Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3840,2,Mod(769,3840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3840.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3840 = 2^{8} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3840.f (of order \(2\), degree \(1\), 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: | \(30.6625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.180227832610816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.7 | ||
Root | \(0.450129 + 1.34067i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3840.769 |
Dual form | 3840.2.f.l.769.1 |
$q$-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 \(\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(1537\) | \(2561\) | \(2821\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22158 | + | 0.254102i | −0.993522 | + | 0.113638i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64265i | 0.998827i | 0.866364 | + | 0.499414i | \(0.166451\pi\) | ||||
−0.866364 | + | 0.499414i | \(0.833549\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.51363 | 0.456377 | 0.228189 | − | 0.973617i | \(-0.426720\pi\) | ||||
0.228189 | + | 0.973617i | \(0.426720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.87086i | 1.07358i | 0.843714 | + | 0.536792i | \(0.180364\pi\) | ||||
−0.843714 | + | 0.536792i | \(0.819636\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.254102 | − | 2.22158i | −0.0656088 | − | 0.573610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.31415i | − | 0.803800i | −0.915684 | − | 0.401900i | \(-0.868350\pi\) | ||
0.915684 | − | 0.401900i | \(-0.131650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.08582 | −1.62560 | −0.812799 | − | 0.582545i | \(-0.802057\pi\) | ||||
−0.812799 | + | 0.582545i | \(0.802057\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64265 | −0.576673 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.82778i | − | 1.00666i | −0.864094 | − | 0.503331i | \(-0.832108\pi\) | ||
0.864094 | − | 0.503331i | \(-0.167892\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.87086 | − | 1.12902i | 0.974173 | − | 0.225803i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18513 | 0.405769 | 0.202885 | − | 0.979203i | \(-0.434968\pi\) | ||||
0.202885 | + | 0.979203i | \(0.434968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.36266 | −1.32237 | −0.661187 | − | 0.750222i | \(-0.729947\pi\) | ||||
−0.661187 | + | 0.750222i | \(0.729947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.51363i | 0.263490i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.671502 | − | 5.87086i | −0.113504 | − | 0.992357i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.87086i | 1.29396i | 0.762506 | + | 0.646981i | \(0.223969\pi\) | ||||
−0.762506 | + | 0.646981i | \(0.776031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.87086 | −0.619834 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.72532 | −1.36267 | −0.681333 | − | 0.731973i | \(-0.738600\pi\) | ||||
−0.681333 | + | 0.731973i | \(0.738600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.01641i | − | 0.155001i | −0.996992 | − | 0.0775003i | \(-0.975306\pi\) | ||
0.996992 | − | 0.0775003i | \(-0.0246939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.22158 | − | 0.254102i | 0.331174 | − | 0.0378792i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.08582i | 1.03357i | 0.856114 | + | 0.516786i | \(0.172872\pi\) | ||||
−0.856114 | + | 0.516786i | \(0.827128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0164068 | 0.00234382 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.31415 | 0.464074 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.50820i | − | 0.619249i | −0.950859 | − | 0.309625i | \(-0.899797\pi\) | ||
0.950859 | − | 0.309625i | \(-0.100203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.36266 | + | 0.384617i | −0.453421 | + | 0.0518617i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.08582i | − | 0.938539i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.79893 | −0.885145 | −0.442573 | − | 0.896733i | \(-0.645934\pi\) | ||||
−0.442573 | + | 0.896733i | \(0.645934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.60104 | −0.461065 | −0.230533 | − | 0.973065i | \(-0.574047\pi\) | ||||
−0.230533 | + | 0.973065i | \(0.574047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.64265i | − | 0.332942i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.983593 | − | 8.59945i | −0.122000 | − | 1.06663i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.01641i | − | 0.124174i | −0.998071 | − | 0.0620869i | \(-0.980224\pi\) | ||
0.998071 | − | 0.0620869i | \(-0.0197756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82778 | 0.581197 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.72532 | 0.798149 | 0.399074 | − | 0.916919i | \(-0.369331\pi\) | ||||
0.399074 | + | 0.916919i | \(0.369331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.5146i | − | 1.81585i | −0.419132 | − | 0.907925i | \(-0.637666\pi\) | ||
0.419132 | − | 0.907925i | \(-0.362334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.12902 | + | 4.87086i | 0.130368 | + | 0.562439i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000i | 0.455842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.36266 | 0.828364 | 0.414182 | − | 0.910194i | \(-0.364068\pi\) | ||||
