | ||||
\(229\) | −14.3050 | + | 8.25900i | −0.945302 | + | 0.545770i | −0.891618 | − | 0.452788i | \(-0.850429\pi\) |
−0.0536833 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(230\) | −14.6576 | + | 25.3877i | −0.966495 | + | 1.67402i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.05272 | + | 0.607791i | −0.0691147 | + | 0.0399034i | ||||
\(233\) | −8.25131 | − | 14.2917i | −0.540561 | − | 0.936279i | −0.998872 | − | 0.0474874i | \(-0.984879\pi\) |
0.458311 | − | 0.888792i | \(-0.348455\pi\) | |||||||
\(234\) | 3.07106 | − | 15.7902i | 0.200761 | − | 1.03224i | ||||
\(235\) | 5.37078 | − | 9.30246i | 0.350351 | − | 0.606826i | ||||
\(236\) | 15.5441 | + | 8.97438i | 1.01183 | + | 0.584182i | ||||
\(237\) | 0.856657 | + | 1.48377i | 0.0556458 | + | 0.0963814i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 30.4210i | − | 1.96777i | −0.178796 | − | 0.983886i | \(-0.557220\pi\) | ||
0.178796 | − | 0.983886i | \(-0.442780\pi\) | |||||||
\(240\) | − | 23.6143i | − | 1.52429i | ||||||
\(241\) | −25.5602 | + | 14.7572i | −1.64648 | + | 0.950593i | −0.668018 | + | 0.744145i | \(0.732857\pi\) |
−0.978458 | + | 0.206448i | \(0.933810\pi\) | |||||||
\(242\) | −18.6594 | − | 10.7730i | −1.19947 | − | 0.692514i | ||||
\(243\) | 18.5837 | 1.19214 | ||||||||
\(244\) | 1.88523 | + | 3.26531i | 0.120689 | + | 0.209040i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −57.6497 | −3.67561 | ||||||||
\(247\) | −8.10982 | + | 2.79146i | −0.516015 | + | 0.177617i | ||||
\(248\) | −4.01530 | + | 6.95471i | −0.254972 | + | 0.441624i | ||||
\(249\) | 10.7828i | 0.683331i | ||||||||
\(250\) | 11.2931 | − | 19.5602i | 0.714236 | − | 1.23709i | ||||
\(251\) | 6.49134 | − | 11.2433i | 0.409730 | − | 0.709673i | −0.585130 | − | 0.810940i | \(-0.698956\pi\) |
0.994859 | + | 0.101267i | \(0.0322897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.96191 | − | 1.71006i | −0.186214 | − | 0.107511i | ||||
\(254\) | 25.9669i | 1.62931i | ||||||||
\(255\) | 34.9920 | + | 20.2026i | 2.19128 | + | 1.26514i | ||||
\(256\) | −3.30268 | − | 5.72042i | −0.206418 | − | 0.357526i | ||||
\(257\) | 2.29261 | − | 3.97091i | 0.143009 | − | 0.247698i | −0.785620 | − | 0.618710i | \(-0.787656\pi\) |
0.928628 | + | 0.371011i | \(0.120989\pi\) | |||||||
\(258\) | −15.0491 | + | 8.68862i | −0.936918 | + | 0.540930i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.07307 | − | 31.2253i | 0.376636 | − | 1.93651i | ||||
\(261\) | −1.35572 | − | 2.34818i | −0.0839170 | − | 0.145348i | ||||
\(262\) | 17.3026i | 1.06896i | ||||||||
\(263\) | −2.66499 | −0.164330 | −0.0821652 | − | 0.996619i | \(-0.526184\pi\) | ||||
−0.0821652 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(264\) | −1.90087 | −0.116990 | ||||||||
\(265\) | − | 17.7219i | − | 1.08865i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.08801 | − | 4.09227i | −0.433779 | − | 0.250443i | ||||
\(268\) | −17.8755 | + | 10.3204i | −1.09192 | + | 0.630421i | ||||
\(269\) | 5.96282 | + | 10.3279i | 0.363559 | + | 0.629703i | 0.988544 | − | 0.150934i | \(-0.0482280\pi\) |
−0.624984 | + | 0.780637i | \(0.714895\pi\) | |||||||
\(270\) | 15.2060 | 0.925409 | ||||||||
\(271\) | −11.2828 | − | 6.51416i | −0.685384 | − | 0.395707i | 0.116496 | − | 0.993191i | \(-0.462834\pi\) |
−0.801881 | + | 0.597484i | \(0.796167\pi\) | |||||||
\(272\) | 14.3790 | 0.871853 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7267 | 0.950082 | ||||||||
\(275\) | 6.12018 | + | 3.53349i | 0.369061 | + | 0.213077i | ||||
\(276\) | 21.3760 | 1.28668 | ||||||||
\(277\) | 10.6824 | + | 18.5025i | 0.641846 | + | 1.11171i | 0.985020 | + | 0.172438i | \(0.0551646\pi\) |
−0.343174 | + | 0.939272i | \(0.611502\pi\) | |||||||
\(278\) | −30.4718 | + | 17.5929i | −1.82758 | + | 1.05515i | ||||
\(279\) | −15.5130 | − | 8.95641i | −0.928737 | − | 0.536206i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.2678i | 1.03011i | 0.857158 | + | 0.515054i | \(0.172228\pi\) | ||||
−0.857158 | + | 0.515054i | \(0.827772\pi\) | |||||||
\(282\) | −14.2276 | −0.847242 | ||||||||
\(283\) | −21.2402 | −1.26260 | −0.631299 | − | 0.775539i | \(-0.717478\pi\) | ||||
−0.631299 | + | 0.775539i | \(0.717478\pi\) | |||||||
\(284\) | − | 15.7967i | − | 0.937360i | ||||||
\(285\) | 9.68870 | + | 16.7813i | 0.573909 | + | 0.994040i | ||||
\(286\) | 6.61741 | + | 1.28703i | 0.391295 | + | 0.0761037i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −14.6742 | + | 8.47218i | −0.864688 | + | 0.499228i | ||||
\(289\) | −3.80160 | + | 6.58457i | −0.223624 | + | 0.387327i | ||||
\(290\) | −4.86993 | − | 8.43496i | −0.285972 | − | 0.495318i | ||||
\(291\) | −0.907439 | − | 0.523910i | −0.0531950 | − | 0.0307122i | ||||
\(292\) | − | 17.5106i | − | 1.02473i | ||||||
\(293\) | 0.363782 | + | 0.210030i | 0.0212524 | + | 0.0122701i | 0.510589 | − | 0.859825i | \(-0.329428\pi\) |
−0.489336 | + | 0.872095i | \(0.662761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.1959 | + | 22.8561i | −0.768298 | + | 1.33073i | ||||
\(296\) | 4.56949 | − | 7.91459i | 0.265596 | − | 0.460026i | ||||
\(297\) | 1.77404i | 0.102940i | ||||||||
\(298\) | 2.65955 | − | 4.60648i | 0.154064 | − | 0.266846i | ||||
\(299\) | −13.6562 | − | 2.65601i | −0.789757 | − | 0.153601i | ||||
\(300\) | −44.1690 | −2.55010 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.7667 | − | 29.0408i | −0.964817 | − | 1.67111i | ||||
\(303\) | −13.1696 | −0.756577 | ||||||||
\(304\) | 5.97195 | + | 3.44791i | 0.342515 | + | 0.197751i | ||||
\(305\) | −4.80132 | + | 2.77204i | −0.274923 | + | 0.158727i | ||||
\(306\) | − | 22.1296i | − | 1.26507i | ||||||
\(307\) | 14.0807i | 0.803628i | 0.915721 | + | 0.401814i | \(0.131620\pi\) | ||||
−0.915721 | + | 0.401814i | \(0.868380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.31673 | + | 16.1370i | 0.530010 | + | 0.918004i | ||||
\(310\) | −55.7246 | − | 32.1726i | −3.16495 | − | 1.82728i | ||||
\(311\) | −5.19240 | + | 8.99349i | −0.294434 | + | 0.509974i | −0.974853 | − | 0.222849i | \(-0.928464\pi\) |
0.680419 | + | 0.732823i | \(0.261798\pi\) | |||||||
\(312\) | −7.31119 | + | 2.51657i | −0.413915 | + | 0.142473i | ||||
\(313\) | 3.42379 | + | 5.93018i | 0.193524 | + | 0.335194i | 0.946416 | − | 0.322951i | \(-0.104675\pi\) |
−0.752892 | + | 0.658145i | \(0.771342\pi\) | |||||||
\(314\) | −23.7173 | + | 13.6932i | −1.33845 | + | 0.772752i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.927818 | − | 1.60703i | 0.0521938 | − | 0.0904024i | ||||
\(317\) | 0.607299 | − | 0.350624i | 0.0341093 | − | 0.0196930i | −0.482848 | − | 0.875704i | \(-0.660398\pi\) |
0.516958 | + | 0.856011i | \(0.327064\pi\) | |||||||
\(318\) | −20.3285 | + | 11.7367i | −1.13997 | + | 0.658160i | ||||
\(319\) | 0.984082 | − | 0.568160i | 0.0550980 | − | 0.0318109i | ||||
\(320\) | −34.6272 | + | 19.9920i | −1.93572 | + | 1.11759i | ||||
\(321\) | −4.33400 | + | 7.50670i | −0.241900 | + | 0.418983i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.2183 | + | 5.89956i | −0.568563 | + | 0.328260i | ||||
\(324\) | −13.3152 | − | 23.0627i | −0.739735 | − | 1.28126i | ||||
