Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), degree \(4\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.293 |
Dual form | 950.2.q.b.107.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | 0.258819 | + | 0.965926i | 0.149429 | + | 0.557678i | 0.999518 | + | 0.0310384i | \(0.00988142\pi\) |
−0.850089 | + | 0.526639i | \(0.823452\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.73205 | − | 1.00000i | 0.577350 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −1.93185 | − | 0.517638i | −0.535799 | − | 0.143567i | −0.0192343 | − | 0.999815i | \(-0.506123\pi\) |
−0.516565 | + | 0.856248i | \(0.672790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 1.79315 | + | 6.69213i | 0.434903 | + | 1.62308i | 0.741298 | + | 0.671176i | \(0.234210\pi\) |
−0.306395 | + | 0.951904i | \(0.599123\pi\) | |||||||
\(18\) | −1.41421 | + | 1.41421i | −0.333333 | + | 0.333333i | ||||
\(19\) | 4.33013 | − | 0.500000i | 0.993399 | − | 0.114708i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.89778 | − | 0.776457i | 0.617808 | − | 0.165541i | ||||
\(23\) | −0.896575 | + | 3.34607i | −0.186949 | + | 0.697703i | 0.807256 | + | 0.590201i | \(0.200952\pi\) |
−0.994205 | + | 0.107501i | \(0.965715\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 3.53553 | + | 3.53553i | 0.680414 | + | 0.680414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.46410 | + | 6.00000i | 0.643268 | + | 1.11417i | 0.984699 | + | 0.174265i | \(0.0557550\pi\) |
−0.341431 | + | 0.939907i | \(0.610912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | −0.776457 | − | 2.89778i | −0.135164 | − | 0.504438i | ||||
\(34\) | −3.46410 | − | 6.00000i | −0.594089 | − | 1.02899i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | − | 1.73205i | 0.166667 | − | 0.288675i | ||||
\(37\) | 1.41421 | + | 1.41421i | 0.232495 | + | 0.232495i | 0.813733 | − | 0.581238i | \(-0.197432\pi\) |
−0.581238 | + | 0.813733i | \(0.697432\pi\) | |||||||
\(38\) | −4.05317 | + | 1.60368i | −0.657511 | + | 0.260152i | ||||
\(39\) | − | 2.00000i | − | 0.320256i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 0.866025i | −0.234261 | − | 0.135250i | 0.378275 | − | 0.925693i | \(-0.376517\pi\) |
−0.612536 | + | 0.790443i | \(0.709851\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.34607 | + | 0.896575i | −0.510270 | + | 0.136726i | −0.504762 | − | 0.863258i | \(-0.668420\pi\) |
−0.00550783 | + | 0.999985i | \(0.501753\pi\) | |||||||
\(44\) | −2.59808 | + | 1.50000i | −0.391675 | + | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 3.46410i | − | 0.510754i | ||||||
\(47\) | 6.69213 | + | 1.79315i | 0.976148 | + | 0.261558i | 0.711421 | − | 0.702766i | \(-0.248052\pi\) |
0.264726 | + | 0.964324i | \(0.414718\pi\) | |||||||
\(48\) | 0.965926 | + | 0.258819i | 0.139419 | + | 0.0373573i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | + | 3.46410i | −0.840168 | + | 0.485071i | ||||
\(52\) | −1.93185 | + | 0.517638i | −0.267900 | + | 0.0717835i | ||||
\(53\) | 5.79555 | + | 1.55291i | 0.796081 | + | 0.213309i | 0.633863 | − | 0.773446i | \(-0.281468\pi\) |
0.162218 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(54\) | −4.33013 | − | 2.50000i | −0.589256 | − | 0.340207i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.60368 | + | 4.05317i | 0.212413 | + | 0.536856i | ||||
\(58\) | −4.89898 | − | 4.89898i | −0.643268 | − | 0.643268i | ||||
\(59\) | 2.59808 | − | 4.50000i | 0.338241 | − | 0.585850i | −0.645861 | − | 0.763455i | \(-0.723502\pi\) |
0.984102 | + | 0.177605i | \(0.0568349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | 0.896575 | + | 3.34607i | 0.113865 | + | 0.424951i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.50000 | + | 2.59808i | 0.184637 | + | 0.319801i | ||||
\(67\) | 0.258819 | − | 0.965926i | 0.0316198 | − | 0.118007i | −0.948312 | − | 0.317339i | \(-0.897211\pi\) |
0.979932 | + | 0.199332i | \(0.0638774\pi\) | |||||||
\(68\) | 4.89898 | + | 4.89898i | 0.594089 | + | 0.594089i | ||||
\(69\) | −3.46410 | −0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 1.73205i | −0.356034 | − | 0.205557i | 0.311305 | − | 0.950310i | \(-0.399234\pi\) |
−0.667340 | + | 0.744753i | \(0.732567\pi\) | |||||||
\(72\) | −0.517638 | + | 1.93185i | −0.0610042 | + | 0.227671i | ||||
\(73\) | −15.0573 | + | 4.03459i | −1.76232 | + | 0.472213i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
−0.775138 | + | 0.631792i | \(0.782320\pi\) | |||||||
\(74\) | −1.73205 | − | 1.00000i | −0.201347 | − | 0.116248i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | − | 2.59808i | 0.401478 | − | 0.298020i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.517638 | + | 1.93185i | 0.0586110 | + | 0.218739i | ||||
\(79\) | −3.46410 | + | 6.00000i | −0.389742 | + | 0.675053i | −0.992415 | − | 0.122936i | \(-0.960769\pi\) |
0.602673 | + | 0.797988i | \(0.294102\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.67303 | + | 0.448288i | 0.184756 | + | 0.0495051i | ||||
\(83\) | −1.22474 | − | 1.22474i | −0.134433 | − | 0.134433i | 0.636688 | − | 0.771121i | \(-0.280304\pi\) |
−0.771121 | + | 0.636688i | \(0.780304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.00000 | − | 1.73205i | 0.323498 | − | 0.186772i | ||||
\(87\) | −4.89898 | + | 4.89898i | −0.525226 | + | 0.525226i | ||||
\(88\) | 2.12132 | − | 2.12132i | 0.226134 | − | 0.226134i | ||||
\(89\) | 3.46410 | + | 6.00000i | 0.367194 | + | 0.635999i | 0.989126 | − | 0.147073i | \(-0.0469852\pi\) |
−0.621932 | + | 0.783072i | \(0.713652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.896575 | + | 3.34607i | 0.0934745 | + | 0.348851i | ||||
\(93\) | 3.34607 | − | 0.896575i | 0.346971 | − | 0.0929705i | ||||
\(94\) | −6.92820 | −0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.965926 | + | 0.258819i | −0.0980749 | + | 0.0262791i | −0.307523 | − | 0.951541i | \(-0.599500\pi\) |
0.209448 | + | 0.977820i | \(0.432833\pi\) | |||||||
\(98\) | −1.81173 | − | 6.76148i | −0.183013 | − | 0.683013i | ||||
\(99\) | −5.19615 | + | 3.00000i | −0.522233 | + | 0.301511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 4.89898 | − | 4.89898i | 0.485071 | − | 0.485071i | ||||
\(103\) | 7.07107 | − | 7.07107i | 0.696733 | − | 0.696733i | −0.266971 | − | 0.963704i | \(-0.586023\pi\) |
0.963704 | + | 0.266971i | \(0.0860229\pi\) | |||||||
\(104\) | 1.73205 | − | 1.00000i | 0.169842 | − | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 4.82963 | + | 1.29410i | 0.464731 | + | 0.124524i | ||||
\(109\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | + | 1.73205i | −0.0949158 | + | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.36396 | + | 6.36396i | −0.598671 | + | 0.598671i | −0.939959 | − | 0.341288i | \(-0.889137\pi\) |
0.341288 | + | 0.939959i | \(0.389137\pi\) | |||||||
\(114\) | −2.59808 | − | 3.50000i | −0.243332 | − | 0.327805i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | + | 3.46410i | 0.557086 | + | 0.321634i | ||||
\(117\) | −3.86370 | + | 1.03528i | −0.357199 | + | 0.0957113i | ||||
\(118\) | −1.34486 | + | 5.01910i | −0.123805 | + | 0.462045i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −5.65685 | − | 5.65685i | −0.512148 | − | 0.512148i | ||||
\(123\) | 0.448288 | − | 1.67303i | 0.0404207 | − | 0.150852i | ||||
\(124\) | −1.73205 | − | 3.00000i | −0.155543 | − | 0.269408i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.69402 | − | 21.2504i | 0.505262 | − | 1.88567i | 0.0426804 | − | 0.999089i | \(-0.486410\pi\) |
0.462582 | − | 0.886576i | \(-0.346923\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | −1.73205 | − | 3.00000i | −0.152499 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50000 | + | 12.9904i | −0.655278 | + | 1.13497i | 0.326546 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189794i | \(0.939218\pi\) | |||||||