0.414182 | + | 0.910194i | \(0.364068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.74173i | 0.849765i | 0.905248 | + | 0.424883i | \(0.139685\pi\) | ||||
−0.905248 | + | 0.424883i | \(0.860315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.842131 | + | 7.36266i | 0.0913420 | + | 0.798593i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.18513i | 0.234271i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7581 | 1.56436 | 0.782180 | − | 0.623053i | \(-0.214108\pi\) | ||||
0.782180 | + | 0.623053i | \(0.214108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2293 | −1.07233 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 7.36266i | − | 0.763472i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.7417 | − | 1.80052i | 1.61507 | − | 0.184729i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.1444i | − | 1.13154i | −0.824563 | − | 0.565769i | \(-0.808579\pi\) | ||
0.824563 | − | 0.565769i | \(-0.191421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.51363 | −0.152126 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3295 | 1.32633 | 0.663167 | − | 0.748471i | \(-0.269212\pi\) | ||||
0.663167 | + | 0.748471i | \(0.269212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.958386i | 0.0944326i | 0.998885 | + | 0.0472163i | \(0.0150350\pi\) | ||||
−0.998885 | + | 0.0472163i | \(0.984965\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.87086 | − | 0.671502i | 0.572938 | − | 0.0655318i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.769233 | −0.0736792 | −0.0368396 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368396 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.87086 | −0.747069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.4585i | − | 1.36014i | −0.733146 | − | 0.680071i | \(-0.761949\pi\) | ||
0.733146 | − | 0.680071i | \(-0.238051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.22675 | + | 10.7253i | 0.114395 | + | 1.00014i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 3.87086i | − | 0.357862i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.75814 | 0.802857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.70892 | −0.791720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.72532i | − | 0.786736i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5341 | + | 3.74590i | −0.942203 | + | 0.335043i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.5290i | − | 1.02303i | −0.859274 | − | 0.511516i | \(-0.829084\pi\) | ||
0.859274 | − | 0.511516i | \(-0.170916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.01641 | 0.0894896 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.37270 | 0.644156 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 18.7253i | − | 1.62369i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.254102 | + | 2.22158i | 0.0218696 | + | 0.191203i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.88792i | − | 0.332167i | −0.986112 | − | 0.166084i | \(-0.946888\pi\) | ||
0.986112 | − | 0.166084i | \(-0.0531122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.6291 | −1.24083 | −0.620414 | − | 0.784275i | \(-0.713035\pi\) | ||||
−0.620414 | + | 0.784275i | \(0.713035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.08582 | −0.596733 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.85907i | 0.489960i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.85446 | + | 0.555246i | −0.403141 | + | 0.0461107i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0164068i | 0.00135321i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.0715 | −0.907010 | −0.453505 | − | 0.891254i | \(-0.649827\pi\) | ||||
−0.453505 | + | 0.891254i | \(0.649827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.637339 | −0.0518659 | −0.0259329 | − | 0.999664i | \(-0.508256\pi\) | ||||
−0.0259329 | + | 0.999664i | \(0.508256\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.31415i | 0.267933i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.3568 | − | 1.87086i | 1.31381 | − | 0.150271i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.129135i | 0.0103061i | 0.999987 | + | 0.00515306i | \(0.00164028\pi\) | ||||
−0.999987 | + | 0.00515306i | \(0.998360\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50820 | 0.357524 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7581 | 1.00548 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.4835i | − | 1.52606i | −0.646362 | − | 0.763031i | \(-0.723710\pi\) | ||
0.646362 | − | 0.763031i | \(-0.276290\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.384617 | − | 3.36266i | −0.0299424 | − | 0.261783i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.80052i | 0.139328i | 0.997571 | + | 0.0696641i | \(0.0221928\pi\) | ||||
−0.997571 | + | 0.0696641i | \(0.977807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.98359 | −0.152584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.08582 | 0.541866 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 23.2335i | − | 1.76641i | −0.468985 | − | 0.883206i | \(-0.655380\pi\) | ||
0.468985 | − | 0.883206i | \(-0.344620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.98359 | + | 12.8720i | 0.225538 | + | 0.973031i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.79893i | − | 0.511039i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.85664 | 0.213515 | 0.106757 | − | 0.994285i | \(-0.465953\pi\) | ||||