\(325\) | 28.2177 | + | 5.48810i | 1.56523 | + | 0.304425i | ||||
\(326\) | 2.44634 | − | 4.23719i | 0.135490 | − | 0.234676i | ||||
\(327\) | 20.4052 | + | 11.7810i | 1.12841 | + | 0.651489i | ||||
\(328\) | 5.72916 | + | 9.92319i | 0.316340 | + | 0.547917i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 15.2307i | − | 0.838424i | ||||||
\(331\) | − | 4.19865i | − | 0.230778i | −0.993320 | − | 0.115389i | \(-0.963188\pi\) | ||
0.993320 | − | 0.115389i | \(-0.0368115\pi\) | |||||||
\(332\) | 10.1139 | − | 5.83924i | 0.555070 | − | 0.320470i | ||||
\(333\) | 17.6541 | + | 10.1926i | 0.967436 | + | 0.558550i | ||||
\(334\) | −29.0923 | −1.59186 | ||||||||
\(335\) | −15.1752 | − | 26.2842i | −0.829109 | − | 1.43606i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4278 | −1.11278 | −0.556388 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556388 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(338\) | 27.1560 | − | 3.81059i | 1.47709 | − | 0.207269i | ||||
\(339\) | −5.55247 | + | 9.61716i | −0.301569 | + | 0.522333i | ||||
\(340\) | − | 43.7617i | − | 2.37331i | ||||||
\(341\) | 3.75349 | − | 6.50123i | 0.203263 | − | 0.352061i | ||||
\(342\) | 5.30642 | − | 9.19098i | 0.286938 | − | 0.496991i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.99113 | + | 1.72693i | 0.161271 | + | 0.0931098i | ||||
\(345\) | 31.4313i | 1.69220i | ||||||||
\(346\) | 6.73045 | + | 3.88583i | 0.361831 | + | 0.208903i | ||||
\(347\) | −3.98500 | − | 6.90222i | −0.213926 | − | 0.370531i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901959\pi\) | |||||||
\(348\) | −3.55103 | + | 6.15057i | −0.190355 | + | 0.329705i | ||||
\(349\) | −18.7038 | + | 10.7986i | −1.00119 | + | 0.578037i | −0.908600 | − | 0.417668i | \(-0.862848\pi\) |
−0.0925892 | + | 0.995704i | \(0.529514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34866 | + | 6.82338i | 0.125362 | + | 0.364205i | ||||
\(352\) | −3.55055 | − | 6.14974i | −0.189245 | − | 0.327782i | ||||
\(353\) | − | 21.6176i | − | 1.15059i | −0.817946 | − | 0.575295i | \(-0.804887\pi\) | ||
0.817946 | − | 0.575295i | \(-0.195113\pi\) | |||||||
\(354\) | 34.9571 | 1.85795 | ||||||||
\(355\) | 23.2275 | 1.23279 | ||||||||
\(356\) | 8.86441i | 0.469813i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7648 | − | 6.21507i | −0.568938 | − | 0.328476i | ||||
\(359\) | 11.8501 | − | 6.84168i | 0.625426 | − | 0.361090i | −0.153552 | − | 0.988141i | \(-0.549071\pi\) |
0.778979 | + | 0.627051i | \(0.215738\pi\) | |||||||
\(360\) | 3.61172 | + | 6.25568i | 0.190354 | + | 0.329703i | ||||
\(361\) | 13.3414 | 0.702180 | ||||||||
\(362\) | −3.86443 | − | 2.23113i | −0.203110 | − | 0.117266i | ||||
\(363\) | −23.1012 | −1.21250 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.7477 | 1.34769 | ||||||||
\(366\) | 6.35953 | + | 3.67168i | 0.332418 | + | 0.191922i | ||||
\(367\) | 11.4128 | 0.595741 | 0.297871 | − | 0.954606i | \(-0.403724\pi\) | ||||
0.297871 | + | 0.954606i | \(0.403724\pi\) | |||||||
\(368\) | 5.59271 | + | 9.68685i | 0.291540 | + | 0.504962i | ||||
\(369\) | −22.1344 | + | 12.7793i | −1.15227 | + | 0.665263i | ||||
\(370\) | 63.4157 | + | 36.6131i | 3.29683 | + | 1.90342i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 46.9190i | 2.43264i | ||||||||
\(373\) | −31.2808 | −1.61966 | −0.809830 | − | 0.586664i | \(-0.800441\pi\) | ||||
−0.809830 | + | 0.586664i | \(0.800441\pi\) | |||||||
\(374\) | 9.27416 | 0.479555 | ||||||||
\(375\) | − | 24.2164i | − | 1.25053i | ||||||
\(376\) | 1.41392 | + | 2.44898i | 0.0729175 | + | 0.126297i | ||||
\(377\) | 3.03282 | − | 3.48811i | 0.156198 | − | 0.179647i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7421 | − | 13.7075i | 1.21955 | − | 0.704108i | 0.254729 | − | 0.967012i | \(-0.418014\pi\) |
0.964822 | + | 0.262904i | \(0.0846803\pi\) | |||||||
\(380\) | 10.4935 | − | 18.1753i | 0.538307 | − | 0.932374i | ||||
\(381\) | 13.9206 | + | 24.1112i | 0.713175 | + | 1.23526i | ||||
\(382\) | 20.7644 | + | 11.9883i | 1.06240 | + | 0.613377i | ||||
\(383\) | 16.1006i | 0.822705i | 0.911476 | + | 0.411352i | \(0.134943\pi\) | ||||
−0.911476 | + | 0.411352i | \(0.865057\pi\) | |||||||
\(384\) | 14.4824 | + | 8.36142i | 0.739052 | + | 0.426692i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8600 | − | 25.7382i | 0.756353 | − | 1.31004i | ||||
\(387\) | −3.85204 | + | 6.67193i | −0.195810 | + | 0.339153i | ||||
\(388\) | 1.13486i | 0.0576139i | ||||||||
\(389\) | 10.5690 | − | 18.3060i | 0.535870 | − | 0.928153i | −0.463251 | − | 0.886227i | \(-0.653317\pi\) |
0.999121 | − | 0.0419264i | \(-0.0133495\pi\) | |||||||
\(390\) | −20.1640 | − | 58.5810i | −1.02104 | − | 2.96636i | ||||
\(391\) | −19.1388 | −0.967893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.27576 | + | 16.0661i | 0.467900 | + | 0.810427i | ||||
\(394\) | 48.4255 | 2.43964 | ||||||||
\(395\) | 2.36298 | + | 1.36427i | 0.118894 | + | 0.0686437i | ||||
\(396\) | −3.97699 | + | 2.29612i | −0.199851 | + | 0.115384i | ||||
\(397\) | 13.0984i | 0.657390i | 0.944436 | + | 0.328695i | \(0.106609\pi\) | ||||
−0.944436 | + | 0.328695i | \(0.893391\pi\) | |||||||
\(398\) | − | 6.64426i | − | 0.333046i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.5562 | − | 20.0159i | −0.577808 | − | 1.00079i | ||||
\(401\) | −16.8396 | − | 9.72236i | −0.840930 | − | 0.485511i | 0.0166501 | − | 0.999861i | \(-0.494700\pi\) |
−0.857580 | + | 0.514350i | \(0.828033\pi\) | |||||||
\(402\) | −20.1001 | + | 34.8144i | −1.00250 | + | 1.73639i | ||||
\(403\) | 5.82979 | − | 29.9745i | 0.290402 | − | 1.49314i | ||||
\(404\) | 7.13182 | + | 12.3527i | 0.354821 | + | 0.614568i | ||||
\(405\) | 33.9114 | − | 19.5788i | 1.68507 | − | 0.972876i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.27154 | + | 7.39853i | −0.211732 | + | 0.366731i | ||||
\(408\) | −9.21206 | + | 5.31859i | −0.456065 | + | 0.263309i | ||||
\(409\) | 20.8330 | − | 12.0279i | 1.03013 | − | 0.594743i | 0.113105 | − | 0.993583i | \(-0.463921\pi\) |
0.917020 | + | 0.398840i | \(0.130587\pi\) | |||||||
\(410\) | −79.5096 | + | 45.9049i | −3.92670 | + | 2.26708i | ||||
\(411\) | 14.6028 | − | 8.43092i | 0.720302 | − | 0.415867i | ||||
\(412\) | 10.0907 | − | 17.4775i | 0.497131 | − | 0.861056i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.9083 | − | 8.60732i | 0.732703 | − | 0.423026i | ||||
\(415\) | 8.58603 | + | 14.8714i | 0.421472 | + | 0.730011i | ||||
\(416\) | −21.7979 | − | 18.9527i | −1.06873 | − | 0.929234i | ||||
\(417\) | −18.8628 | + | 32.6713i | −0.923714 | + | 1.59992i | ||||
\(418\) | 3.85179 | + | 2.22383i | 0.188397 | + | 0.108771i | ||||
\(419\) | 19.5119 | + | 33.7956i | 0.953218 | + | 1.65102i | 0.738394 | + | 0.674370i | \(0.235585\pi\) |
0.214825 | + | 0.976653i | \(0.431082\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.0284i | − | 1.07360i | −0.843710 | − | 0.536799i | \(-0.819633\pi\) | ||
0.843710 | − | 0.536799i | \(-0.180367\pi\) | |||||||
\(422\) | − | 31.3536i | − | 1.52627i | ||||||
\(423\) | −5.46263 | + | 3.15385i | −0.265602 | + | 0.153346i | ||||
\(424\) | 4.04045 | + | 2.33275i | 0.196221 | + | 0.113289i | ||||