\(132\) | −2.12132 | − | 2.12132i | −0.184637 | − | 0.184637i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.00000i | 0.0863868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | − | 3.46410i | −0.514496 | − | 0.297044i | ||||
\(137\) | −15.0573 | − | 4.03459i | −1.28643 | − | 0.344698i | −0.450127 | − | 0.892964i | \(-0.648621\pi\) |
−0.836304 | + | 0.548266i | \(0.815288\pi\) | |||||||
\(138\) | 3.34607 | − | 0.896575i | 0.284836 | − | 0.0763216i | ||||
\(139\) | 4.33013 | − | 2.50000i | 0.367277 | − | 0.212047i | −0.304991 | − | 0.952355i | \(-0.598654\pi\) |
0.672268 | + | 0.740308i | \(0.265320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820i | 0.583460i | ||||||||
\(142\) | 3.34607 | + | 0.896575i | 0.280796 | + | 0.0752389i | ||||
\(143\) | 5.79555 | + | 1.55291i | 0.484649 | + | 0.129861i | ||||
\(144\) | − | 2.00000i | − | 0.166667i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.5000 | − | 7.79423i | 1.11727 | − | 0.645055i | ||||
\(147\) | −6.76148 | + | 1.81173i | −0.557678 | + | 0.149429i | ||||
\(148\) | 1.93185 | + | 0.517638i | 0.158797 | + | 0.0425496i | ||||
\(149\) | 15.5885 | + | 9.00000i | 1.27706 | + | 0.737309i | 0.976306 | − | 0.216394i | \(-0.0694297\pi\) |
0.300750 | + | 0.953703i | \(0.402763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410i | 0.281905i | 0.990016 | + | 0.140952i | \(0.0450164\pi\) | ||||
−0.990016 | + | 0.140952i | \(0.954984\pi\) | |||||||
\(152\) | −2.70831 | + | 3.41542i | −0.219673 | + | 0.277027i | ||||
\(153\) | 9.79796 | + | 9.79796i | 0.792118 | + | 0.792118i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | − | 1.73205i | −0.0800641 | − | 0.138675i | ||||
\(157\) | −1.79315 | − | 6.69213i | −0.143109 | − | 0.534090i | −0.999832 | − | 0.0183138i | \(-0.994170\pi\) |
0.856723 | − | 0.515776i | \(-0.172496\pi\) | |||||||
\(158\) | 1.79315 | − | 6.69213i | 0.142655 | − | 0.532397i | ||||
\(159\) | 6.00000i | 0.475831i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.258819 | + | 0.965926i | −0.0203347 | + | 0.0758903i | ||||
\(163\) | 8.57321 | + | 8.57321i | 0.671506 | + | 0.671506i | 0.958063 | − | 0.286557i | \(-0.0925108\pi\) |
−0.286557 | + | 0.958063i | \(0.592511\pi\) | |||||||
\(164\) | −1.73205 | −0.135250 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50000 | + | 0.866025i | 0.116423 | + | 0.0672166i | ||||
\(167\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.79423 | − | 4.50000i | −0.599556 | − | 0.346154i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.00000 | − | 5.19615i | 0.535303 | − | 0.397360i | ||||
\(172\) | −2.44949 | + | 2.44949i | −0.186772 | + | 0.186772i | ||||
\(173\) | −1.55291 | − | 5.79555i | −0.118066 | − | 0.440628i | 0.881432 | − | 0.472311i | \(-0.156580\pi\) |
−0.999498 | + | 0.0316829i | \(0.989913\pi\) | |||||||
\(174\) | 3.46410 | − | 6.00000i | 0.262613 | − | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 5.01910 | + | 1.34486i | 0.377258 | + | 0.101086i | ||||
\(178\) | −4.89898 | − | 4.89898i | −0.367194 | − | 0.367194i | ||||
\(179\) | 22.5167 | 1.68297 | 0.841487 | − | 0.540277i | \(-0.181681\pi\) | ||||
0.841487 | + | 0.540277i | \(0.181681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.0000 | − | 12.1244i | 1.56092 | − | 0.901196i | 0.563753 | − | 0.825943i | \(-0.309357\pi\) |
0.997164 | − | 0.0752530i | \(-0.0239764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.65685 | + | 5.65685i | −0.418167 | + | 0.418167i | ||||
\(184\) | −1.73205 | − | 3.00000i | −0.127688 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | + | 1.73205i | −0.219971 | + | 0.127000i | ||||
\(187\) | −5.37945 | − | 20.0764i | −0.393385 | − | 1.46813i | ||||
\(188\) | 6.69213 | − | 1.79315i | 0.488074 | − | 0.130779i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.0000 | −1.73658 | −0.868290 | − | 0.496058i | \(-0.834780\pi\) | ||||
−0.868290 | + | 0.496058i | \(0.834780\pi\) | |||||||
\(192\) | 0.965926 | − | 0.258819i | 0.0697097 | − | 0.0186787i | ||||
\(193\) | −5.69402 | − | 21.2504i | −0.409864 | − | 1.52963i | −0.794904 | − | 0.606735i | \(-0.792479\pi\) |
0.385040 | − | 0.922900i | \(-0.374188\pi\) | |||||||
\(194\) | 0.866025 | − | 0.500000i | 0.0621770 | − | 0.0358979i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.50000 | + | 6.06218i | 0.250000 | + | 0.433013i | ||||
\(197\) | 7.34847 | − | 7.34847i | 0.523557 | − | 0.523557i | −0.395087 | − | 0.918644i | \(-0.629286\pi\) |
0.918644 | + | 0.395087i | \(0.129286\pi\) | |||||||
\(198\) | 4.24264 | − | 4.24264i | 0.301511 | − | 0.301511i | ||||
\(199\) | 12.1244 | − | 7.00000i | 0.859473 | − | 0.496217i | −0.00436292 | − | 0.999990i | \(-0.501389\pi\) |
0.863836 | + | 0.503774i | \(0.168055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | −8.48528 | − | 8.48528i | −0.597022 | − | 0.597022i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.46410 | + | 6.00000i | −0.242536 | + | 0.420084i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.00000 | + | 8.66025i | −0.348367 | + | 0.603388i | ||||
\(207\) | 1.79315 | + | 6.69213i | 0.124633 | + | 0.465135i | ||||
\(208\) | −1.41421 | + | 1.41421i | −0.0980581 | + | 0.0980581i | ||||
\(209\) | −12.9904 | + | 1.50000i | −0.898563 | + | 0.103757i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | − | 5.19615i | −0.619586 | − | 0.357718i | 0.157122 | − | 0.987579i | \(-0.449778\pi\) |
−0.776708 | + | 0.629861i | \(0.783112\pi\) | |||||||
\(212\) | 5.79555 | − | 1.55291i | 0.398040 | − | 0.106655i | ||||
\(213\) | 0.896575 | − | 3.34607i | 0.0614323 | − | 0.229269i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.79423 | − | 13.5000i | −0.526685 | − | 0.912245i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.8564i | − | 0.932083i | ||||||
\(222\) | 0.517638 | − | 1.93185i | 0.0347416 | − | 0.129657i | ||||
\(223\) | −6.72930 | − | 25.1141i | −0.450627 | − | 1.68176i | −0.700636 | − | 0.713519i | \(-0.747100\pi\) |
0.250009 | − | 0.968244i | \(-0.419566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.50000 | − | 7.79423i | 0.299336 | − | 0.518464i | ||||
\(227\) | −14.8492 | − | 14.8492i | −0.985579 | − | 0.985579i | 0.0143186 | − | 0.999897i | \(-0.495442\pi\) |
−0.999897 | + | 0.0143186i | \(0.995442\pi\) | |||||||
\(228\) | 3.41542 | + | 2.70831i | 0.226191 | + | 0.179362i | ||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.69213 | − | 1.79315i | −0.439360 | − | 0.117726i | ||||
\(233\) | 21.7494 | − | 5.82774i | 1.42485 | − | 0.381788i | 0.537650 | − | 0.843168i | \(-0.319312\pi\) |
0.887202 | + | 0.461380i | \(0.152646\pi\) | |||||||
\(234\) | 3.46410 | − | 2.00000i | 0.226455 | − | 0.130744i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 5.19615i | − | 0.338241i | ||||||
\(237\) | −6.69213 | − | 1.79315i | −0.434701 | − | 0.116478i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50000 | + | 2.59808i | −0.289870 | + | 0.167357i | −0.637883 | − | 0.770133i | \(-0.720190\pi\) |
0.348013 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(242\) | 1.93185 | − | 0.517638i | 0.124184 | − | 0.0332750i | ||||
\(243\) | 15.4548 | + | 4.14110i | 0.991427 | + | 0.265652i | ||||
\(244\) | 6.92820 | + | 4.00000i | 0.443533 | + | 0.256074i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.73205i | 0.110432i | ||||||||
\(247\) | −8.62398 | − | 1.27551i | −0.548731 | − | 0.0811589i | ||||
\(248\) | 2.44949 | + | 2.44949i | 0.155543 | + | 0.155543i | ||||
\(249\) | 0.866025 | − | 1.50000i | 0.0548821 | − | 0.0950586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5000 | − | 18.1865i | −0.662754 | − | 1.14792i | −0.979889 | − | 0.199543i | \(-0.936054\pi\) |
0.317135 | − | 0.948380i | \(-0.397279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.68973 | − | 10.0382i | 0.169102 | − | 0.631096i | ||||
\(254\) | 22.0000i | 1.38040i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.776457 | − | 2.89778i | 0.0484341 | − | 0.180758i | −0.937471 | − | 0.348063i | \(-0.886840\pi\) |