0.106757 | + | 0.994285i | \(0.465953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.28530 | −0.392853 | −0.196427 | − | 0.980519i | \(-0.562934\pi\) | ||||
−0.196427 | + | 0.980519i | \(0.562934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.60104i | − | 0.266196i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | − | 17.4858i | −0.147043 | − | 1.28558i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.01641i | − | 0.366836i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.64265 | 0.192224 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.96719 | −0.431770 | −0.215885 | − | 0.976419i | \(-0.569264\pi\) | ||||
−0.215885 | + | 0.976419i | \(0.569264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.9409i | − | 1.07547i | −0.843115 | − | 0.537733i | \(-0.819281\pi\) | ||
0.843115 | − | 0.537733i | \(-0.180719\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.59945 | − | 0.983593i | 0.615819 | − | 0.0704366i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.23353i | − | 0.230379i | −0.993344 | − | 0.115190i | \(-0.963252\pi\) | ||
0.993344 | − | 0.115190i | \(-0.0367476\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.12080 | −0.575668 | −0.287834 | − | 0.957680i | \(-0.592935\pi\) | ||||
−0.287834 | + | 0.957680i | \(0.592935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.01641 | 0.0716918 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.77454i | 0.405293i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.3840 | − | 2.21712i | 1.35384 | − | 0.154850i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.82778i | 0.335554i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7253 | −0.741886 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7141 | −0.944119 | −0.472059 | − | 0.881567i | \(-0.656489\pi\) | ||||
−0.472059 | + | 0.881567i | \(0.656489\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.72532i | 0.460812i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.258271 | + | 2.25803i | 0.0176139 | + | 0.153997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 19.4569i | − | 1.32082i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.5146 | 1.04838 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8286 | 0.862947 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.84472i | − | 0.659251i | −0.944112 | − | 0.329626i | \(-0.893077\pi\) | ||
0.944112 | − | 0.329626i | \(-0.106923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.87086 | + | 1.12902i | −0.324724 | + | 0.0752677i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5.70892i | − | 0.378914i | −0.981889 | − | 0.189457i | \(-0.939327\pi\) | ||
0.981889 | − | 0.189457i | \(-0.0606728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.769233 | −0.0508324 | −0.0254162 | − | 0.999677i | \(-0.508091\pi\) | ||||
−0.0254162 | + | 0.999677i | \(0.508091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.4008i | − | 1.20548i | −0.797939 | − | 0.602739i | \(-0.794076\pi\) | ||
0.797939 | − | 0.602739i | \(-0.205924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.80052 | − | 15.7417i | −0.117453 | − | 1.02688i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.36266i | 0.478256i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0328 | −0.648969 | −0.324484 | − | 0.945891i | \(-0.605191\pi\) | ||||
−0.324484 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7581 | 0.692992 | 0.346496 | − | 0.938051i | \(-0.387371\pi\) | ||||
0.346496 | + | 0.938051i | \(0.387371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0364490 | + | 0.00416898i | −0.00232864 | + | 0.000266347i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 27.4282i | − | 1.74522i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.74173 | −0.490612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.6580 | 0.798966 | 0.399483 | − | 0.916741i | \(-0.369190\pi\) | ||||
0.399483 | + | 0.916741i | \(0.369190\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.30749i | − | 0.459418i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.36266 | + | 0.842131i | −0.461068 | + | 0.0527363i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3110i | 0.830316i | 0.909749 | + | 0.415158i | \(0.136274\pi\) | ||||
−0.909749 | + | 0.415158i | \(0.863726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.7999 | −1.29244 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.18513 | −0.135256 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.4256i | 1.13617i | 0.822969 | + | 0.568087i | \(0.192316\pi\) | ||||
−0.822969 | + | 0.568087i | \(0.807684\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.14554 | + | 10.0153i | 0.0703701 | + | 0.615238i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.7581i | 0.903183i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.86940 | 0.235921 | 0.117961 | − | 0.993018i | \(-0.462364\pi\) | ||||
0.117961 | + | 0.993018i | \(0.462364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3955 | −1.05670 | −0.528350 | − | 0.849027i | \(-0.677189\pi\) | ||||
−0.528350 | + | 0.849027i | \(0.677189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10.2293i | − | 0.619108i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.37270 | − | 1.70892i | 0.444591 | − | 0.103052i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.887271i | − | 0.0533110i | −0.999645 | − | 0.0266555i | \(-0.991514\pi\) | ||