\(425\) | 39.5465 | 1.91828 | ||||||||
\(426\) | −15.3828 | − | 26.6438i | −0.745301 | − | 1.29090i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.38803 | 0.453787 | ||||||||
\(429\) | 6.83447 | − | 2.35248i | 0.329971 | − | 0.113579i | ||||
\(430\) | −13.8370 | + | 23.9664i | −0.667281 | + | 1.15576i | ||||
\(431\) | − | 35.8797i | − | 1.72826i | −0.503267 | − | 0.864131i | \(-0.667869\pi\) | ||
0.503267 | − | 0.864131i | \(-0.332131\pi\) | |||||||
\(432\) | 2.90098 | − | 5.02464i | 0.139573 | − | 0.241748i | ||||
\(433\) | −6.10678 | + | 10.5773i | −0.293473 | + | 0.508310i | −0.974629 | − | 0.223828i | \(-0.928144\pi\) |
0.681155 | + | 0.732139i | \(0.261478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.04381 | − | 5.22145i | −0.433618 | − | 0.250349i | ||||
\(436\) | − | 25.5192i | − | 1.22215i | ||||||
\(437\) | −7.94884 | − | 4.58927i | −0.380245 | − | 0.219534i | ||||
\(438\) | −17.0519 | − | 29.5347i | −0.814770 | − | 1.41122i | ||||
\(439\) | 7.87765 | − | 13.6445i | 0.375980 | − | 0.651216i | −0.614493 | − | 0.788922i | \(-0.710639\pi\) |
0.990473 | + | 0.137706i | \(0.0439728\pi\) | |||||||
\(440\) | −2.62165 | + | 1.51361i | −0.124982 | + | 0.0721586i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.6706 | − | 12.2781i | 1.69668 | − | 0.584009i | ||||
\(443\) | 7.53532 | + | 13.0516i | 0.358014 | + | 0.620099i | 0.987629 | − | 0.156809i | \(-0.0501207\pi\) |
−0.629615 | + | 0.776907i | \(0.716787\pi\) | |||||||
\(444\) | − | 53.3947i | − | 2.53400i | ||||||
\(445\) | −13.0342 | −0.617883 | ||||||||
\(446\) | 9.24099 | 0.437574 | ||||||||
\(447\) | − | 5.70305i | − | 0.269745i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.6585 | + | 15.3913i | 1.25809 | + | 0.726360i | 0.972703 | − | 0.232052i | \(-0.0745441\pi\) |
0.285388 | + | 0.958412i | \(0.407877\pi\) | |||||||
\(450\) | −30.8049 | + | 17.7852i | −1.45216 | + | 0.838404i | ||||
\(451\) | −5.35559 | − | 9.27616i | −0.252185 | − | 0.436797i | ||||
\(452\) | 12.0274 | 0.565722 | ||||||||
\(453\) | −31.1370 | − | 17.9770i | −1.46295 | − | 0.844632i | ||||
\(454\) | −28.6166 | −1.34304 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.10133 | −0.238892 | ||||||||
\(457\) | 6.71687 | + | 3.87799i | 0.314202 | + | 0.181405i | 0.648805 | − | 0.760955i | \(-0.275269\pi\) |
−0.334603 | + | 0.942359i | \(0.608602\pi\) | |||||||
\(458\) | 34.8429 | 1.62810 | ||||||||
\(459\) | 4.96373 | + | 8.59743i | 0.231687 | + | 0.401294i | ||||
\(460\) | 29.4814 | − | 17.0211i | 1.37458 | − | 0.793613i | ||||
\(461\) | −1.27498 | − | 0.736110i | −0.0593817 | − | 0.0342840i | 0.470015 | − | 0.882658i | \(-0.344248\pi\) |
−0.529397 | + | 0.848374i | \(0.677582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.0366i | − | 0.652335i | −0.945312 | − | 0.326168i | \(-0.894243\pi\) | ||
0.945312 | − | 0.326168i | \(-0.105757\pi\) | |||||||
\(464\) | −3.71630 | −0.172525 | ||||||||
\(465\) | −68.9898 | −3.19933 | ||||||||
\(466\) | 34.8104i | 1.61256i | ||||||||
\(467\) | −15.6903 | − | 27.1764i | −0.726060 | − | 1.25757i | −0.958536 | − | 0.284971i | \(-0.908016\pi\) |
0.232476 | − | 0.972602i | \(-0.425317\pi\) | |||||||
\(468\) | −12.2566 | + | 14.0966i | −0.566562 | + | 0.651614i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −19.6225 | + | 11.3291i | −0.905119 | + | 0.522571i | ||||
\(471\) | −14.6816 | + | 25.4293i | −0.676492 | + | 1.17172i | ||||
\(472\) | −3.47399 | − | 6.01713i | −0.159903 | − | 0.276961i | ||||
\(473\) | −2.79610 | − | 1.61433i | −0.128565 | − | 0.0742268i | ||||
\(474\) | − | 3.61404i | − | 0.165999i | ||||||
\(475\) | 16.4246 | + | 9.48277i | 0.753614 | + | 0.435099i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.20337 | + | 9.01251i | −0.238246 | + | 0.412654i | ||||
\(478\) | −32.0849 | + | 55.5726i | −1.46753 | + | 2.54183i | ||||
\(479\) | − | 41.1951i | − | 1.88225i | −0.338059 | − | 0.941125i | \(-0.609770\pi\) | ||
0.338059 | − | 0.941125i | \(-0.390230\pi\) | |||||||
\(480\) | −32.6299 | + | 56.5167i | −1.48935 | + | 2.57962i | ||||
\(481\) | −6.63441 | + | 34.1116i | −0.302503 | + | 1.55535i | ||||
\(482\) | 62.2572 | 2.83574 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.5101 | + | 21.6681i | 0.568641 | + | 0.984914i | ||||
\(485\) | −1.66870 | −0.0757719 | ||||||||
\(486\) | −33.9484 | − | 19.6001i | −1.53993 | − | 0.889078i | ||||
\(487\) | −24.5314 | + | 14.1632i | −1.11163 | + | 0.641798i | −0.939250 | − | 0.343234i | \(-0.888478\pi\) |
−0.172376 | + | 0.985031i | \(0.555144\pi\) | |||||||
\(488\) | − | 1.45955i | − | 0.0660706i | ||||||
\(489\) | − | 5.24584i | − | 0.237225i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3931 | + | 30.1258i | 0.784941 | + | 1.35956i | 0.929034 | + | 0.369993i | \(0.120640\pi\) |
−0.144094 | + | 0.989564i | \(0.546027\pi\) | |||||||
\(492\) | 57.9765 | + | 33.4728i | 2.61378 | + | 1.50907i | ||||
\(493\) | 3.17940 | − | 5.50687i | 0.143193 | − | 0.248017i | ||||
\(494\) | 17.7590 | + | 3.45398i | 0.799016 | + | 0.155402i | ||||
\(495\) | −3.37622 | − | 5.84778i | −0.151750 | − | 0.262838i | ||||
\(496\) | −21.2621 | + | 12.2757i | −0.954695 | + | 0.551194i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.3725 | − | 19.6978i | 0.509615 | − | 0.882680i | ||||
\(499\) | −0.0601788 | + | 0.0347442i | −0.00269397 | + | 0.00155537i | −0.501346 | − | 0.865247i | \(-0.667162\pi\) |
0.498652 | + | 0.866802i | \(0.333828\pi\) | |||||||
\(500\) | −22.7142 | + | 13.1140i | −1.01581 | + | 0.586477i | ||||
\(501\) | −27.0133 | + | 15.5961i | −1.20686 | + | 0.696783i | ||||
\(502\) | −23.7165 | + | 13.6928i | −1.05852 | + | 0.611138i | ||||
\(503\) | 12.8686 | − | 22.2891i | 0.573782 | − | 0.993820i | −0.422391 | − | 0.906414i | \(-0.638809\pi\) |
0.996173 | − | 0.0874060i | \(-0.0278578\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1634 | + | 10.4866i | −0.808260 | + | 0.466649i | ||||
\(506\) | 3.60719 | + | 6.24783i | 0.160359 | + | 0.277750i | ||||
\(507\) | 23.1725 | − | 18.0964i | 1.02913 | − | 0.803688i | ||||
\(508\) | 15.0770 | − | 26.1141i | 0.668933 | − | 1.15863i | ||||
\(509\) | −6.09682 | − | 3.52000i | −0.270237 | − | 0.156021i | 0.358759 | − | 0.933430i | \(-0.383200\pi\) |
−0.628995 | + | 0.777409i | \(0.716533\pi\) | |||||||
\(510\) | −42.6152 | − | 73.8117i | −1.88703 | − | 3.26844i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 28.7215i | 1.26932i | ||||||||
\(513\) | 4.76097i | 0.210202i | ||||||||
\(514\) | −8.37619 | + | 4.83599i | −0.369458 | + | 0.213307i | ||||
\(515\) | 25.6990 | + | 14.8373i | 1.13243 | + | 0.653810i | ||||
\(516\) | 20.1793 | 0.888342 | ||||||||
\(517\) | −1.32173 | − | 2.28930i | −0.0581295 | − | 0.100683i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.33263 | 0.365762 | ||||||||
\(520\) | −8.07961 | + | 9.29252i | −0.354314 | + | 0.407504i | ||||
\(521\) | 8.16266 | − | 14.1381i | 0.357613 | − | 0.619403i | −0.629949 | − | 0.776637i | \(-0.716924\pi\) |
0.987561 | + | 0.157234i | \(0.0502575\pi\) | |||||||
\(522\) | 5.71948i | 0.250335i | ||||||||
\(523\) | −3.54473 | + | 6.13965i | −0.155000 | + | 0.268468i | −0.933059 | − | 0.359723i | \(-0.882871\pi\) |