0.985905 | + | 0.167304i | \(0.0535063\pi\) | |||||||
\(258\) | 2.44949 | + | 2.44949i | 0.152499 | + | 0.152499i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | + | 6.92820i | 0.742781 | + | 0.428845i | ||||
\(262\) | 3.88229 | − | 14.4889i | 0.239848 | − | 0.895126i | ||||
\(263\) | 6.69213 | − | 1.79315i | 0.412654 | − | 0.110570i | −0.0465183 | − | 0.998917i | \(-0.514813\pi\) |
0.459173 | + | 0.888347i | \(0.348146\pi\) | |||||||
\(264\) | 2.59808 | + | 1.50000i | 0.159901 | + | 0.0923186i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.89898 | + | 4.89898i | −0.299813 | + | 0.299813i | ||||
\(268\) | −0.258819 | − | 0.965926i | −0.0158099 | − | 0.0590033i | ||||
\(269\) | −3.46410 | + | 6.00000i | −0.211210 | + | 0.365826i | −0.952093 | − | 0.305807i | \(-0.901074\pi\) |
0.740883 | + | 0.671634i | \(0.234407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 6.69213 | + | 1.79315i | 0.405770 | + | 0.108726i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.5885 | 0.941733 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.00000 | + | 1.73205i | −0.180579 | + | 0.104257i | ||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | −3.53553 | + | 3.53553i | −0.212047 | + | 0.212047i | ||||
\(279\) | −3.46410 | − | 6.00000i | −0.207390 | − | 0.359211i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.5000 | − | 11.2583i | 1.16327 | − | 0.671616i | 0.211186 | − | 0.977446i | \(-0.432267\pi\) |
0.952086 | + | 0.305830i | \(0.0989340\pi\) | |||||||
\(282\) | −1.79315 | − | 6.69213i | −0.106781 | − | 0.398511i | ||||
\(283\) | −15.0573 | + | 4.03459i | −0.895063 | + | 0.239831i | −0.676895 | − | 0.736080i | \(-0.736675\pi\) |
−0.218168 | + | 0.975911i | \(0.570008\pi\) | |||||||
\(284\) | −3.46410 | −0.205557 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.517638 | + | 1.93185i | 0.0305021 | + | 0.113835i | ||||
\(289\) | −26.8468 | + | 15.5000i | −1.57922 | + | 0.911765i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.500000 | − | 0.866025i | −0.0293105 | − | 0.0507673i | ||||
\(292\) | −11.0227 | + | 11.0227i | −0.645055 | + | 0.645055i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 6.06218 | − | 3.50000i | 0.353553 | − | 0.204124i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | −10.6066 | − | 10.6066i | −0.615457 | − | 0.615457i | ||||
\(298\) | −17.3867 | − | 4.65874i | −1.00718 | − | 0.269874i | ||||
\(299\) | 3.46410 | − | 6.00000i | 0.200334 | − | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.896575 | − | 3.34607i | −0.0515921 | − | 0.192544i | ||||
\(303\) | −8.48528 | + | 8.48528i | −0.487467 | + | 0.487467i | ||||
\(304\) | 1.73205 | − | 4.00000i | 0.0993399 | − | 0.229416i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.0000 | − | 6.92820i | −0.685994 | − | 0.396059i | ||||
\(307\) | 22.2163 | − | 5.95284i | 1.26795 | − | 0.339746i | 0.438705 | − | 0.898631i | \(-0.355437\pi\) |
0.829245 | + | 0.558885i | \(0.188771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.66025 | + | 5.00000i | 0.492665 | + | 0.284440i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 1.41421 | + | 1.41421i | 0.0800641 | + | 0.0800641i | ||||
\(313\) | 2.24144 | − | 8.36516i | 0.126694 | − | 0.472827i | −0.873201 | − | 0.487361i | \(-0.837960\pi\) |
0.999894 | + | 0.0145337i | \(0.00462638\pi\) | |||||||
\(314\) | 3.46410 | + | 6.00000i | 0.195491 | + | 0.338600i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.92820i | 0.389742i | ||||||||
\(317\) | −4.65874 | + | 17.3867i | −0.261661 | + | 0.976532i | 0.702601 | + | 0.711584i | \(0.252022\pi\) |
−0.964262 | + | 0.264949i | \(0.914645\pi\) | |||||||
\(318\) | −1.55291 | − | 5.79555i | −0.0870831 | − | 0.324999i | ||||
\(319\) | −10.3923 | − | 18.0000i | −0.581857 | − | 1.00781i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1106 | + | 28.0812i | 0.618212 | + | 1.56248i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.5000 | − | 6.06218i | −0.581541 | − | 0.335753i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.67303 | − | 0.448288i | 0.0923778 | − | 0.0247525i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1244i | 0.666415i | 0.942854 | + | 0.333207i | \(0.108131\pi\) | ||||
−0.942854 | + | 0.333207i | \(0.891869\pi\) | |||||||
\(332\) | −1.67303 | − | 0.448288i | −0.0918196 | − | 0.0246030i | ||||
\(333\) | 3.86370 | + | 1.03528i | 0.211730 | + | 0.0567328i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5570 | − | 3.36465i | 0.684025 | − | 0.183284i | 0.0999609 | − | 0.994991i | \(-0.468128\pi\) |
0.584064 | + | 0.811707i | \(0.301462\pi\) | |||||||
\(338\) | 8.69333 | + | 2.32937i | 0.472855 | + | 0.126701i | ||||
\(339\) | −7.79423 | − | 4.50000i | −0.423324 | − | 0.244406i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3923i | 0.562775i | ||||||||
\(342\) | −5.41662 | + | 6.83083i | −0.292897 | + | 0.369369i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.73205 | − | 3.00000i | 0.0933859 | − | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | 8.51747 | + | 31.7876i | 0.457242 | + | 1.70645i | 0.681413 | + | 0.731899i | \(0.261366\pi\) |
−0.224171 | + | 0.974550i | \(0.571968\pi\) | |||||||
\(348\) | −1.79315 | + | 6.69213i | −0.0961230 | + | 0.358736i | ||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 8.66025i | −0.266880 | − | 0.462250i | ||||
\(352\) | 0.776457 | − | 2.89778i | 0.0413853 | − | 0.154452i | ||||
\(353\) | 25.7196 | + | 25.7196i | 1.36892 | + | 1.36892i | 0.861985 | + | 0.506933i | \(0.169221\pi\) |
0.506933 | + | 0.861985i | \(0.330779\pi\) | |||||||
\(354\) | −5.19615 | −0.276172 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | + | 3.46410i | 0.317999 | + | 0.183597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.7494 | + | 5.82774i | −1.14949 | + | 0.308006i | ||||
\(359\) | −25.9808 | − | 15.0000i | −1.37121 | − | 0.791670i | −0.380131 | − | 0.924932i | \(-0.624121\pi\) |
−0.991081 | + | 0.133263i | \(0.957455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5000 | − | 4.33013i | 0.973684 | − | 0.227901i | ||||
\(362\) | −17.1464 | + | 17.1464i | −0.901196 | + | 0.901196i | ||||
\(363\) | −0.517638 | − | 1.93185i | −0.0271690 | − | 0.101396i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.00000 | − | 6.92820i | 0.209083 | − | 0.362143i | ||||
\(367\) | 16.7303 | + | 4.48288i | 0.873316 | + | 0.234004i | 0.667521 | − | 0.744591i | \(-0.267355\pi\) |
0.205795 | + | 0.978595i | \(0.434022\pi\) | |||||||
\(368\) | 2.44949 | + | 2.44949i | 0.127688 | + | 0.127688i | ||||
\(369\) | −3.46410 | −0.180334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.44949 | − | 2.44949i | 0.127000 | − | 0.127000i | ||||
\(373\) | −22.6274 | + | 22.6274i | −1.17160 | + | 1.17160i | −0.189776 | + | 0.981827i | \(0.560776\pi\) |
−0.981827 | + | 0.189776i | \(0.939224\pi\) | |||||||
\(374\) | 10.3923 | + | 18.0000i | 0.537373 | + | 0.930758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | + | 3.46410i | −0.309426 | + | 0.178647i | ||||
\(377\) | −3.58630 | − | 13.3843i | −0.184704 | − | 0.689325i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3923 | −0.533817 | −0.266908 | − | 0.963722i | \(-0.586002\pi\) | ||||
−0.266908 | + | 0.963722i | \(0.586002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.0000 | 1.12709 | ||||||||
\(382\) | 23.1822 | − | 6.21166i | 1.18611 | − | 0.317816i | ||||
\(383\) | −9.31749 | − | 34.7733i | −0.476101 | − | 1.77683i | −0.617165 | − | 0.786834i | \(-0.711719\pi\) |
0.141064 | − | 0.990000i | \(-0.454948\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.0000 | + | 19.0526i | 0.559885 | + | 0.969750i | ||||
\(387\) | −4.89898 | + | 4.89898i | −0.249029 | + | 0.249029i | ||||
\(388\) | −0.707107 | + | 0.707107i | −0.0358979 | + | 0.0358979i | ||||