0.999645 | − | 0.0266555i | \(-0.00848571\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.36266 | 0.440791 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4835 | 0.804356 | 0.402178 | − | 0.915562i | \(-0.368253\pi\) | ||||
0.402178 | + | 0.915562i | \(0.368253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.4342i | 1.69024i | 0.534577 | + | 0.845120i | \(0.320471\pi\) | ||||
−0.534577 | + | 0.845120i | \(0.679529\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.80052 | + | 15.7417i | 0.106653 | + | 0.932460i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 23.0580i | − | 1.36107i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.01641 | 0.353906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1444 | 0.653294 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.99166i | 0.466878i | 0.972371 | + | 0.233439i | \(0.0749979\pi\) | ||||
−0.972371 | + | 0.233439i | \(0.925002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.1044 | − | 1.72762i | 0.879412 | − | 0.100586i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.51363i | − | 0.0878299i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.6877 | 1.08074 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.68601 | 0.154819 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.3295i | 0.765760i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | − | 0.915029i | 0.458079 | − | 0.0523944i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4506i | 0.995961i | 0.867188 | + | 0.497980i | \(0.165925\pi\) | ||||
−0.867188 | + | 0.497980i | \(0.834075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.958386 | −0.0545207 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4506 | −1.21635 | −0.608177 | − | 0.793801i | \(-0.708099\pi\) | ||||
−0.608177 | + | 0.793801i | \(0.708099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.73879i | 0.437422i | 0.975790 | + | 0.218711i | \(0.0701853\pi\) | ||||
−0.975790 | + | 0.218711i | \(0.929815\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.671502 | + | 5.87086i | 0.0378348 | + | 0.330786i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.2335i | 0.630938i | 0.948936 | + | 0.315469i | \(0.102162\pi\) | ||||
−0.948936 | + | 0.315469i | \(0.897838\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.30749 | 0.185184 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.4835i | 1.30665i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.37027 | + | 18.8545i | 0.242419 | + | 1.04586i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 0.769233i | − | 0.0425387i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.7253 | −1.03236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00084 | −0.439766 | −0.219883 | − | 0.975526i | \(-0.570568\pi\) | ||||
−0.219883 | + | 0.975526i | \(0.570568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 7.87086i | − | 0.431321i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.258271 | + | 2.25803i | 0.0141108 | + | 0.123369i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 21.5692i | − | 1.17495i | −0.809243 | − | 0.587474i | \(-0.800123\pi\) | ||
0.809243 | − | 0.587474i | \(-0.199877\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4585 | 0.785279 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1444 | −0.603501 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5419i | 1.00117i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.7253 | + | 1.22675i | −0.577432 | + | 0.0660459i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 21.7089i | − | 1.16540i | −0.812689 | − | 0.582698i | \(-0.801997\pi\) | ||
0.812689 | − | 0.582698i | \(-0.198003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.7422 | −1.32442 | −0.662211 | − | 0.749318i | \(-0.730382\pi\) | ||||
−0.662211 | + | 0.749318i | \(0.730382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.87086 | 0.206611 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3.31415i | − | 0.176394i | −0.996103 | − | 0.0881972i | \(-0.971889\pi\) | ||
0.996103 | − | 0.0881972i | \(-0.0281106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9409 | + | 1.70892i | −0.792979 | + | 0.0906998i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.75814i | 0.463530i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.7581 | −0.884461 | −0.442230 | − | 0.896902i | \(-0.645813\pi\) | ||||
−0.442230 | + | 0.896902i | \(0.645813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.2088 | 1.64257 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 8.70892i | − | 0.457100i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.94229 | + | 34.4671i | 0.206349 | + | 1.80409i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5324i | 1.48938i | 0.667411 | + | 0.744690i | \(0.267403\pi\) | ||||
−0.667411 | + | 0.744690i | \(0.732597\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.72532 | 0.454222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.9136 | 0.618523 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 37.5798i | − | 1.94581i | −0.231211 | − | 0.972904i | \(-0.574269\pi\) | ||