0.778059 | + | 0.628191i | \(0.216204\pi\) | |||||||
\(524\) | 10.0463 | − | 17.4007i | 0.438874 | − | 0.760152i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.86836 | + | 2.81075i | 0.212271 | + | 0.122555i | ||||
\(527\) | − | 42.0086i | − | 1.82993i | ||||||
\(528\) | −5.03280 | − | 2.90569i | −0.219025 | − | 0.126454i | ||||
\(529\) | 4.05594 | + | 7.02510i | 0.176345 | + | 0.305439i | ||||
\(530\) | −18.6912 | + | 32.3741i | −0.811894 | + | 1.40624i | ||||
\(531\) | 13.4216 | − | 7.74899i | 0.582449 | − | 0.336277i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.8796 | − | 28.5880i | −1.42417 | − | 1.23828i | ||||
\(534\) | 8.63218 | + | 14.9514i | 0.373551 | + | 0.647009i | ||||
\(535\) | 13.8042i | 0.596807i | ||||||||
\(536\) | 7.99010 | 0.345120 | ||||||||
\(537\) | −13.3274 | −0.575118 | ||||||||
\(538\) | − | 25.1558i | − | 1.08454i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −15.2922 | − | 8.82897i | −0.658073 | − | 0.379938i | ||||
\(541\) | −22.0977 | + | 12.7581i | −0.950055 | + | 0.548515i | −0.893098 | − | 0.449862i | \(-0.851473\pi\) |
−0.0569571 | + | 0.998377i | \(0.518140\pi\) | |||||||
\(542\) | 13.7409 | + | 23.7999i | 0.590222 | + | 1.02229i | ||||
\(543\) | −4.78436 | −0.205316 | ||||||||
\(544\) | −34.4136 | − | 19.8687i | −1.47547 | − | 0.851864i | ||||
\(545\) | 37.5235 | 1.60733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3073 | −0.568978 | −0.284489 | − | 0.958679i | \(-0.591824\pi\) | ||||
−0.284489 | + | 0.958679i | \(0.591824\pi\) | |||||||
\(548\) | −15.8158 | − | 9.13126i | −0.675618 | − | 0.390068i | ||||
\(549\) | 3.25562 | 0.138947 | ||||||||
\(550\) | −7.45350 | − | 12.9098i | −0.317818 | − | 0.550478i | ||||
\(551\) | 2.64097 | − | 1.52476i | 0.112509 | − | 0.0649571i | ||||
\(552\) | −7.16607 | − | 4.13733i | −0.305008 | − | 0.176096i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 45.0669i | − | 1.91471i | ||||||
\(555\) | 78.5118 | 3.33264 | ||||||||
\(556\) | 40.8594 | 1.73282 | ||||||||
\(557\) | − | 17.0071i | − | 0.720612i | −0.932834 | − | 0.360306i | \(-0.882672\pi\) | ||
0.932834 | − | 0.360306i | \(-0.117328\pi\) | |||||||
\(558\) | 18.8926 | + | 32.7229i | 0.799786 | + | 1.38527i | ||||
\(559\) | −12.8916 | − | 2.50732i | −0.545259 | − | 0.106048i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.61140 | − | 4.97179i | 0.363573 | − | 0.209909i | ||||
\(562\) | 18.2122 | − | 31.5445i | 0.768235 | − | 1.33062i | ||||
\(563\) | 12.4596 | + | 21.5807i | 0.525111 | + | 0.909519i | 0.999572 | + | 0.0292428i | \(0.00930961\pi\) |
−0.474461 | + | 0.880276i | \(0.657357\pi\) | |||||||
\(564\) | 14.3083 | + | 8.26088i | 0.602486 | + | 0.347846i | ||||
\(565\) | 17.6851i | 0.744019i | ||||||||
\(566\) | 38.8013 | + | 22.4019i | 1.63094 | + | 0.941623i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.05745 | + | 5.29566i | −0.128288 | + | 0.222201i | ||||
\(569\) | 2.94065 | − | 5.09335i | 0.123278 | − | 0.213524i | −0.797780 | − | 0.602948i | \(-0.793993\pi\) |
0.921059 | + | 0.389424i | \(0.127326\pi\) | |||||||
\(570\) | − | 40.8745i | − | 1.71204i | ||||||
\(571\) | 4.46311 | − | 7.73034i | 0.186775 | − | 0.323504i | −0.757398 | − | 0.652954i | \(-0.773530\pi\) |
0.944173 | + | 0.329449i | \(0.106863\pi\) | |||||||
\(572\) | −5.90764 | − | 5.13655i | −0.247011 | − | 0.214770i | ||||
\(573\) | 25.7074 | 1.07394 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.3816 | + | 26.6417i | 0.641457 | + | 1.11104i | ||||
\(576\) | 23.4796 | 0.978317 | ||||||||
\(577\) | 31.3443 | + | 18.0967i | 1.30488 | + | 0.753374i | 0.981237 | − | 0.192804i | \(-0.0617583\pi\) |
0.323645 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(578\) | 13.8894 | − | 8.01905i | 0.577723 | − | 0.333549i | ||||
\(579\) | − | 31.8652i | − | 1.32427i | ||||||
\(580\) | 11.3104i | 0.469638i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.10513 | + | 1.91414i | 0.0458091 | + | 0.0793437i | ||||
\(583\) | −3.77699 | − | 2.18065i | −0.156427 | − | 0.0903132i | ||||
\(584\) | −3.38919 | + | 5.87025i | −0.140246 | + | 0.242913i | ||||
\(585\) | −20.7276 | − | 18.0222i | −0.856982 | − | 0.745124i | ||||
\(586\) | −0.443035 | − | 0.767358i | −0.0183016 | − | 0.0316993i | ||||
\(587\) | −31.6008 | + | 18.2447i | −1.30431 | + | 0.753041i | −0.981139 | − | 0.193301i | \(-0.938080\pi\) |
−0.323166 | + | 0.946342i | \(0.604747\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0732 | − | 17.4472i | 0.415058 | − | 0.718901i | ||||
\(590\) | 48.2123 | − | 27.8354i | 1.98487 | − | 1.14596i | ||||
\(591\) | 44.9649 | − | 25.9605i | 1.84961 | − | 1.06787i | ||||
\(592\) | 24.1967 | − | 13.9699i | 0.994476 | − | 0.574161i | ||||
\(593\) | 30.3048 | − | 17.4965i | 1.24447 | − | 0.718495i | 0.274468 | − | 0.961596i | \(-0.411498\pi\) |
0.970001 | + | 0.243102i | \(0.0781649\pi\) | |||||||
\(594\) | 1.87107 | − | 3.24079i | 0.0767711 | − | 0.132971i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.34926 | + | 3.08839i | −0.219114 | + | 0.126506i | ||||
\(597\) | −3.56193 | − | 6.16944i | −0.145780 | − | 0.252498i | ||||
\(598\) | 22.1456 | + | 19.2550i | 0.905601 | + | 0.787397i | ||||
\(599\) | 16.2526 | − | 28.1503i | 0.664062 | − | 1.15019i | −0.315476 | − | 0.948934i | \(-0.602164\pi\) |
0.979539 | − | 0.201256i | \(-0.0645025\pi\) | |||||||
\(600\) | 14.8072 | + | 8.54894i | 0.604501 | + | 0.349009i | ||||
\(601\) | 10.0390 | + | 17.3881i | 0.409500 | + | 0.709275i | 0.994834 | − | 0.101518i | \(-0.0323699\pi\) |
−0.585334 | + | 0.810792i | \(0.699037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.8225i | 0.725788i | ||||||||
\(604\) | 38.9406i | 1.58447i | ||||||||
\(605\) | −31.8608 | + | 18.3949i | −1.29533 | + | 0.747858i | ||||
\(606\) | 24.0581 | + | 13.8900i | 0.977294 | + | 0.564241i | ||||
\(607\) | −9.71601 | −0.394361 | −0.197180 | − | 0.980367i | \(-0.563178\pi\) | ||||
−0.197180 | + | 0.980367i | \(0.563178\pi\) | |||||||
\(608\) | −9.52856 | − | 16.5039i | −0.386434 | − | 0.669323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.6946 | 0.473502 | ||||||||
\(611\) | −8.11449 | − | 7.05535i | −0.328277 | − | 0.285429i | ||||
\(612\) | −12.8490 | + | 22.2551i | −0.519389 | + | 0.899607i | ||||
\(613\) | − | 11.8816i | − | 0.479893i | −0.970786 | − | 0.239947i | \(-0.922870\pi\) | ||
0.970786 | − | 0.239947i | \(-0.0771299\pi\) | |||||||
\(614\) | 14.8508 | − | 25.7224i | 0.599331 | − | 1.03807i | ||||
\(615\) | −49.2184 | + | 85.2488i | −1.98468 | + | 3.43756i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3105 | − | 9.99422i | −0.696895 | − | 0.402352i | 0.109295 | − | 0.994009i | \(-0.465141\pi\) |
−0.806190 | + | 0.591657i | \(0.798474\pi\) | |||||||
\(618\) | − | 39.3052i | − | 1.58109i | ||||||
\(619\) | −36.1285 | − | 20.8588i | −1.45213 | − | 0.838386i | −0.453525 | − | 0.891244i | \(-0.649834\pi\) |
−0.998602 | + | 0.0528581i | \(0.983167\pi\) | |||||||
\(620\) | 37.3603 | + | 64.7100i | 1.50043 | + | 2.59882i | ||||
\(621\) | −3.86129 | + | 6.68794i | −0.154948 | + | 0.268378i | ||||