\(389\) | 20.7846 | − | 12.0000i | 1.05382 | − | 0.608424i | 0.130105 | − | 0.991500i | \(-0.458469\pi\) |
0.923717 | + | 0.383076i | \(0.125135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | −4.94975 | − | 4.94975i | −0.250000 | − | 0.250000i | ||||
\(393\) | −14.4889 | − | 3.88229i | −0.730868 | − | 0.195835i | ||||
\(394\) | −5.19615 | + | 9.00000i | −0.261778 | + | 0.453413i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 4.48288 | + | 16.7303i | 0.224989 | + | 0.839671i | 0.982409 | + | 0.186743i | \(0.0597931\pi\) |
−0.757420 | + | 0.652928i | \(0.773540\pi\) | |||||||
\(398\) | −9.89949 | + | 9.89949i | −0.496217 | + | 0.496217i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | + | 4.33013i | 0.374532 | + | 0.216236i | 0.675437 | − | 0.737418i | \(-0.263955\pi\) |
−0.300904 | + | 0.953654i | \(0.597289\pi\) | |||||||
\(402\) | −0.965926 | + | 0.258819i | −0.0481760 | + | 0.0129087i | ||||
\(403\) | −1.79315 | + | 6.69213i | −0.0893232 | + | 0.333359i | ||||
\(404\) | 10.3923 | + | 6.00000i | 0.517036 | + | 0.298511i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.24264 | − | 4.24264i | −0.210300 | − | 0.210300i | ||||
\(408\) | 1.79315 | − | 6.69213i | 0.0887742 | − | 0.331310i | ||||
\(409\) | 9.52628 | + | 16.5000i | 0.471044 | + | 0.815872i | 0.999451 | − | 0.0331186i | \(-0.0105439\pi\) |
−0.528407 | + | 0.848991i | \(0.677211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 15.5885i | − | 0.768922i | ||||||
\(412\) | 2.58819 | − | 9.65926i | 0.127511 | − | 0.475877i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.46410 | − | 6.00000i | −0.170251 | − | 0.294884i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | 3.53553 | + | 3.53553i | 0.173136 | + | 0.173136i | ||||
\(418\) | 12.1595 | − | 4.81105i | 0.594741 | − | 0.235316i | ||||
\(419\) | − | 12.0000i | − | 0.586238i | −0.956076 | − | 0.293119i | \(-0.905307\pi\) | ||
0.956076 | − | 0.293119i | \(-0.0946933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.0000 | + | 12.1244i | 1.02348 | + | 0.590905i | 0.915109 | − | 0.403206i | \(-0.132104\pi\) |
0.108368 | + | 0.994111i | \(0.465437\pi\) | |||||||
\(422\) | 10.0382 | + | 2.68973i | 0.488652 | + | 0.130934i | ||||
\(423\) | 13.3843 | − | 3.58630i | 0.650765 | − | 0.174372i | ||||
\(424\) | −5.19615 | + | 3.00000i | −0.252347 | + | 0.145693i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.46410i | 0.167836i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000i | 0.289683i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | + | 1.73205i | −0.144505 | + | 0.0834300i | −0.570509 | − | 0.821291i | \(-0.693254\pi\) |
0.426004 | + | 0.904721i | \(0.359921\pi\) | |||||||
\(432\) | 4.82963 | − | 1.29410i | 0.232366 | − | 0.0622622i | ||||
\(433\) | −25.1141 | − | 6.72930i | −1.20691 | − | 0.323389i | −0.401358 | − | 0.915921i | \(-0.631462\pi\) |
−0.805547 | + | 0.592532i | \(0.798128\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.20925 | + | 14.9372i | −0.105683 | + | 0.714542i | ||||
\(438\) | 11.0227 | + | 11.0227i | 0.526685 | + | 0.526685i | ||||
\(439\) | 12.1244 | − | 21.0000i | 0.578664 | − | 1.00228i | −0.416969 | − | 0.908921i | \(-0.636908\pi\) |
0.995633 | − | 0.0933546i | \(-0.0297590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | + | 12.1244i | 0.333333 | + | 0.577350i | ||||
\(442\) | 3.58630 | + | 13.3843i | 0.170583 | + | 0.636624i | ||||
\(443\) | 5.82774 | − | 21.7494i | 0.276884 | − | 1.03335i | −0.677684 | − | 0.735353i | \(-0.737016\pi\) |
0.954568 | − | 0.297993i | \(-0.0963172\pi\) | |||||||
\(444\) | 2.00000i | 0.0949158i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.0000 | + | 22.5167i | 0.615568 | + | 1.06619i | ||||
\(447\) | −4.65874 | + | 17.3867i | −0.220351 | + | 0.822361i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.9808 | −1.22611 | −0.613054 | − | 0.790041i | \(-0.710059\pi\) | ||||
−0.613054 | + | 0.790041i | \(0.710059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50000 | + | 2.59808i | 0.211897 | + | 0.122339i | ||||
\(452\) | −2.32937 | + | 8.69333i | −0.109564 | + | 0.408900i | ||||
\(453\) | −3.34607 | + | 0.896575i | −0.157212 | + | 0.0421248i | ||||
\(454\) | 18.1865 | + | 10.5000i | 0.853536 | + | 0.492789i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | − | 1.73205i | −0.187317 | − | 0.0811107i | ||||
\(457\) | 13.4722 | − | 13.4722i | 0.630203 | − | 0.630203i | −0.317916 | − | 0.948119i | \(-0.602983\pi\) |
0.948119 | + | 0.317916i | \(0.102983\pi\) | |||||||
\(458\) | 1.03528 | + | 3.86370i | 0.0483753 | + | 0.180539i | ||||
\(459\) | −17.3205 | + | 30.0000i | −0.808452 | + | 1.40028i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | + | 25.9808i | −0.698620 | + | 1.21004i | 0.270326 | + | 0.962769i | \(0.412869\pi\) |
−0.968945 | + | 0.247276i | \(0.920465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.1464 | − | 17.1464i | −0.796862 | − | 0.796862i | 0.185737 | − | 0.982599i | \(-0.440533\pi\) |
−0.982599 | + | 0.185737i | \(0.940533\pi\) | |||||||
\(464\) | 6.92820 | 0.321634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.5000 | + | 11.2583i | −0.903320 | + | 0.521532i | ||||
\(467\) | −18.3712 | + | 18.3712i | −0.850117 | + | 0.850117i | −0.990147 | − | 0.140031i | \(-0.955280\pi\) |
0.140031 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(468\) | −2.82843 | + | 2.82843i | −0.130744 | + | 0.130744i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | − | 3.46410i | 0.276465 | − | 0.159617i | ||||
\(472\) | 1.34486 | + | 5.01910i | 0.0619023 | + | 0.231023i | ||||
\(473\) | 10.0382 | − | 2.68973i | 0.461557 | − | 0.123674i | ||||
\(474\) | 6.92820 | 0.318223 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5911 | − | 3.10583i | 0.530720 | − | 0.142206i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.7846 | − | 12.0000i | 0.949673 | − | 0.548294i | 0.0566937 | − | 0.998392i | \(-0.481944\pi\) |
0.892979 | + | 0.450098i | \(0.148611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | 3.67423 | − | 3.67423i | 0.167357 | − | 0.167357i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73205 | + | 1.00000i | −0.0787296 | + | 0.0454545i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | 26.8701 | + | 26.8701i | 1.21760 | + | 1.21760i | 0.968471 | + | 0.249128i | \(0.0801440\pi\) |
0.249128 | + | 0.968471i | \(0.419856\pi\) | |||||||
\(488\) | −7.72741 | − | 2.07055i | −0.349803 | − | 0.0937295i | ||||
\(489\) | −6.06218 | + | 10.5000i | −0.274141 | + | 0.474826i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | −0.448288 | − | 1.67303i | −0.0202104 | − | 0.0754261i | ||||
\(493\) | −33.9411 | + | 33.9411i | −1.52863 | + | 1.52863i | ||||
\(494\) | 8.66025 | − | 1.00000i | 0.389643 | − | 0.0449921i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | − | 1.73205i | −0.134704 | − | 0.0777714i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.448288 | + | 1.67303i | −0.0200883 | + | 0.0749704i | ||||
\(499\) | −26.8468 | − | 15.5000i | −1.20183 | − | 0.693875i | −0.240866 | − | 0.970558i | \(-0.577431\pi\) |
−0.960961 | + | 0.276683i | \(0.910765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.8492 | + | 14.8492i | 0.662754 | + | 0.662754i | ||||
\(503\) | −8.06918 | + | 30.1146i | −0.359787 | + | 1.34274i | 0.514565 | + | 0.857451i | \(0.327953\pi\) |
−0.874352 | + | 0.485292i | \(0.838713\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.3923i | 0.461994i | ||||||||
\(507\) | 2.32937 | − | 8.69333i | 0.103451 | − | 0.386084i | ||||
\(508\) | −5.69402 | − | 21.2504i | −0.252631 | − | 0.942833i | ||||
\(509\) | −13.8564 | − | 24.0000i | −0.614174 | − | 1.06378i | −0.990529 | − | 0.137305i | \(-0.956156\pi\) |
0.376354 | − | 0.926476i | \(-0.377178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 17.0771 | + | 13.5415i | 0.753971 | + | 0.597874i | ||||