0.231211 | − | 0.972904i | \(-0.425731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.74590 | − | 10.5341i | −0.193437 | − | 0.543981i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.45836i | 0.435628i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.74456 | −0.346445 | −0.173222 | − | 0.984883i | \(-0.555418\pi\) | ||||
−0.173222 | + | 0.984883i | \(0.555418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.5290 | 0.590648 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.8312i | − | 1.11552i | −0.830001 | − | 0.557762i | \(-0.811660\pi\) | ||
0.830001 | − | 0.557762i | \(-0.188340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.01641 | − | 8.88633i | −0.0518009 | − | 0.452889i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.01641i | 0.0516669i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.81344 | 0.446859 | 0.223429 | − | 0.974720i | \(-0.428275\pi\) | ||||
0.223429 | + | 0.974720i | \(0.428275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.37270i | 0.371904i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.3568 | + | 1.87086i | −0.822998 | + | 0.0941334i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.821644i | − | 0.0412372i | −0.999787 | − | 0.0206186i | \(-0.993436\pi\) | ||
0.999787 | − | 0.0206186i | \(-0.00656356\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.7253 | 0.937439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7253 | −0.635472 | −0.317736 | − | 0.948179i | \(-0.602923\pi\) | ||||
−0.317736 | + | 0.948179i | \(0.602923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 28.4999i | − | 1.41968i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.22158 | + | 0.254102i | −0.110391 | + | 0.0126264i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.9136i | 0.590535i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.25827 | 0.111664 | 0.0558321 | − | 0.998440i | \(-0.482219\pi\) | ||||
0.0558321 | + | 0.998440i | \(0.482219\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.88792 | 0.191777 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 17.9672i | − | 0.884107i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.96719 | − | 17.1989i | −0.0965654 | − | 0.844261i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 14.6291i | − | 0.716392i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.4579 | 1.63453 | 0.817263 | − | 0.576264i | \(-0.195490\pi\) | ||||
0.817263 | + | 0.576264i | \(0.195490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3398 | 0.552669 | 0.276335 | − | 0.961061i | \(-0.410880\pi\) | ||||
0.276335 | + | 0.961061i | \(0.410880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7.08582i | − | 0.344524i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.74173 | − | 16.1428i | −0.181501 | − | 0.783040i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.51627i | − | 0.460525i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.85907 | −0.282878 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6597 | 0.513459 | 0.256730 | − | 0.966483i | \(-0.417355\pi\) | ||||
0.256730 | + | 0.966483i | \(0.417355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.5132i | 1.27414i | 0.770805 | + | 0.637072i | \(0.219854\pi\) | ||||
−0.770805 | + | 0.637072i | \(0.780146\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.555246 | − | 4.85446i | −0.0266220 | − | 0.232753i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.2088i | 1.63643i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.8789 | 1.56923 | 0.784613 | − | 0.619986i | \(-0.212862\pi\) | ||||
0.784613 | + | 0.619986i | \(0.212862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0164068 | −0.000781274 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5.70892i | − | 0.271239i | −0.990761 | − | 0.135619i | \(-0.956698\pi\) | ||
0.990761 | − | 0.135619i | \(-0.0433024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.7864 | + | 3.75007i | −1.55423 | + | 0.177770i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.0715i | − | 0.523662i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.2069 | −0.621890 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 0.637339i | − | 0.0299448i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.7253 | − | 2.59929i | 1.06538 | − | 0.121857i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.94229i | − | 0.184413i | −0.995740 | − | 0.0922064i | \(-0.970608\pi\) | ||
0.995740 | − | 0.0922064i | \(-0.0293920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.31415 | −0.154691 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.8969 | −1.57874 | −0.789369 | − | 0.613920i | \(-0.789592\pi\) | ||||
−0.789369 | + | 0.613920i | \(0.789592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.8688i | 1.06280i | 0.847120 | + | 0.531402i | \(0.178335\pi\) | ||||
−0.847120 | + | 0.531402i | \(0.821665\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.87086 | + | 16.3568i | 0.0867593 | + | 0.758527i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.7417i | − | 0.728440i | −0.931313 | − | 0.364220i | \(-0.881336\pi\) | ||
0.931313 | − | 0.364220i | \(-0.118664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.68601 | 0.124028 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.129135 | −0.00595024 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.53847i | − | 0.0707388i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.5140 | + | 8.00000i | −1.58361 | + | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.50820i | 0.206416i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.6925 | −0.945465 | −0.472732 | − | 0.881206i | \(-0.656732\pi\) | ||||