\(622\) | 18.9708 | − | 10.9528i | 0.760659 | − | 0.439166i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.2042 | − | 4.51302i | −0.928911 | − | 0.180665i | ||||
\(625\) | 0.649140 | + | 1.12434i | 0.0259656 | + | 0.0449737i | ||||
\(626\) | − | 14.4442i | − | 0.577307i | ||||||
\(627\) | 4.76871 | 0.190444 | ||||||||
\(628\) | 31.8023 | 1.26905 | ||||||||
\(629\) | 47.8066i | 1.90618i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2780 | + | 8.82074i | 0.608206 | + | 0.351148i | 0.772263 | − | 0.635303i | \(-0.219125\pi\) |
−0.164057 | + | 0.986451i | \(0.552458\pi\) | |||||||
\(632\) | −0.622082 | + | 0.359159i | −0.0247451 | + | 0.0142866i | ||||
\(633\) | −16.8084 | − | 29.1130i | −0.668073 | − | 1.15714i | ||||
\(634\) | −1.47921 | −0.0587468 | ||||||||
\(635\) | 38.3982 | + | 22.1692i | 1.52379 | + | 0.879759i | ||||
\(636\) | 27.2584 | 1.08086 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.39694 | −0.0948958 | ||||||||
\(639\) | −11.8124 | − | 6.81987i | −0.467290 | − | 0.269790i | ||||
\(640\) | 26.6319 | 1.05272 | ||||||||
\(641\) | −5.46012 | − | 9.45721i | −0.215662 | − | 0.373537i | 0.737815 | − | 0.675003i | \(-0.235858\pi\) |
−0.953477 | + | 0.301465i | \(0.902524\pi\) | |||||||
\(642\) | 15.8346 | − | 9.14208i | 0.624940 | − | 0.360809i | ||||
\(643\) | −15.2725 | − | 8.81757i | −0.602288 | − | 0.347731i | 0.167653 | − | 0.985846i | \(-0.446381\pi\) |
−0.769941 | + | 0.638115i | \(0.779714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.6716i | 1.16832i | ||||||||
\(646\) | 24.8889 | 0.979241 | ||||||||
\(647\) | 16.6726 | 0.655469 | 0.327735 | − | 0.944770i | \(-0.393715\pi\) | ||||
0.327735 | + | 0.944770i | \(0.393715\pi\) | |||||||
\(648\) | 10.3087i | 0.404963i | ||||||||
\(649\) | 3.24747 | + | 5.62479i | 0.127474 | + | 0.220792i | ||||
\(650\) | −45.7593 | − | 39.7866i | −1.79483 | − | 1.56056i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.92042 | + | 2.84080i | −0.192698 | + | 0.111254i | ||||
\(653\) | 3.38664 | − | 5.86584i | 0.132530 | − | 0.229548i | −0.792121 | − | 0.610364i | \(-0.791023\pi\) |
0.924651 | + | 0.380816i | \(0.124357\pi\) | |||||||
\(654\) | −24.8506 | − | 43.0426i | −0.971737 | − | 1.68310i | ||||
\(655\) | 25.5860 | + | 14.7721i | 0.999727 | + | 0.577193i | ||||
\(656\) | 35.0306i | 1.36772i | ||||||||
\(657\) | −13.0940 | − | 7.55983i | −0.510846 | − | 0.294937i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.7680 | + | 29.0431i | −0.653190 | + | 1.13136i | 0.329154 | + | 0.944276i | \(0.393236\pi\) |
−0.982344 | + | 0.187082i | \(0.940097\pi\) | |||||||
\(660\) | −8.84332 | + | 15.3171i | −0.344226 | + | 0.596216i | ||||
\(661\) | 25.1661i | 0.978848i | 0.872046 | + | 0.489424i | \(0.162793\pi\) | ||||
−0.872046 | + | 0.489424i | \(0.837207\pi\) | |||||||
\(662\) | −4.42829 | + | 7.67002i | −0.172110 | + | 0.298104i | ||||
\(663\) | 26.5393 | − | 30.5233i | 1.03070 | − | 1.18543i | ||||
\(664\) | −4.52075 | −0.175439 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.5001 | − | 37.2393i | −0.833112 | − | 1.44299i | ||||
\(667\) | 4.94651 | 0.191529 | ||||||||
\(668\) | 29.2572 | + | 16.8917i | 1.13200 | + | 0.653558i | ||||
\(669\) | 8.58060 | − | 4.95401i | 0.331745 | − | 0.191533i | ||||
\(670\) | 64.0207i | 2.47334i | ||||||||
\(671\) | 1.36438i | 0.0526713i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.927341 | − | 1.60620i | −0.0357464 | − | 0.0619145i | 0.847599 | − | 0.530638i | \(-0.178048\pi\) |
−0.883345 | + | 0.468723i | \(0.844714\pi\) | |||||||
\(674\) | 37.3172 | + | 21.5451i | 1.43741 | + | 0.829887i | ||||
\(675\) | 7.97855 | − | 13.8193i | 0.307094 | − | 0.531903i | ||||
\(676\) | −29.5225 | − | 11.9352i | −1.13548 | − | 0.459047i | ||||
\(677\) | −7.36044 | − | 12.7487i | −0.282885 | − | 0.489971i | 0.689209 | − | 0.724562i | \(-0.257958\pi\) |
−0.972094 | + | 0.234592i | \(0.924625\pi\) | |||||||
\(678\) | 20.2863 | − | 11.7123i | 0.779092 | − | 0.449809i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.47009 | + | 14.6706i | −0.324813 | + | 0.562593i | ||||
\(681\) | −26.5716 | + | 15.3411i | −1.01823 | + | 0.587873i | ||||
\(682\) | −13.7136 | + | 7.91756i | −0.525122 | + | 0.303179i | ||||
\(683\) | −6.87930 | + | 3.97177i | −0.263229 | + | 0.151975i | −0.625807 | − | 0.779978i | \(-0.715230\pi\) |
0.362578 | + | 0.931954i | \(0.381897\pi\) | |||||||
\(684\) | −10.6730 | + | 6.16206i | −0.408092 | + | 0.235612i | ||||
\(685\) | 13.4266 | − | 23.2556i | 0.513005 | − | 0.888551i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.3529 | − | 18.6790i | 1.23434 | − | 0.712647i | ||||
\(688\) | 5.27960 | + | 9.14454i | 0.201283 | + | 0.348632i | ||||
\(689\) | −17.4142 | − | 3.38691i | −0.663427 | − | 0.129031i | ||||
\(690\) | 33.1504 | − | 57.4182i | 1.26201 | − | 2.18587i | ||||
\(691\) | 8.86002 | + | 5.11534i | 0.337051 | + | 0.194597i | 0.658967 | − | 0.752172i | \(-0.270994\pi\) |
−0.321916 | + | 0.946768i | \(0.604327\pi\) | |||||||
\(692\) | −4.51240 | − | 7.81571i | −0.171536 | − | 0.297109i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.8118i | 0.638168i | ||||||||
\(695\) | 60.0797i | 2.27895i | ||||||||
\(696\) | 2.38089 | − | 1.37461i | 0.0902475 | − | 0.0521044i | ||||
\(697\) | −51.9089 | − | 29.9696i | −1.96619 | − | 1.13518i | ||||
\(698\) | 45.5570 | 1.72436 | ||||||||
\(699\) | 18.6616 | + | 32.3228i | 0.705845 | + | 1.22256i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5978 | −0.626891 | −0.313445 | − | 0.949606i | \(-0.601483\pi\) | ||||
−0.313445 | + | 0.949606i | \(0.601483\pi\) | |||||||
\(702\) | 2.90609 | − | 14.9420i | 0.109683 | − | 0.563948i | ||||
\(703\) | −11.4635 | + | 19.8553i | −0.432353 | + | 0.748857i | ||||
\(704\) | 9.83992i | 0.370856i | ||||||||
\(705\) | −12.1468 | + | 21.0389i | −0.457475 | + | 0.792371i | ||||
\(706\) | −22.8000 | + | 39.4907i | −0.858088 | + | 1.48625i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −35.1552 | − | 20.2969i | −1.32121 | − | 0.762804i | ||||
\(709\) | − | 47.8659i | − | 1.79764i | −0.438318 | − | 0.898820i | \(-0.644426\pi\) | ||
0.438318 | − | 0.898820i | \(-0.355574\pi\) | |||||||
\(710\) | −42.4316 | − | 24.4979i | −1.59243 | − | 0.919389i | ||||
\(711\) | −0.801130 | − | 1.38760i | −0.0300447 | − | 0.0520390i | ||||
\(712\) | 1.71571 | − | 2.97170i | 0.0642990 | − | 0.111369i | ||||
\(713\) | 28.3004 | − | 16.3393i | 1.05986 | − | 0.611910i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.55279 | − | 8.68661i | 0.282458 | − | 0.324861i | ||||
\(716\) | 7.21722 | + | 12.5006i | 0.269720 | + | 0.467169i | ||||
\(717\) | 68.8017i | 2.56944i | ||||||||
\(718\) | −28.8635 | −1.07718 | ||||||||
\(719\) | −38.0922 | −1.42060 | −0.710300 | − | 0.703899i | \(-0.751441\pi\) | ||||
−0.710300 | + | 0.703899i | \(0.751441\pi\) | |||||||
\(720\) | 22.0836i | 0.823009i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.3719 | − | 14.0711i | −0.907028 | − | 0.523673i | ||||
\(723\) | 57.8081 | − | 33.3755i | 2.14991 | − | 1.24125i | ||||
\(724\) | 2.59089 | + | 4.48756i | 0.0962898 | + | 0.166779i | ||||
\(725\) | −10.2209 | −0.379596 | ||||||||
\(726\) | 42.2009 | + | 24.3647i | 1.56622 | + | 0.904259i | ||||