\(514\) | 3.00000i | 0.132324i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00000 | − | 1.73205i | −0.132068 | − | 0.0762493i | ||||
\(517\) | −20.0764 | − | 5.37945i | −0.882959 | − | 0.236588i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.19615 | − | 3.00000i | 0.228086 | − | 0.131685i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 25.9808i | − | 1.13824i | −0.822255 | − | 0.569119i | \(-0.807284\pi\) | ||
0.822255 | − | 0.569119i | \(-0.192716\pi\) | |||||||
\(522\) | −13.3843 | − | 3.58630i | −0.585813 | − | 0.156968i | ||||
\(523\) | −19.3185 | − | 5.17638i | −0.844740 | − | 0.226347i | −0.189606 | − | 0.981860i | \(-0.560721\pi\) |
−0.655134 | + | 0.755513i | \(0.727388\pi\) | |||||||
\(524\) | 15.0000i | 0.655278i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | + | 3.46410i | −0.261612 | + | 0.151042i | ||||
\(527\) | 23.1822 | − | 6.21166i | 1.00983 | − | 0.270584i | ||||
\(528\) | −2.89778 | − | 0.776457i | −0.126110 | − | 0.0337910i | ||||
\(529\) | 9.52628 | + | 5.50000i | 0.414186 | + | 0.239130i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 10.3923i | − | 0.450988i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.44949 | + | 2.44949i | 0.106099 | + | 0.106099i | ||||
\(534\) | 3.46410 | − | 6.00000i | 0.149906 | − | 0.259645i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.500000 | + | 0.866025i | 0.0215967 | + | 0.0374066i | ||||
\(537\) | 5.82774 | + | 21.7494i | 0.251486 | + | 0.938557i | ||||
\(538\) | 1.79315 | − | 6.69213i | 0.0773082 | − | 0.288518i | ||||
\(539\) | − | 21.0000i | − | 0.904534i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | −4.14110 | + | 15.4548i | −0.177876 | + | 0.663841i | ||||
\(543\) | 17.1464 | + | 17.1464i | 0.735824 | + | 0.735824i | ||||
\(544\) | −6.92820 | −0.297044 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.24693 | + | 27.0459i | −0.309856 | + | 1.15640i | 0.618827 | + | 0.785527i | \(0.287608\pi\) |
−0.928684 | + | 0.370873i | \(0.879059\pi\) | |||||||
\(548\) | −15.0573 | + | 4.03459i | −0.643216 | + | 0.172349i | ||||
\(549\) | 13.8564 | + | 8.00000i | 0.591377 | + | 0.341432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.0000 | + | 24.2487i | 0.766826 | + | 1.03303i | ||||
\(552\) | 2.44949 | − | 2.44949i | 0.104257 | − | 0.104257i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.50000 | − | 4.33013i | 0.106024 | − | 0.183638i | ||||
\(557\) | 33.4607 | + | 8.96575i | 1.41777 | + | 0.379891i | 0.884693 | − | 0.466174i | \(-0.154368\pi\) |
0.533080 | + | 0.846065i | \(0.321034\pi\) | |||||||
\(558\) | 4.89898 | + | 4.89898i | 0.207390 | + | 0.207390i | ||||
\(559\) | 6.92820 | 0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | − | 10.3923i | 0.759961 | − | 0.438763i | ||||
\(562\) | −15.9217 | + | 15.9217i | −0.671616 | + | 0.671616i | ||||
\(563\) | −14.8492 | + | 14.8492i | −0.625821 | + | 0.625821i | −0.947014 | − | 0.321193i | \(-0.895916\pi\) |
0.321193 | + | 0.947014i | \(0.395916\pi\) | |||||||
\(564\) | 3.46410 | + | 6.00000i | 0.145865 | + | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.5000 | − | 7.79423i | 0.567447 | − | 0.327616i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.34607 | − | 0.896575i | 0.140398 | − | 0.0376195i | ||||
\(569\) | −34.6410 | −1.45223 | −0.726113 | − | 0.687575i | \(-0.758675\pi\) | ||||
−0.726113 | + | 0.687575i | \(0.758675\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | 5.79555 | − | 1.55291i | 0.242324 | − | 0.0649306i | ||||
\(573\) | −6.21166 | − | 23.1822i | −0.259496 | − | 0.968451i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | − | 1.73205i | −0.0416667 | − | 0.0721688i | ||||
\(577\) | 13.4722 | − | 13.4722i | 0.560855 | − | 0.560855i | −0.368695 | − | 0.929550i | \(-0.620195\pi\) |
0.929550 | + | 0.368695i | \(0.120195\pi\) | |||||||
\(578\) | 21.9203 | − | 21.9203i | 0.911765 | − | 0.911765i | ||||
\(579\) | 19.0526 | − | 11.0000i | 0.791797 | − | 0.457144i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.707107 | + | 0.707107i | 0.0293105 | + | 0.0293105i | ||||
\(583\) | −17.3867 | − | 4.65874i | −0.720082 | − | 0.192945i | ||||
\(584\) | 7.79423 | − | 13.5000i | 0.322527 | − | 0.558634i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.896575 | − | 3.34607i | −0.0370056 | − | 0.138107i | 0.944952 | − | 0.327210i | \(-0.106109\pi\) |
−0.981957 | + | 0.189103i | \(0.939442\pi\) | |||||||
\(588\) | −4.94975 | + | 4.94975i | −0.204124 | + | 0.204124i | ||||
\(589\) | −1.73205 | − | 15.0000i | −0.0713679 | − | 0.618064i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 5.19615i | 0.370211 | + | 0.213741i | ||||
\(592\) | 1.93185 | − | 0.517638i | 0.0793986 | − | 0.0212748i | ||||
\(593\) | −1.34486 | + | 5.01910i | −0.0552269 | + | 0.206110i | −0.988026 | − | 0.154287i | \(-0.950692\pi\) |
0.932799 | + | 0.360397i | \(0.117359\pi\) | |||||||
\(594\) | 12.9904 | + | 7.50000i | 0.533002 | + | 0.307729i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 9.89949 | + | 9.89949i | 0.405159 | + | 0.405159i | ||||
\(598\) | −1.79315 | + | 6.69213i | −0.0733274 | + | 0.273662i | ||||
\(599\) | 8.66025 | + | 15.0000i | 0.353848 | + | 0.612883i | 0.986920 | − | 0.161210i | \(-0.0515395\pi\) |
−0.633072 | + | 0.774093i | \(0.718206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.5167i | − | 0.918474i | −0.888314 | − | 0.459237i | \(-0.848123\pi\) | ||
0.888314 | − | 0.459237i | \(-0.151877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.517638 | − | 1.93185i | −0.0210799 | − | 0.0786711i | ||||
\(604\) | 1.73205 | + | 3.00000i | 0.0704761 | + | 0.122068i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.00000 | − | 10.3923i | 0.243733 | − | 0.422159i | ||||
\(607\) | −28.2843 | − | 28.2843i | −1.14802 | − | 1.14802i | −0.986941 | − | 0.161082i | \(-0.948502\pi\) |
−0.161082 | − | 0.986941i | \(-0.551498\pi\) | |||||||
\(608\) | −0.637756 | + | 4.31199i | −0.0258644 | + | 0.174874i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | − | 6.92820i | −0.485468 | − | 0.280285i | ||||
\(612\) | 13.3843 | + | 3.58630i | 0.541027 | + | 0.144968i | ||||
\(613\) | 36.8067 | − | 9.86233i | 1.48661 | − | 0.398336i | 0.578019 | − | 0.816024i | \(-0.303826\pi\) |
0.908591 | + | 0.417688i | \(0.137159\pi\) | |||||||
\(614\) | −19.9186 | + | 11.5000i | −0.803849 | + | 0.464102i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.4034 | + | 4.93117i | 0.740891 | + | 0.198521i | 0.609474 | − | 0.792806i | \(-0.291381\pi\) |
0.131417 | + | 0.991327i | \(0.458047\pi\) | |||||||
\(618\) | −9.65926 | − | 2.58819i | −0.388552 | − | 0.104112i | ||||
\(619\) | 28.0000i | 1.12542i | 0.826656 | + | 0.562708i | \(0.190240\pi\) | ||||
−0.826656 | + | 0.562708i | \(0.809760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.0000 | + | 8.66025i | −0.601929 | + | 0.347524i | ||||
\(622\) | 17.3867 | − | 4.65874i | 0.697142 | − | 0.186799i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.73205 | − | 1.00000i | −0.0693375 | − | 0.0400320i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.66025i | 0.346133i | ||||||||
\(627\) | −4.81105 | − | 12.1595i | −0.192135 | − | 0.485604i | ||||
\(628\) | −4.89898 | − | 4.89898i | −0.195491 | − | 0.195491i | ||||
\(629\) | −6.92820 | + | 12.0000i | −0.276246 | + | 0.478471i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | + | 6.92820i | 0.159237 | + | 0.275807i | 0.934594 | − | 0.355716i | \(-0.115763\pi\) |
−0.775356 | + | 0.631524i | \(0.782430\pi\) | |||||||
\(632\) | −1.79315 | − | 6.69213i | −0.0713277 | − | 0.266199i | ||||
\(633\) | 2.68973 | − | 10.0382i | 0.106907 | − | 0.398982i | ||||
\(634\) | − | 18.0000i | − | 0.714871i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.00000 | + | 5.19615i | 0.118958 | + | 0.206041i | ||||
\(637\) | 3.62347 | − | 13.5230i | 0.143567 | − | 0.535799i | ||||
\(638\) | 14.6969 | + | 14.6969i | 0.581857 | + | 0.581857i | ||||