−0.472732 | + | 0.881206i | \(0.656732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.4671 | −1.38918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7581i | 0.580515i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.83180 | + | 24.7581i | 0.128586 | + | 1.12421i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.8401i | 1.39750i | 0.715366 | + | 0.698750i | \(0.246260\pi\) | ||||
−0.715366 | + | 0.698750i | \(0.753740\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.4835 | 0.881072 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9737 | 0.495238 | 0.247619 | − | 0.968858i | \(-0.420352\pi\) | ||||
0.247619 | + | 0.968858i | \(0.420352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.24186i | − | 0.326157i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.36266 | − | 0.384617i | 0.151140 | − | 0.0172872i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7727i | 0.797213i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.71729 | −0.166409 | −0.0832044 | − | 0.996533i | \(-0.526515\pi\) | ||||
−0.0832044 | + | 0.996533i | \(0.526515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.80052 | −0.0804412 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 39.9451i | − | 1.78107i | −0.454919 | − | 0.890533i | \(-0.650332\pi\) | ||
0.454919 | − | 0.890533i | \(-0.349668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.6126 | + | 3.38705i | −1.31774 | + | 0.150722i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.98359i | − | 0.0880945i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.0728979 | 0.00323114 | 0.00161557 | − | 0.999999i | \(-0.499486\pi\) | ||||
0.00161557 | + | 0.999999i | \(0.499486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.9997 | 1.81372 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.08582i | 0.312846i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.243528 | − | 2.12914i | −0.0107311 | − | 0.0938209i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7253i | 0.471699i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.2335 | 1.01984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.9672 | 0.524292 | 0.262146 | − | 0.965028i | \(-0.415570\pi\) | ||||
0.262146 | + | 0.965028i | \(0.415570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0656i | − | 0.702501i | −0.936282 | − | 0.351250i | \(-0.885757\pi\) | ||
0.936282 | − | 0.351250i | \(-0.114243\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.8720 | + | 2.98359i | −0.561779 | + | 0.130215i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.4010i | 1.06292i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.307491 | −0.0133692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.79893 | 0.295048 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 33.7745i | − | 1.46294i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.01641 | − | 8.88633i | −0.0439431 | − | 0.384190i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.85664i | 0.123273i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0248338 | 0.00106967 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8559 | 0.681698 | 0.340849 | − | 0.940118i | \(-0.389285\pi\) | ||||
0.340849 | + | 0.940118i | \(0.389285\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5.28530i | − | 0.226814i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.70892 | − | 0.195463i | 0.0732019 | − | 0.00837274i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.95078i | 0.211680i | 0.994383 | + | 0.105840i | \(0.0337531\pi\) | ||||
−0.994383 | + | 0.105840i | \(0.966247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.60104 | 0.153688 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.4835 | −0.659618 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.4569i | 0.827393i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.4858 | − | 2.00000i | 0.742230 | − | 0.0848953i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.26634i | − | 0.0536565i | −0.999640 | − | 0.0268283i | \(-0.991459\pi\) | ||
0.999640 | − | 0.0268283i | \(-0.00854073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.93437 | 0.166406 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.01641 | 0.211793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 5.70892i | − | 0.240602i | −0.992737 | − | 0.120301i | \(-0.961614\pi\) | ||
0.992737 | − | 0.120301i | \(-0.0383860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.67393 | + | 32.1208i | 0.154564 | + | 1.35133i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.64265i | 0.110981i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.75814 | −0.115627 | −0.0578135 | − | 0.998327i | \(-0.518413\pi\) | ||||
−0.0578135 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.7735 | −1.07859 | −0.539294 | − | 0.842118i | \(-0.681309\pi\) | ||||
−0.539294 | + | 0.842118i | \(0.681309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.96719i | − | 0.249283i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.45065 | − | 23.5155i | −0.227308 | − | 0.980663i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.7135i | 1.36188i | 0.732338 | + | 0.680941i | \(0.238429\pi\) | ||||