\(727\) | −15.4059 | −0.571374 | −0.285687 | − | 0.958323i | \(-0.592222\pi\) | ||||
−0.285687 | + | 0.958323i | \(0.592222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.41460 | −0.348689 | ||||||||
\(730\) | −47.0354 | − | 27.1559i | −1.74086 | − | 1.00508i | ||||
\(731\) | −18.0674 | −0.668246 | ||||||||
\(732\) | −4.26372 | − | 7.38498i | −0.157592 | − | 0.272957i | ||||
\(733\) | 10.0717 | − | 5.81490i | 0.372007 | − | 0.214778i | −0.302328 | − | 0.953204i | \(-0.597764\pi\) |
0.674335 | + | 0.738426i | \(0.264430\pi\) | |||||||
\(734\) | −20.8487 | − | 12.0370i | −0.769538 | − | 0.444293i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 30.9117i | − | 1.13942i | ||||||
\(737\) | −7.46911 | −0.275128 | ||||||||
\(738\) | 53.9130 | 1.98456 | ||||||||
\(739\) | 2.68901i | 0.0989168i | 0.998776 | + | 0.0494584i | \(0.0157495\pi\) | ||||
−0.998776 | + | 0.0494584i | \(0.984250\pi\) | |||||||
\(740\) | −42.5168 | − | 73.6413i | −1.56295 | − | 2.70711i | ||||
\(741\) | 18.3416 | − | 6.31331i | 0.673794 | − | 0.231925i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.13665 | + | 1.23360i | −0.0783862 | + | 0.0452563i | −0.538681 | − | 0.842510i | \(-0.681077\pi\) |
0.460295 | + | 0.887766i | \(0.347744\pi\) | |||||||
\(744\) | 9.08120 | − | 15.7291i | 0.332933 | − | 0.576657i | ||||
\(745\) | −4.54118 | − | 7.86556i | −0.166376 | − | 0.288172i | ||||
\(746\) | 57.1433 | + | 32.9917i | 2.09217 | + | 1.20791i | ||||
\(747\) | − | 10.0839i | − | 0.368949i | ||||||
\(748\) | −9.32673 | − | 5.38479i | −0.341019 | − | 0.196887i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −25.5409 | + | 44.2382i | −0.932623 | + | 1.61535i | ||||
\(751\) | −18.9592 | + | 32.8383i | −0.691832 | + | 1.19829i | 0.279405 | + | 0.960173i | \(0.409863\pi\) |
−0.971237 | + | 0.238115i | \(0.923471\pi\) | |||||||
\(752\) | 8.64534i | 0.315263i | ||||||||
\(753\) | −14.6811 | + | 25.4285i | −0.535010 | + | 0.926664i | ||||
\(754\) | −9.21920 | + | 3.17332i | −0.335743 | + | 0.115565i | ||||
\(755\) | −57.2583 | −2.08384 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3225 | − | 30.0035i | −0.629598 | − | 1.09050i | −0.987632 | − | 0.156788i | \(-0.949886\pi\) |
0.358034 | − | 0.933709i | \(-0.383447\pi\) | |||||||
\(758\) | −57.8290 | −2.10044 | ||||||||
\(759\) | 6.69881 | + | 3.86756i | 0.243151 | + | 0.140384i | ||||
\(760\) | −7.03569 | + | 4.06206i | −0.255211 | + | 0.147346i | ||||
\(761\) | 22.8595i | 0.828655i | 0.910128 | + | 0.414328i | \(0.135983\pi\) | ||||
−0.910128 | + | 0.414328i | \(0.864017\pi\) | |||||||
\(762\) | − | 58.7280i | − | 2.12749i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.9214 | − | 24.1126i | −0.503659 | − | 0.872363i | ||||
\(765\) | −32.7239 | − | 18.8931i | −1.18313 | − | 0.683083i | ||||
\(766\) | 16.9813 | − | 29.4124i | 0.613558 | − | 1.06271i | ||||
\(767\) | 19.9372 | + | 17.3349i | 0.719891 | + | 0.625927i | ||||
\(768\) | 7.46951 | + | 12.9376i | 0.269533 | + | 0.466844i | ||||
\(769\) | 44.8839 | − | 25.9137i | 1.61855 | − | 0.934473i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
0.987294 | − | 0.158902i | \(-0.0507953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.18507 | + | 8.98080i | −0.186736 | + | 0.323436i | ||||
\(772\) | −29.8884 | + | 17.2561i | −1.07571 | + | 0.621060i | ||||
\(773\) | −4.93605 | + | 2.84983i | −0.177538 | + | 0.102501i | −0.586135 | − | 0.810213i | \(-0.699351\pi\) |
0.408598 | + | 0.912715i | \(0.366018\pi\) | |||||||
\(774\) | 14.0737 | − | 8.12545i | 0.505868 | − | 0.292063i | ||||
\(775\) | −58.4770 | + | 33.7617i | −2.10056 | + | 1.21276i | ||||
\(776\) | 0.219653 | − | 0.380450i | 0.00788508 | − | 0.0136574i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.6146 | + | 22.2941i | −1.38440 | + | 0.799283i | ||||
\(779\) | −14.3727 | − | 24.8943i | −0.514956 | − | 0.891930i | ||||
\(780\) | −13.7351 | + | 70.6208i | −0.491797 | + | 2.52863i | ||||
\(781\) | 2.85809 | − | 4.95037i | 0.102271 | − | 0.177138i | ||||
\(782\) | 34.9625 | + | 20.1856i | 1.25026 | + | 0.721836i | ||||
\(783\) | −1.28289 | − | 2.22204i | −0.0458469 | − | 0.0794092i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.7622i | 1.66902i | ||||||||
\(786\) | − | 39.1324i | − | 1.39580i | ||||||
\(787\) | −14.5614 | + | 8.40705i | −0.519059 | + | 0.299679i | −0.736550 | − | 0.676384i | \(-0.763546\pi\) |
0.217490 | + | 0.976062i | \(0.430213\pi\) | |||||||
\(788\) | −48.7000 | − | 28.1170i | −1.73487 | − | 1.00163i | ||||
\(789\) | 6.02727 | 0.214577 | ||||||||
\(790\) | −2.87777 | − | 4.98444i | −0.102386 | − | 0.177338i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.77766 | 0.0631664 | ||||||||
\(793\) | 1.80631 | + | 5.24772i | 0.0641438 | + | 0.186352i | ||||
\(794\) | 13.8148 | − | 23.9280i | 0.490270 | − | 0.849172i | ||||
\(795\) | 40.0807i | 1.42152i | ||||||||
\(796\) | −3.85781 | + | 6.68192i | −0.136736 | + | 0.236834i | ||||
\(797\) | −21.0651 | + | 36.4858i | −0.746163 | + | 1.29239i | 0.203487 | + | 0.979078i | \(0.434773\pi\) |
−0.949650 | + | 0.313314i | \(0.898561\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8108 | − | 7.39632i | −0.453214 | − | 0.261663i | ||||
\(800\) | 63.8727i | 2.25824i | ||||||||
\(801\) | 6.62859 | + | 3.82702i | 0.234210 | + | 0.135221i | ||||
\(802\) | 20.5082 | + | 35.5213i | 0.724171 | + | 1.25430i | ||||
\(803\) | 3.16820 | − | 5.48748i | 0.111803 | − | 0.193649i | ||||
\(804\) | 40.4281 | − | 23.3412i | 1.42579 | − | 0.823180i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.2637 | + | 48.6083i | −1.48868 | + | 1.71215i | ||||
\(807\) | −13.4858 | − | 23.3581i | −0.474723 | − | 0.822244i | ||||
\(808\) | − | 5.52147i | − | 0.194245i | ||||||
\(809\) | −30.1686 | −1.06067 | −0.530336 | − | 0.847787i | \(-0.677934\pi\) | ||||
−0.530336 | + | 0.847787i | \(0.677934\pi\) | |||||||
\(810\) | −82.5984 | −2.90221 | ||||||||
\(811\) | − | 23.7929i | − | 0.835480i | −0.908567 | − | 0.417740i | \(-0.862822\pi\) | ||
0.908567 | − | 0.417740i | \(-0.137178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.5178 | + | 14.7327i | 0.894950 | + | 0.516699i | ||||
\(814\) | 15.6064 | − | 9.01034i | 0.547003 | − | 0.315812i | ||||
\(815\) | −4.17712 | − | 7.23499i | −0.146318 | − | 0.253431i | ||||
\(816\) | −32.5202 | −1.13843 | ||||||||
\(817\) | −7.50384 | − | 4.33234i | −0.262526 | − | 0.151569i | ||||
\(818\) | −50.7432 | −1.77419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 106.614 | 3.72312 | ||||||||
\(821\) | 31.0771 | + | 17.9424i | 1.08460 | + | 0.626193i | 0.932133 | − | 0.362116i | \(-0.117946\pi\) |
0.152465 | + | 0.988309i | \(0.451279\pi\) | |||||||
\(822\) | −35.5682 | −1.24058 | ||||||||
\(823\) | −6.11728 | − | 10.5954i | −0.213235 | − | 0.369334i | 0.739490 | − | 0.673167i | \(-0.235067\pi\) |
−0.952725 | + | 0.303833i | \(0.901733\pi\) | |||||||
\(824\) | −6.76557 | + | 3.90610i | −0.235690 | + | 0.136076i | ||||
\(825\) | −13.8417 | − | 7.99151i | −0.481906 | − | 0.278229i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.3474i | − | 0.950962i | −0.879726 | − | 0.475481i | \(-0.842274\pi\) | ||