\(639\) | −6.92820 | −0.274075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.5000 | − | 19.9186i | −1.36267 | − | 0.786737i | −0.372690 | − | 0.927956i | \(-0.621564\pi\) |
−0.989978 | + | 0.141219i | \(0.954898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.4797 | + | 10.3106i | −1.51749 | + | 0.406611i | −0.918916 | − | 0.394454i | \(-0.870934\pi\) |
−0.598577 | + | 0.801065i | \(0.704267\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.0000 | − | 24.2487i | −0.708201 | − | 0.954053i | ||||
\(647\) | −7.34847 | + | 7.34847i | −0.288898 | + | 0.288898i | −0.836644 | − | 0.547746i | \(-0.815486\pi\) |
0.547746 | + | 0.836644i | \(0.315486\pi\) | |||||||
\(648\) | 0.258819 | + | 0.965926i | 0.0101674 | + | 0.0379452i | ||||
\(649\) | −7.79423 | + | 13.5000i | −0.305950 | + | 0.529921i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.7112 | + | 3.13801i | 0.458647 | + | 0.122894i | ||||
\(653\) | −4.89898 | − | 4.89898i | −0.191712 | − | 0.191712i | 0.604724 | − | 0.796435i | \(-0.293284\pi\) |
−0.796435 | + | 0.604724i | \(0.793284\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | + | 0.866025i | −0.0585652 | + | 0.0338126i | ||||
\(657\) | −22.0454 | + | 22.0454i | −0.860073 | + | 0.860073i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.73205 | − | 3.00000i | −0.0674711 | − | 0.116863i | 0.830316 | − | 0.557292i | \(-0.188160\pi\) |
−0.897787 | + | 0.440429i | \(0.854826\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | − | 3.46410i | 0.233373 | − | 0.134738i | −0.378754 | − | 0.925497i | \(-0.623647\pi\) |
0.612127 | + | 0.790759i | \(0.290314\pi\) | |||||||
\(662\) | −3.13801 | − | 11.7112i | −0.121962 | − | 0.455170i | ||||
\(663\) | 13.3843 | − | 3.58630i | 0.519802 | − | 0.139280i | ||||
\(664\) | 1.73205 | 0.0672166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −23.1822 | + | 6.21166i | −0.897619 | + | 0.240516i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.5167 | − | 13.0000i | 0.870544 | − | 0.502609i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | − | 20.7846i | −0.463255 | − | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.41421 | − | 1.41421i | 0.0545139 | − | 0.0545139i | −0.679324 | − | 0.733838i | \(-0.737727\pi\) |
0.733838 | + | 0.679324i | \(0.237727\pi\) | |||||||
\(674\) | −11.2583 | + | 6.50000i | −0.433655 | + | 0.250371i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −12.7279 | − | 12.7279i | −0.489174 | − | 0.489174i | 0.418872 | − | 0.908045i | \(-0.362426\pi\) |
−0.908045 | + | 0.418872i | \(0.862426\pi\) | |||||||
\(678\) | 8.69333 | + | 2.32937i | 0.333865 | + | 0.0894590i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5000 | − | 18.1865i | 0.402361 | − | 0.696909i | ||||
\(682\) | −2.68973 | − | 10.0382i | −0.102995 | − | 0.384382i | ||||
\(683\) | −8.48528 | + | 8.48528i | −0.324680 | + | 0.324680i | −0.850559 | − | 0.525879i | \(-0.823736\pi\) |
0.525879 | + | 0.850559i | \(0.323736\pi\) | |||||||
\(684\) | 3.46410 | − | 8.00000i | 0.132453 | − | 0.305888i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.86370 | − | 1.03528i | 0.147409 | − | 0.0394982i | ||||
\(688\) | −0.896575 | + | 3.34607i | −0.0341816 | + | 0.127568i | ||||
\(689\) | −10.3923 | − | 6.00000i | −0.395915 | − | 0.228582i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | −4.24264 | − | 4.24264i | −0.161281 | − | 0.161281i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.4545 | − | 28.5000i | −0.624604 | − | 1.08185i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 6.92820i | − | 0.262613i | ||||||
\(697\) | 3.10583 | − | 11.5911i | 0.117642 | − | 0.439045i | ||||
\(698\) | −1.03528 | − | 3.86370i | −0.0391858 | − | 0.146243i | ||||
\(699\) | 11.2583 | + | 19.5000i | 0.425829 | + | 0.737558i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | + | 20.7846i | −0.453234 | + | 0.785024i | −0.998585 | − | 0.0531839i | \(-0.983063\pi\) |
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(702\) | 7.07107 | + | 7.07107i | 0.266880 | + | 0.266880i | ||||
\(703\) | 6.83083 | + | 5.41662i | 0.257630 | + | 0.204292i | ||||
\(704\) | 3.00000i | 0.113067i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.5000 | − | 18.1865i | −1.18552 | − | 0.684459i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.01910 | − | 1.34486i | 0.188629 | − | 0.0505431i | ||||
\(709\) | 29.4449 | − | 17.0000i | 1.10583 | − | 0.638448i | 0.168080 | − | 0.985773i | \(-0.446243\pi\) |
0.937745 | + | 0.347325i | \(0.112910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.8564i | 0.519656i | ||||||||
\(712\) | −6.69213 | − | 1.79315i | −0.250798 | − | 0.0672012i | ||||
\(713\) | 11.5911 | + | 3.10583i | 0.434090 | + | 0.116314i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.5000 | − | 11.2583i | 0.728749 | − | 0.420744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.9778 | + | 7.76457i | 1.08144 | + | 0.289771i | ||||
\(719\) | 5.19615 | + | 3.00000i | 0.193784 | + | 0.111881i | 0.593753 | − | 0.804648i | \(-0.297646\pi\) |
−0.399969 | + | 0.916529i | \(0.630979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.7489 | + | 8.97073i | −0.623330 | + | 0.333856i | ||||
\(723\) | −3.67423 | − | 3.67423i | −0.136646 | − | 0.136646i | ||||
\(724\) | 12.1244 | − | 21.0000i | 0.450598 | − | 0.780459i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.00000 | + | 1.73205i | 0.0371135 | + | 0.0642824i | ||||
\(727\) | −1.79315 | − | 6.69213i | −0.0665043 | − | 0.248197i | 0.924669 | − | 0.380773i | \(-0.124342\pi\) |
−0.991173 | + | 0.132575i | \(0.957675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | −2.07055 | + | 7.72741i | −0.0765298 | + | 0.285613i | ||||
\(733\) | 22.0454 | + | 22.0454i | 0.814266 | + | 0.814266i | 0.985270 | − | 0.171005i | \(-0.0547013\pi\) |
−0.171005 | + | 0.985270i | \(0.554701\pi\) | |||||||
\(734\) | −17.3205 | −0.639312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | − | 1.73205i | −0.110581 | − | 0.0638442i | ||||
\(737\) | −0.776457 | + | 2.89778i | −0.0286012 | + | 0.106741i | ||||
\(738\) | 3.34607 | − | 0.896575i | 0.123170 | − | 0.0330034i | ||||
\(739\) | −9.52628 | − | 5.50000i | −0.350430 | − | 0.202321i | 0.314445 | − | 0.949276i | \(-0.398182\pi\) |
−0.664875 | + | 0.746955i | \(0.731515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.00000 | − | 8.66025i | −0.0367359 | − | 0.318142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.55291 | + | 5.79555i | 0.0569709 | + | 0.212618i | 0.988543 | − | 0.150938i | \(-0.0482292\pi\) |
−0.931572 | + | 0.363556i | \(0.881563\pi\) | |||||||
\(744\) | −1.73205 | + | 3.00000i | −0.0635001 | + | 0.109985i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.0000 | − | 27.7128i | 0.585802 | − | 1.01464i | ||||
\(747\) | −3.34607 | − | 0.896575i | −0.122426 | − | 0.0328040i | ||||
\(748\) | −14.6969 | − | 14.6969i | −0.537373 | − | 0.537373i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0000 | − | 8.66025i | 0.547358 | − | 0.316017i | −0.200698 | − | 0.979653i | \(-0.564321\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(752\) | 4.89898 | − | 4.89898i | 0.178647 | − | 0.178647i | ||||
\(753\) | 14.8492 | − | 14.8492i | 0.541136 | − | 0.541136i | ||||
\(754\) | 6.92820 | + | 12.0000i | 0.252310 | + | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.86233 | − | 36.8067i | −0.358452 | − | 1.33776i | −0.876084 | − | 0.482159i | \(-0.839853\pi\) |
0.517631 | − | 0.855604i | \(-0.326814\pi\) | |||||||
\(758\) | 10.0382 | − | 2.68973i | 0.364604 | − | 0.0976953i | ||||
\(759\) | 10.3923 | 0.377217 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | 0.543750 | 0.271875 | − | 0.962333i | \(-0.412356\pi\) | ||||
0.271875 | + | 0.962333i | \(0.412356\pi\) | |||||||