−0.732338 | + | 0.680941i | \(0.761571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.9409 | 0.620921 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.4587 | −0.848769 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.82376i | − | 0.282611i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.983593 | + | 8.59945i | 0.0406666 | + | 0.355543i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.4835i | 1.79475i | 0.441264 | + | 0.897377i | \(0.354530\pi\) | ||||
−0.441264 | + | 0.897377i | \(0.645470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 52.1705 | 2.14965 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.23353 | 0.133009 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.83021i | 0.321548i | 0.986991 | + | 0.160774i | \(0.0513991\pi\) | ||||
−0.986991 | + | 0.160774i | \(0.948601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.4569 | + | 2.22546i | −0.797656 | + | 0.0912348i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8.12080i | − | 0.332362i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.7581 | −1.33846 | −0.669231 | − | 0.743055i | \(-0.733376\pi\) | ||||
−0.669231 | + | 0.743055i | \(0.733376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.8074 | −0.726377 | −0.363189 | − | 0.931716i | \(-0.618312\pi\) | ||||
−0.363189 | + | 0.931716i | \(0.618312\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.01641i | 0.0413913i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.3476 | − | 2.21295i | 0.786591 | − | 0.0899692i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.41188i | 0.138484i | 0.997600 | + | 0.0692420i | \(0.0220581\pi\) | ||||
−0.997600 | + | 0.0692420i | \(0.977942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.77454 | −0.233996 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.4282 | −1.10963 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 36.6290i | − | 1.47943i | −0.672920 | − | 0.739716i | \(-0.734960\pi\) | ||
0.672920 | − | 0.739716i | \(-0.265040\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.21712 | + | 19.3840i | 0.0894029 | + | 0.781640i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.3979i | 1.62636i | 0.582012 | + | 0.813180i | \(0.302266\pi\) | ||||
−0.582012 | + | 0.813180i | \(0.697734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.5172 | −0.985430 | −0.492715 | − | 0.870191i | \(-0.663996\pi\) | ||||
−0.492715 | + | 0.870191i | \(0.663996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.82778 | −0.193732 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.0006i | 1.56252i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4506 | − | 10.9986i | 0.898026 | − | 0.439943i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 10.7253i | − | 0.428328i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.0852 | 1.04009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.7805 | −0.747640 | −0.373820 | − | 0.927501i | \(-0.621952\pi\) | ||||
−0.373820 | + | 0.927501i | \(0.621952\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 13.7141i | − | 0.545087i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.92953 | + | 25.6126i | 0.116255 | + | 1.01640i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0635083i | 0.00251629i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.72532 | −0.266050 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5163 | −0.612856 | −0.306428 | − | 0.951894i | \(-0.599134\pi\) | ||||
−0.306428 | + | 0.951894i | \(0.599134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4506i | 0.688186i | 0.938936 | + | 0.344093i | \(0.111814\pi\) | ||||
−0.938936 | + | 0.344093i | \(0.888186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.25803 | + | 0.258271i | −0.0889099 | + | 0.0101694i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.1403i | − | 0.516600i | −0.966065 | − | 0.258300i | \(-0.916838\pi\) | ||
0.966065 | − | 0.258300i | \(-0.0831624\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2911 | −0.403960 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.4569 | 0.762577 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.7993i | − | 0.579141i | −0.957157 | − | 0.289570i | \(-0.906488\pi\) | ||
0.957157 | − | 0.289570i | \(-0.0935124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.3791 | + | 1.87342i | −0.639983 | + | 0.0732004i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.5146i | 0.605284i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.99614 | −0.311485 | −0.155743 | − | 0.987798i | \(-0.549777\pi\) | ||||
−0.155743 | + | 0.987798i | \(0.549777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.915029 | 0.0355905 | 0.0177953 | − | 0.999842i | \(-0.494335\pi\) | ||||
0.0177953 | + | 0.999842i | \(0.494335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.8286i | 0.498223i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.75814 | + | 41.5999i | 0.184513 | + | 1.61317i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.5494i | − | 0.408473i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.84472 | 0.380619 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.45065 | −0.210420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.3978i | 1.32594i | 0.748647 | + | 0.662969i | \(0.230704\pi\) | ||||