0.879726 | − | 0.475481i | \(-0.157726\pi\) | |||||||
\(828\) | −19.9904 | −0.694715 | ||||||||
\(829\) | 23.5738 | 0.818751 | 0.409376 | − | 0.912366i | \(-0.365747\pi\) | ||||
0.409376 | + | 0.912366i | \(0.365747\pi\) | |||||||
\(830\) | − | 36.2226i | − | 1.25730i | ||||||
\(831\) | −24.1599 | − | 41.8463i | −0.838099 | − | 1.45163i | ||||
\(832\) | 13.0271 | + | 37.8466i | 0.451634 | + | 1.31210i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 68.9165 | − | 39.7889i | 2.38638 | − | 1.37778i | ||||
\(835\) | −24.8376 | + | 43.0199i | −0.859539 | + | 1.48877i | ||||
\(836\) | −2.58242 | − | 4.47288i | −0.0893148 | − | 0.154698i | ||||
\(837\) | −14.6796 | − | 8.47530i | −0.507403 | − | 0.292949i | ||||
\(838\) | − | 82.3163i | − | 2.84357i | ||||||
\(839\) | −9.16975 | − | 5.29416i | −0.316575 | − | 0.182775i | 0.333290 | − | 0.942824i | \(-0.391841\pi\) |
−0.649865 | + | 0.760050i | \(0.725175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6783 | − | 23.6915i | 0.471665 | − | 0.816947i | ||||
\(842\) | −23.2332 | + | 40.2411i | −0.800669 | + | 1.38680i | ||||
\(843\) | − | 39.0536i | − | 1.34508i | ||||||
\(844\) | −18.2046 | + | 31.5313i | −0.626629 | + | 1.08535i | ||||
\(845\) | 17.5496 | − | 43.4099i | 0.603723 | − | 1.49335i | ||||
\(846\) | 13.3054 | 0.457449 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.13174 | + | 12.3525i | 0.244905 | + | 0.424188i | ||||
\(849\) | 48.0379 | 1.64866 | ||||||||
\(850\) | −72.2428 | − | 41.7094i | −2.47791 | − | 1.43062i | ||||
\(851\) | −32.2065 | + | 18.5944i | −1.10402 | + | 0.637408i | ||||
\(852\) | 35.7265i | 1.22397i | ||||||||
\(853\) | 21.3925i | 0.732464i | 0.930524 | + | 0.366232i | \(0.119352\pi\) | ||||
−0.930524 | + | 0.366232i | \(0.880648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.06070 | − | 15.6936i | −0.309870 | − | 0.536710i | ||||
\(856\) | −3.14724 | − | 1.81706i | −0.107570 | − | 0.0621058i | ||||
\(857\) | −3.61065 | + | 6.25382i | −0.123337 | + | 0.213626i | −0.921082 | − | 0.389369i | \(-0.872693\pi\) |
0.797744 | + | 0.602996i | \(0.206026\pi\) | |||||||
\(858\) | −14.9662 | − | 2.91081i | −0.510939 | − | 0.0993734i | ||||
\(859\) | 28.5536 | + | 49.4563i | 0.974238 | + | 1.68743i | 0.682429 | + | 0.730952i | \(0.260924\pi\) |
0.291809 | + | 0.956477i | \(0.405743\pi\) | |||||||
\(860\) | 27.8309 | − | 16.0682i | 0.949027 | − | 0.547921i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.8421 | + | 65.5444i | −1.28891 | + | 2.23245i | ||||
\(863\) | 44.4584 | − | 25.6681i | 1.51338 | − | 0.873751i | 0.513503 | − | 0.858088i | \(-0.328347\pi\) |
0.999877 | − | 0.0156631i | \(-0.00498592\pi\) | |||||||
\(864\) | −13.8860 | + | 8.01707i | −0.472411 | + | 0.272746i | ||||
\(865\) | 11.4922 | − | 6.63505i | 0.390748 | − | 0.225598i | ||||
\(866\) | 22.3115 | − | 12.8816i | 0.758177 | − | 0.437734i | ||||
\(867\) | 8.59788 | − | 14.8920i | 0.291999 | − | 0.505758i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.581520 | − | 0.335741i | 0.0197267 | − | 0.0113892i | ||||
\(870\) | 11.0141 | + | 19.0769i | 0.373412 | + | 0.646768i | ||||
\(871\) | −28.7280 | + | 9.88838i | −0.973410 | + | 0.335055i | ||||
\(872\) | −4.93925 | + | 8.55504i | −0.167264 | + | 0.289710i | ||||
\(873\) | 0.848621 | + | 0.489952i | 0.0287215 | + | 0.0165824i | ||||
\(874\) | 9.68055 | + | 16.7672i | 0.327449 | + | 0.567159i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 39.6029i | 1.33806i | ||||||||
\(877\) | 21.4277i | 0.723563i | 0.932263 | + | 0.361781i | \(0.117831\pi\) | ||||
−0.932263 | + | 0.361781i | \(0.882169\pi\) | |||||||
\(878\) | −28.7815 | + | 16.6170i | −0.971330 | + | 0.560798i | ||||
\(879\) | −0.822748 | − | 0.475014i | −0.0277506 | − | 0.0160218i | ||||
\(880\) | −9.25489 | −0.311982 | ||||||||
\(881\) | −14.5309 | − | 25.1683i | −0.489560 | − | 0.847943i | 0.510368 | − | 0.859956i | \(-0.329509\pi\) |
−0.999928 | + | 0.0120134i | \(0.996176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.83594 | 0.162742 | 0.0813711 | − | 0.996684i | \(-0.474070\pi\) | ||||
0.0813711 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(884\) | −43.0017 | − | 8.36347i | −1.44630 | − | 0.281294i | ||||
\(885\) | 29.8446 | − | 51.6924i | 1.00322 | − | 1.73762i | ||||
\(886\) | − | 31.7899i | − | 1.06800i | ||||||
\(887\) | −12.4949 | + | 21.6418i | −0.419538 | + | 0.726660i | −0.995893 | − | 0.0905387i | \(-0.971141\pi\) |
0.576355 | + | 0.817199i | \(0.304474\pi\) | |||||||
\(888\) | −10.3346 | + | 17.9000i | −0.346806 | + | 0.600685i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 23.8108 | + | 13.7471i | 0.798138 | + | 0.460805i | ||||
\(891\) | − | 9.63651i | − | 0.322835i | ||||||
\(892\) | −9.29338 | − | 5.36553i | −0.311165 | − | 0.179651i | ||||
\(893\) | −3.54710 | − | 6.14376i | −0.118699 | − | 0.205593i | ||||
\(894\) | −6.01497 | + | 10.4182i | −0.201171 | + | 0.348438i | ||||
\(895\) | −18.3809 | + | 10.6122i | −0.614406 | + | 0.354727i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.8855 | + | 6.00696i | 1.03124 | + | 0.200567i | ||||
\(898\) | −32.4662 | − | 56.2331i | −1.08341 | − | 1.87652i | ||||
\(899\) | 10.8573i | 0.362111i | ||||||||
\(900\) | 41.3061 | 1.37687 | ||||||||
\(901\) | −24.4056 | −0.813068 | ||||||||
\(902\) | 22.5940i | 0.752300i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.03206 | − | 2.32791i | −0.134104 | − | 0.0774252i | ||||
\(905\) | −6.59852 | + | 3.80966i | −0.219342 | + | 0.126637i | ||||
\(906\) | 37.9204 | + | 65.6801i | 1.25982 | + | 2.18208i | ||||
\(907\) | −15.0412 | −0.499435 | −0.249717 | − | 0.968319i | \(-0.580338\pi\) | ||||
−0.249717 | + | 0.968319i | \(0.580338\pi\) | |||||||
\(908\) | 28.7789 | + | 16.6155i | 0.955060 | + | 0.551404i | ||||
\(909\) | 12.3160 | 0.408497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.22150 | −0.305522 | −0.152761 | − | 0.988263i | \(-0.548816\pi\) | ||||
−0.152761 | + | 0.988263i | \(0.548816\pi\) | |||||||
\(912\) | −13.5065 | − | 7.79795i | −0.447243 | − | 0.258216i | ||||
\(913\) | 4.22598 | 0.139860 | ||||||||
\(914\) | −8.18018 | − | 14.1685i | −0.270576 | − | 0.468652i | ||||
\(915\) | 10.8589 | − | 6.26939i | 0.358984 | − | 0.207260i | ||||
\(916\) | −35.0404 | − | 20.2306i | −1.15777 | − | 0.668437i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 20.9409i | − | 0.691151i | ||||||
\(919\) | −45.0803 | −1.48706 | −0.743531 | − | 0.668701i | \(-0.766851\pi\) | ||||
−0.743531 | + | 0.668701i | \(0.766851\pi\) | |||||||
\(920\) | −13.1778 | −0.434459 | ||||||||
\(921\) | − | 31.8456i | − | 1.04935i | ||||||
\(922\) | 1.55274 | + | 2.68943i | 0.0511368 | + | 0.0885716i | ||||
\(923\) | 4.43910 | − | 22.8241i | 0.146115 | − | 0.751265i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66.5480 | − | 38.4215i | 2.18808 | − | 1.26329i | ||||
\(926\) | −14.8043 | + | 25.6418i | −0.486499 | + | 0.842642i | ||||
\(927\) | −8.71284 | − | 15.0911i | −0.286167 | − | 0.495656i | ||||
\(928\) | 8.89433 | + | 5.13514i | 0.291971 | + | 0.168569i | ||||
\(929\) | − | 46.9169i | − | 1.53929i | −0.638469 | − | 0.769647i | \(-0.720432\pi\) | ||