\(762\) | −21.2504 | + | 5.69402i | −0.769820 | + | 0.206273i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.7846 | + | 12.0000i | −0.751961 | + | 0.434145i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | + | 31.1769i | 0.650366 | + | 1.12647i | ||||
\(767\) | −7.34847 | + | 7.34847i | −0.265338 | + | 0.265338i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −12.1244 | + | 7.00000i | −0.437215 | + | 0.252426i | −0.702416 | − | 0.711767i | \(-0.747895\pi\) |
0.265200 | + | 0.964193i | \(0.414562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | −15.5563 | − | 15.5563i | −0.559885 | − | 0.559885i | ||||
\(773\) | −46.3644 | − | 12.4233i | −1.66761 | − | 0.446836i | −0.703147 | − | 0.711044i | \(-0.748223\pi\) |
−0.964466 | + | 0.264209i | \(0.914889\pi\) | |||||||
\(774\) | 3.46410 | − | 6.00000i | 0.124515 | − | 0.215666i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.500000 | − | 0.866025i | 0.0179490 | − | 0.0310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.9706 | + | 16.9706i | −0.608424 | + | 0.608424i | ||||
\(779\) | −6.92820 | − | 3.00000i | −0.248229 | − | 0.107486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 5.19615i | 0.322045 | + | 0.185933i | ||||
\(782\) | 23.1822 | − | 6.21166i | 0.828994 | − | 0.222128i | ||||
\(783\) | −8.96575 | + | 33.4607i | −0.320410 | + | 1.19579i | ||||
\(784\) | 6.06218 | + | 3.50000i | 0.216506 | + | 0.125000i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.0000 | 0.535032 | ||||||||
\(787\) | 21.9203 | + | 21.9203i | 0.781375 | + | 0.781375i | 0.980063 | − | 0.198688i | \(-0.0636681\pi\) |
−0.198688 | + | 0.980063i | \(0.563668\pi\) | |||||||
\(788\) | 2.68973 | − | 10.0382i | 0.0958175 | − | 0.357596i | ||||
\(789\) | 3.46410 | + | 6.00000i | 0.123325 | + | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.55291 | − | 5.79555i | 0.0551804 | − | 0.205936i | ||||
\(793\) | −4.14110 | − | 15.4548i | −0.147055 | − | 0.548817i | ||||
\(794\) | −8.66025 | − | 15.0000i | −0.307341 | − | 0.532330i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | − | 12.1244i | 0.248108 | − | 0.429736i | ||||
\(797\) | −38.1838 | − | 38.1838i | −1.35254 | − | 1.35254i | −0.882812 | − | 0.469726i | \(-0.844353\pi\) |
−0.469726 | − | 0.882812i | \(-0.655647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.0000i | 1.69812i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0000 | + | 6.92820i | 0.423999 | + | 0.244796i | ||||
\(802\) | −8.36516 | − | 2.24144i | −0.295384 | − | 0.0791480i | ||||
\(803\) | 45.1719 | − | 12.1038i | 1.59408 | − | 0.427133i | ||||
\(804\) | 0.866025 | − | 0.500000i | 0.0305424 | − | 0.0176336i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.92820i | − | 0.244036i | ||||||
\(807\) | −6.69213 | − | 1.79315i | −0.235574 | − | 0.0631219i | ||||
\(808\) | −11.5911 | − | 3.10583i | −0.407774 | − | 0.109263i | ||||
\(809\) | − | 3.00000i | − | 0.105474i | −0.998608 | − | 0.0527372i | \(-0.983205\pi\) | ||
0.998608 | − | 0.0527372i | \(-0.0167946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.00000 | + | 5.19615i | −0.316033 | + | 0.182462i | −0.649623 | − | 0.760257i | \(-0.725073\pi\) |
0.333590 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.4548 | + | 4.14110i | 0.542024 | + | 0.145235i | ||||
\(814\) | 5.19615 | + | 3.00000i | 0.182125 | + | 0.105150i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.92820i | 0.242536i | ||||||||
\(817\) | −14.0406 | + | 5.55532i | −0.491218 | + | 0.194356i | ||||
\(818\) | −13.4722 | − | 13.4722i | −0.471044 | − | 0.471044i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0000 | − | 36.3731i | −0.732905 | − | 1.26943i | −0.955636 | − | 0.294549i | \(-0.904831\pi\) |
0.222731 | − | 0.974880i | \(-0.428503\pi\) | |||||||
\(822\) | 4.03459 | + | 15.0573i | 0.140722 | + | 0.525183i | ||||
\(823\) | 11.6555 | − | 43.4988i | 0.406285 | − | 1.51627i | −0.395390 | − | 0.918513i | \(-0.629390\pi\) |
0.801674 | − | 0.597761i | \(-0.203943\pi\) | |||||||
\(824\) | 10.0000i | 0.348367i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.54103 | − | 31.8756i | 0.297001 | − | 1.10842i | −0.642615 | − | 0.766189i | \(-0.722150\pi\) |
0.939615 | − | 0.342232i | \(-0.111183\pi\) | |||||||
\(828\) | 4.89898 | + | 4.89898i | 0.170251 | + | 0.170251i | ||||
\(829\) | 41.5692 | 1.44376 | 0.721879 | − | 0.692019i | \(-0.243279\pi\) | ||||
0.721879 | + | 0.692019i | \(0.243279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.517638 | + | 1.93185i | −0.0179459 | + | 0.0669749i | ||||
\(833\) | −46.8449 | + | 12.5521i | −1.62308 | + | 0.434903i | ||||
\(834\) | −4.33013 | − | 2.50000i | −0.149940 | − | 0.0865679i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.5000 | + | 7.79423i | −0.363150 | + | 0.269569i | ||||
\(837\) | 12.2474 | − | 12.2474i | 0.423334 | − | 0.423334i | ||||
\(838\) | 3.10583 | + | 11.5911i | 0.107289 | + | 0.400408i | ||||
\(839\) | 13.8564 | − | 24.0000i | 0.478376 | − | 0.828572i | −0.521316 | − | 0.853363i | \(-0.674559\pi\) |
0.999693 | + | 0.0247915i | \(0.00789218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.50000 | + | 16.4545i | −0.327586 | + | 0.567396i | ||||
\(842\) | −23.4225 | − | 6.27603i | −0.807191 | − | 0.216286i | ||||
\(843\) | 15.9217 | + | 15.9217i | 0.548372 | + | 0.548372i | ||||
\(844\) | −10.3923 | −0.357718 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0000 | + | 6.92820i | −0.412568 | + | 0.238197i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.24264 | − | 4.24264i | 0.145693 | − | 0.145693i | ||||
\(849\) | −7.79423 | − | 13.5000i | −0.267497 | − | 0.463319i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | + | 3.46410i | −0.205677 | + | 0.118748i | ||||
\(852\) | −0.896575 | − | 3.34607i | −0.0307162 | − | 0.114634i | ||||
\(853\) | 50.1910 | − | 13.4486i | 1.71851 | − | 0.460472i | 0.741022 | − | 0.671481i | \(-0.234341\pi\) |
0.977484 | + | 0.211008i | \(0.0676747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0800 | + | 6.98811i | −0.890876 | + | 0.238709i | −0.675094 | − | 0.737732i | \(-0.735897\pi\) |
−0.215782 | + | 0.976442i | \(0.569230\pi\) | |||||||
\(858\) | −1.55291 | − | 5.79555i | −0.0530156 | − | 0.197857i | ||||
\(859\) | −4.33013 | + | 2.50000i | −0.147742 | + | 0.0852989i | −0.572049 | − | 0.820220i | \(-0.693851\pi\) |
0.424307 | + | 0.905519i | \(0.360518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.44949 | − | 2.44949i | 0.0834300 | − | 0.0834300i | ||||
\(863\) | 29.6985 | − | 29.6985i | 1.01095 | − | 1.01095i | 0.0110088 | − | 0.999939i | \(-0.496496\pi\) |
0.999939 | − | 0.0110088i | \(-0.00350427\pi\) | |||||||
\(864\) | −4.33013 | + | 2.50000i | −0.147314 | + | 0.0850517i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.0000 | 0.883516 | ||||||||
\(867\) | −21.9203 | − | 21.9203i | −0.744453 | − | 0.744453i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.3923 | − | 18.0000i | 0.352535 | − | 0.610608i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.00000 | + | 1.73205i | −0.0338837 | + | 0.0586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.41421 | + | 1.41421i | −0.0478639 | + | 0.0478639i | ||||
\(874\) | −1.73205 | − | 15.0000i | −0.0585875 | − | 0.507383i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.5000 | − | 7.79423i | −0.456123 | − | 0.263343i | ||||
\(877\) | 19.3185 | − | 5.17638i | 0.652340 | − | 0.174794i | 0.0825533 | − | 0.996587i | \(-0.473693\pi\) |
0.569787 | + | 0.821793i | \(0.307026\pi\) | |||||||
\(878\) | −6.27603 | + | 23.4225i | −0.211806 | + | 0.790470i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | −9.89949 | − | 9.89949i | −0.333333 | − | 0.333333i | ||||
\(883\) | 10.3106 | − | 38.4797i | 0.346980 | − | 1.29495i | −0.543302 | − | 0.839537i | \(-0.682826\pi\) |
0.890282 | − | 0.455409i | \(-0.150507\pi\) | |||||||
\(884\) | −6.92820 | − | 12.0000i | −0.233021 | − | 0.403604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.5167i | 0.756462i | ||||||||