0.638469 | − | 0.769647i | \(-0.279568\pi\) | |||||||
\(930\) | 126.030 | + | 72.7632i | 4.13267 | + | 2.38600i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.2117 | − | 35.0078i | 0.662058 | − | 1.14672i | ||||
\(933\) | 11.7434 | − | 20.3401i | 0.384461 | − | 0.665906i | ||||
\(934\) | 66.1939i | 2.16593i | ||||||||
\(935\) | 7.91781 | − | 13.7140i | 0.258940 | − | 0.448497i | ||||
\(936\) | 6.83730 | − | 2.35345i | 0.223484 | − | 0.0769249i | ||||
\(937\) | 28.3912 | 0.927501 | 0.463750 | − | 0.885966i | \(-0.346503\pi\) | ||||
0.463750 | + | 0.885966i | \(0.346503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.74342 | − | 13.4120i | −0.252697 | − | 0.437684i | ||||
\(940\) | 26.3117 | 0.858192 | ||||||||
\(941\) | 15.4774 | + | 8.93589i | 0.504549 | + | 0.291302i | 0.730590 | − | 0.682816i | \(-0.239245\pi\) |
−0.226041 | + | 0.974118i | \(0.572578\pi\) | |||||||
\(942\) | 53.6402 | − | 30.9692i | 1.74769 | − | 1.00903i | ||||
\(943\) | − | 46.6268i | − | 1.51838i | ||||||
\(944\) | − | 21.2415i | − | 0.691353i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.40524 | + | 5.89805i | 0.110714 | + | 0.191762i | ||||
\(947\) | −8.24659 | − | 4.76117i | −0.267978 | − | 0.154717i | 0.359990 | − | 0.932956i | \(-0.382780\pi\) |
−0.627969 | + | 0.778239i | \(0.716113\pi\) | |||||||
\(948\) | −2.09840 | + | 3.63453i | −0.0681528 | + | 0.118044i | ||||
\(949\) | 4.92074 | − | 25.3005i | 0.159734 | − | 0.821290i | ||||
\(950\) | −20.0028 | − | 34.6459i | −0.648978 | − | 1.12406i | ||||
\(951\) | −1.37350 | + | 0.792989i | −0.0445387 | + | 0.0257144i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.70900 | + | 11.6203i | −0.217326 | + | 0.376419i | −0.953990 | − | 0.299840i | \(-0.903067\pi\) |
0.736664 | + | 0.676259i | \(0.236400\pi\) | |||||||
\(954\) | 19.0109 | − | 10.9759i | 0.615500 | − | 0.355359i | ||||
\(955\) | 35.4552 | − | 20.4701i | 1.14730 | − | 0.662397i | ||||
\(956\) | 64.5335 | − | 37.2584i | 2.08716 | − | 1.20502i | ||||
\(957\) | −2.22565 | + | 1.28498i | −0.0719450 | + | 0.0415375i | ||||
\(958\) | −43.4482 | + | 75.2545i | −1.40375 | + | 2.43136i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 78.3145 | − | 45.2149i | 2.52759 | − | 1.45931i | ||||
\(961\) | 20.3637 | + | 35.2710i | 0.656895 | + | 1.13778i | ||||
\(962\) | 48.0969 | − | 55.3172i | 1.55071 | − | 1.78350i | ||||
\(963\) | 4.05308 | − | 7.02013i | 0.130609 | − | 0.226221i | ||||
\(964\) | −62.6102 | − | 36.1480i | −2.01654 | − | 1.16425i | ||||
\(965\) | −25.3734 | − | 43.9480i | −0.816798 | − | 1.41474i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.9316i | − | 0.415851i | −0.978145 | − | 0.207926i | \(-0.933329\pi\) | ||
0.978145 | − | 0.207926i | \(-0.0666712\pi\) | |||||||
\(968\) | − | 9.68534i | − | 0.311299i | ||||||
\(969\) | 23.1103 | − | 13.3427i | 0.742409 | − | 0.428630i | ||||
\(970\) | 3.04836 | + | 1.75997i | 0.0978769 | + | 0.0565093i | ||||
\(971\) | −47.5213 | −1.52503 | −0.762516 | − | 0.646969i | \(-0.776036\pi\) | ||||
−0.762516 | + | 0.646969i | \(0.776036\pi\) | |||||||
\(972\) | 22.7605 | + | 39.4224i | 0.730044 | + | 1.26447i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 59.7515 | 1.91456 | ||||||||
\(975\) | −63.8184 | − | 12.4121i | −2.04383 | − | 0.397507i | ||||
\(976\) | 2.23108 | − | 3.86434i | 0.0714151 | − | 0.123695i | ||||
\(977\) | 36.4942i | 1.16755i | 0.811915 | + | 0.583776i | \(0.198425\pi\) | ||||
−0.811915 | + | 0.583776i | \(0.801575\pi\) | |||||||
\(978\) | −5.53276 | + | 9.58302i | −0.176918 | + | 0.306431i | ||||
\(979\) | −1.60384 | + | 2.77793i | −0.0512589 | + | 0.0887831i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.0826 | − | 11.0174i | −0.609261 | − | 0.351757i | ||||
\(982\) | − | 73.3777i | − | 2.34158i | ||||||
\(983\) | 38.2647 | + | 22.0921i | 1.22045 | + | 0.704629i | 0.965015 | − | 0.262196i | \(-0.0844466\pi\) |
0.255439 | + | 0.966825i | \(0.417780\pi\) | |||||||
\(984\) | −12.9573 | − | 22.4428i | −0.413065 | − | 0.715449i | ||||
\(985\) | 41.3433 | − | 71.6087i | 1.31731 | − | 2.28164i | ||||
\(986\) | −11.6161 | + | 6.70658i | −0.369933 | + | 0.213581i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.8542 | − | 13.7849i | −0.504391 | − | 0.438555i | ||||
\(989\) | −7.02731 | − | 12.1717i | −0.223455 | − | 0.387036i | ||||
\(990\) | 14.2435i | 0.452689i | ||||||||
\(991\) | −50.7097 | −1.61085 | −0.805424 | − | 0.592699i | \(-0.798062\pi\) | ||||
−0.805424 | + | 0.592699i | \(0.798062\pi\) | |||||||
\(992\) | 67.8495 | 2.15422 | ||||||||
\(993\) | 9.49586i | 0.301342i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.82511 | − | 5.67253i | −0.311477 | − | 0.179831i | ||||
\(996\) | −22.8740 | + | 13.2063i | −0.724790 | + | 0.418458i | ||||
\(997\) | −25.1384 | − | 43.5410i | −0.796141 | − | 1.37896i | −0.922112 | − | 0.386923i | \(-0.873538\pi\) |
0.125971 | − | 0.992034i | \(-0.459795\pi\) | |||||||
\(998\) | 0.146578 | 0.00463985 | ||||||||
\(999\) | 16.7057 | + | 9.64505i | 0.528546 | + | 0.305156i |
(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 | 637.2.u.i.361.1 | 12 | ||
7.2 | even | 3 | 637.2.k.g.569.6 | 12 | |||
7.3 | odd | 6 | 91.2.q.a.36.6 | ✓ | 12 | ||
7.4 | even | 3 | 637.2.q.h.491.6 | 12 | |||
7.5 | odd | 6 | 637.2.k.h.569.6 | 12 | |||
7.6 | odd | 2 | 637.2.u.h.361.1 | 12 | |||
13.4 | even | 6 | 637.2.k.g.459.1 | 12 | |||
21.17 | even | 6 | 819.2.ct.a.127.1 | 12 | |||
28.3 | even | 6 | 1456.2.cc.c.673.5 | 12 | |||
91.3 | odd | 6 | 1183.2.c.i.337.11 | 12 | |||
91.4 | even | 6 | 637.2.q.h.589.6 | 12 | |||
91.10 | odd | 6 | 1183.2.c.i.337.2 | 12 | |||
91.11 | odd | 12 | 8281.2.a.by.1.2 | 6 | |||
91.17 | odd | 6 | 91.2.q.a.43.6 | yes | 12 | ||
91.24 | even | 12 | 1183.2.a.m.1.2 | 6 | |||
91.30 | even | 6 | inner | 637.2.u.i.30.1 | 12 | ||
91.67 | odd | 12 | 8281.2.a.ch.1.5 | 6 | |||
91.69 | odd | 6 | 637.2.k.h.459.1 | 12 | |||
91.80 | even | 12 | 1183.2.a.p.1.5 | 6 | |||
91.82 | odd | 6 | 637.2.u.h.30.1 | 12 | |||
273.17 | even | 6 | 819.2.ct.a.316.1 | 12 | |||
364.199 | even | 6 | 1456.2.cc.c.225.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.6 | ✓ | 12 | 7.3 | odd | 6 | ||
91.2.q.a.43.6 | yes | 12 | 91.17 | odd | 6 | ||
637.2.k.g.459.1 | 12 | 13.4 | even | 6 | |||
637.2.k.g.569.6 | 12 | 7.2 | even | 3 | |||
637.2.k.h.459.1 | 12 | 91.69 | odd | 6 | |||
637.2.k.h.569.6 | 12 | 7.5 | odd | 6 | |||
637.2.q.h.491.6 | 12 | 7.4 | even | 3 | |||
637.2.q.h.589.6 | 12 | 91.4 | even | 6 | |||
637.2.u.h.30.1 | 12 | 91.82 | odd | 6 | |||
637.2.u.h.361.1 | 12 | 7.6 | odd | 2 | |||
637.2.u.i.30.1 | 12 | 91.30 | even | 6 | inner | ||
637.2.u.i.361.1 | 12 | 1.1 | even | 1 | trivial | ||
819.2.ct.a.127.1 | 12 | 21.17 | even | 6 | |||
819.2.ct.a.316.1 | 12 | 273.17 | even | 6 | |||
1183.2.a.m.1.2 | 6 | 91.24 | even | 12 | |||
1183.2.a.p.1.5 | 6 | 91.80 | even | 12 | |||
1183.2.c.i.337.2 | 12 | 91.10 | odd | 6 | |||
1183.2.c.i.337.11 | 12 | 91.3 | odd | 6 | |||
1456.2.cc.c.225.5 | 12 | 364.199 | even | 6 | |||
1456.2.cc.c.673.5 | 12 | 28.3 | even | 6 | |||
8281.2.a.by.1.2 | 6 | 91.11 | odd | 12 | |||
8281.2.a.ch.1.5 | 6 | 91.67 | odd | 12 |