\(887\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(888\) | −0.517638 | − | 1.93185i | −0.0173708 | − | 0.0648287i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | + | 2.59808i | −0.0502519 | + | 0.0870388i | ||||
\(892\) | −18.3848 | − | 18.3848i | −0.615568 | − | 0.615568i | ||||
\(893\) | 29.8744 | + | 4.41851i | 0.999707 | + | 0.147860i | ||||
\(894\) | − | 18.0000i | − | 0.602010i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.69213 | + | 1.79315i | 0.223444 | + | 0.0598716i | ||||
\(898\) | 25.0955 | − | 6.72432i | 0.837447 | − | 0.224393i | ||||
\(899\) | 20.7846 | − | 12.0000i | 0.693206 | − | 0.400222i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5692i | 1.38487i | ||||||||
\(902\) | −5.01910 | − | 1.34486i | −0.167118 | − | 0.0447790i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 9.00000i | − | 0.299336i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.00000 | − | 1.73205i | 0.0996683 | − | 0.0575435i | ||||
\(907\) | 16.4207 | − | 4.39992i | 0.545242 | − | 0.146097i | 0.0243242 | − | 0.999704i | \(-0.492257\pi\) |
0.520917 | + | 0.853607i | \(0.325590\pi\) | |||||||
\(908\) | −20.2844 | − | 5.43520i | −0.673163 | − | 0.180373i | ||||
\(909\) | 20.7846 | + | 12.0000i | 0.689382 | + | 0.398015i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.3923i | − | 0.344312i | −0.985070 | − | 0.172156i | \(-0.944927\pi\) | ||
0.985070 | − | 0.172156i | \(-0.0550734\pi\) | |||||||
\(912\) | 4.31199 | + | 0.637756i | 0.142784 | + | 0.0211182i | ||||
\(913\) | 3.67423 | + | 3.67423i | 0.121599 | + | 0.121599i | ||||
\(914\) | −9.52628 | + | 16.5000i | −0.315101 | + | 0.545771i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.00000 | − | 3.46410i | −0.0660819 | − | 0.114457i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.96575 | − | 33.4607i | 0.295914 | − | 1.10437i | ||||
\(919\) | 38.0000i | 1.25350i | 0.779219 | + | 0.626752i | \(0.215616\pi\) | ||||
−0.779219 | + | 0.626752i | \(0.784384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.5000 | + | 19.9186i | 0.378938 | + | 0.656340i | ||||
\(922\) | 7.76457 | − | 28.9778i | 0.255713 | − | 0.954332i | ||||
\(923\) | 4.89898 | + | 4.89898i | 0.161252 | + | 0.161252i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.0000 | + | 12.1244i | 0.690103 | + | 0.398431i | ||||
\(927\) | 5.17638 | − | 19.3185i | 0.170015 | − | 0.634503i | ||||
\(928\) | −6.69213 | + | 1.79315i | −0.219680 | + | 0.0588631i | ||||
\(929\) | −2.59808 | − | 1.50000i | −0.0852401 | − | 0.0492134i | 0.456774 | − | 0.889583i | \(-0.349005\pi\) |
−0.542014 | + | 0.840369i | \(0.682338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.50000 | + | 30.3109i | 0.114708 | + | 0.993399i | ||||
\(932\) | 15.9217 | − | 15.9217i | 0.521532 | − | 0.521532i | ||||
\(933\) | −4.65874 | − | 17.3867i | −0.152520 | − | 0.569214i | ||||
\(934\) | 12.9904 | − | 22.5000i | 0.425058 | − | 0.736222i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | − | 3.46410i | 0.0653720 | − | 0.113228i | ||||
\(937\) | −31.7876 | − | 8.51747i | −1.03846 | − | 0.278254i | −0.300983 | − | 0.953630i | \(-0.597315\pi\) |
−0.737474 | + | 0.675376i | \(0.763981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.66025 | 0.282617 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | + | 1.73205i | −0.0977972 | + | 0.0564632i | −0.548101 | − | 0.836412i | \(-0.684649\pi\) |
0.450304 | + | 0.892875i | \(0.351316\pi\) | |||||||
\(942\) | −4.89898 | + | 4.89898i | −0.159617 | + | 0.159617i | ||||
\(943\) | 4.24264 | − | 4.24264i | 0.138159 | − | 0.138159i | ||||
\(944\) | −2.59808 | − | 4.50000i | −0.0845602 | − | 0.146463i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.00000 | + | 5.19615i | −0.292615 | + | 0.168941i | ||||
\(947\) | −6.27603 | − | 23.4225i | −0.203944 | − | 0.761128i | −0.989769 | − | 0.142679i | \(-0.954428\pi\) |
0.785825 | − | 0.618448i | \(-0.212238\pi\) | |||||||
\(948\) | −6.69213 | + | 1.79315i | −0.217350 | + | 0.0582388i | ||||
\(949\) | 31.1769 | 1.01205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.88229 | + | 14.4889i | 0.125760 | + | 0.469341i | 0.999866 | − | 0.0163940i | \(-0.00521862\pi\) |
−0.874106 | + | 0.485735i | \(0.838552\pi\) | |||||||
\(954\) | −10.3923 | + | 6.00000i | −0.336463 | + | 0.194257i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.6969 | − | 14.6969i | 0.475085 | − | 0.475085i | ||||
\(958\) | −16.9706 | + | 16.9706i | −0.548294 | + | 0.548294i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 2.82843 | + | 2.82843i | 0.0911922 | + | 0.0911922i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.59808 | + | 4.50000i | −0.0836784 | + | 0.144935i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.68973 | + | 10.0382i | 0.0864958 | + | 0.322807i | 0.995593 | − | 0.0937769i | \(-0.0298940\pi\) |
−0.909097 | + | 0.416583i | \(0.863227\pi\) | |||||||
\(968\) | 1.41421 | − | 1.41421i | 0.0454545 | − | 0.0454545i | ||||
\(969\) | −24.2487 | + | 18.0000i | −0.778981 | + | 0.578243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.5000 | + | 21.6506i | 1.20343 | + | 0.694802i | 0.961317 | − | 0.275445i | \(-0.0888254\pi\) |
0.242116 | + | 0.970247i | \(0.422159\pi\) | |||||||
\(972\) | 15.4548 | − | 4.14110i | 0.495713 | − | 0.132826i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32.9090 | − | 19.0000i | −1.05447 | − | 0.608799i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | 6.36396 | + | 6.36396i | 0.203601 | + | 0.203601i | 0.801541 | − | 0.597940i | \(-0.204014\pi\) |
−0.597940 | + | 0.801541i | \(0.704014\pi\) | |||||||
\(978\) | 3.13801 | − | 11.7112i | 0.100343 | − | 0.374484i | ||||
\(979\) | −10.3923 | − | 18.0000i | −0.332140 | − | 0.575282i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.5291 | − | 57.9555i | −0.495303 | − | 1.84849i | −0.528328 | − | 0.849040i | \(-0.677181\pi\) |
0.0330251 | − | 0.999455i | \(-0.489486\pi\) | |||||||
\(984\) | 0.866025 | + | 1.50000i | 0.0276079 | + | 0.0478183i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.0000 | − | 41.5692i | 0.764316 | − | 1.32383i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.10634 | + | 3.20736i | −0.257897 | + | 0.102040i | ||||
\(989\) | − | 12.0000i | − | 0.381578i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.0000 | + | 24.2487i | 1.33417 | + | 0.770286i | 0.985936 | − | 0.167121i | \(-0.0534469\pi\) |
0.348238 | + | 0.937406i | \(0.386780\pi\) | |||||||
\(992\) | 3.34607 | + | 0.896575i | 0.106238 | + | 0.0284663i | ||||
\(993\) | −11.7112 | + | 3.13801i | −0.371645 | + | 0.0995819i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1.73205i | − | 0.0548821i | ||||||
\(997\) | −13.3843 | − | 3.58630i | −0.423884 | − | 0.113579i | 0.0405699 | − | 0.999177i | \(-0.487083\pi\) |
−0.464454 | + | 0.885597i | \(0.653749\pi\) | |||||||
\(998\) | 29.9437 | + | 8.02339i | 0.947851 | + | 0.253976i | ||||
\(999\) | 10.0000i | 0.316386i |
(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 | 950.2.q.b.293.1 | yes | 8 | |
5.2 | odd | 4 | inner | 950.2.q.b.407.1 | yes | 8 | |
5.3 | odd | 4 | inner | 950.2.q.b.407.2 | yes | 8 | |
5.4 | even | 2 | inner | 950.2.q.b.293.2 | yes | 8 | |
19.12 | odd | 6 | inner | 950.2.q.b.943.1 | yes | 8 | |
95.12 | even | 12 | inner | 950.2.q.b.107.1 | ✓ | 8 | |
95.69 | odd | 6 | inner | 950.2.q.b.943.2 | yes | 8 | |
95.88 | even | 12 | inner | 950.2.q.b.107.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.q.b.107.1 | ✓ | 8 | 95.12 | even | 12 | inner | |
950.2.q.b.107.2 | yes | 8 | 95.88 | even | 12 | inner | |
950.2.q.b.293.1 | yes | 8 | 1.1 | even | 1 | trivial | |
950.2.q.b.293.2 | yes | 8 | 5.4 | even | 2 | inner | |
950.2.q.b.407.1 | yes | 8 | 5.2 | odd | 4 | inner | |
950.2.q.b.407.2 | yes | 8 | 5.3 | odd | 4 | inner | |
950.2.q.b.943.1 | yes | 8 | 19.12 | odd | 6 | inner | |
950.2.q.b.943.2 | yes | 8 | 95.69 | odd | 6 | inner |