−0.748647 | + | 0.662969i | \(0.769296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.12902 | − | 4.87086i | −0.0434559 | − | 0.187480i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 40.1676i | − | 1.54377i | −0.635764 | − | 0.771884i | \(-0.719315\pi\) | ||
0.635764 | − | 0.771884i | \(-0.280685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.4506 | 1.13021 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.70892 | 0.218766 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.2580i | − | 1.27258i | −0.771449 | − | 0.636291i | \(-0.780468\pi\) | ||
0.771449 | − | 0.636291i | \(-0.219532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.987927 | + | 8.63734i | 0.0377468 | + | 0.330016i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.769233i | − | 0.0293481i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4506 | 0.664817 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.2241 | −1.91062 | −0.955308 | − | 0.295611i | \(-0.904477\pi\) | ||||
−0.955308 | + | 0.295611i | \(0.904477\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 4.00000i | − | 0.151947i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.4999 | − | 3.71729i | 1.23279 | − | 0.141005i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.9170i | 1.09531i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.4008 | 0.695983 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.7543 | 0.897188 | 0.448594 | − | 0.893736i | \(-0.351925\pi\) | ||||
0.448594 | + | 0.893736i | \(0.351925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 55.7715i | − | 2.10346i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.7417 | − | 1.80052i | 0.592868 | − | 0.0678114i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.2252i | 1.32478i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.3146 | −1.36382 | −0.681911 | − | 0.731435i | \(-0.738851\pi\) | ||||
−0.681911 | + | 0.731435i | \(0.738851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.36266 | −0.276121 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.5453i | 1.33118i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.48880 | − | 13.0164i | −0.0556779 | − | 0.486786i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 10.0328i | − | 0.374682i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.7253 | −1.14586 | −0.572931 | − | 0.819604i | \(-0.694194\pi\) | ||||
−0.572931 | + | 0.819604i | \(0.694194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.53268 | −0.0943219 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.7581i | 0.400099i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.6435 | − | 2.46705i | 0.395289 | − | 0.0916240i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.47445i | 0.203036i | 0.994834 | + | 0.101518i | \(0.0323700\pi\) | ||||
−0.994834 | + | 0.101518i | \(0.967630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.36852 | −0.124589 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17.1455i | − | 0.633285i | −0.948545 | − | 0.316643i | \(-0.897444\pi\) | ||
0.948545 | − | 0.316643i | \(-0.102556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.00416898 | − | 0.0364490i | −0.000153775 | − | 0.00134444i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.53847i | − | 0.0566701i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.6019 | −0.426782 | −0.213391 | − | 0.976967i | \(-0.568451\pi\) | ||||
−0.213391 | + | 0.976967i | \(0.568451\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.4282 | 1.00760 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.6613i | 0.868048i | 0.900901 | + | 0.434024i | \(0.142907\pi\) | ||||
−0.900901 | + | 0.434024i | \(0.857093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.5962 | − | 2.81328i | 0.901135 | − | 0.103071i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.74173i | − | 0.283255i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.5706 | −0.386241 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4283 | −0.417024 | −0.208512 | − | 0.978020i | \(-0.566862\pi\) | ||||
−0.208512 | + | 0.978020i | \(0.566862\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.6580i | 0.461283i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.41590 | − | 0.161949i | 0.0515299 | − | 0.00589392i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1784i | 0.697049i | 0.937300 | + | 0.348525i | \(0.113317\pi\) | ||||
−0.937300 | + | 0.348525i | \(0.886683\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.30749 | 0.265245 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.03281 | −0.146189 | −0.0730947 | − | 0.997325i | \(-0.523288\pi\) | ||||
−0.0730947 | + | 0.997325i | \(0.523288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.03281i | − | 0.0735928i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.842131 | − | 7.36266i | −0.0304473 | − | 0.266198i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 26.3177i | − | 0.950279i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.95078 | 0.106408 | 0.0532039 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532039 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3110 | −0.479383 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 45.2663i | − | 1.62812i | −0.580783 | − | 0.814059i | \(-0.697253\pi\) | ||
0.580783 | − | 0.814059i | \(-0.302747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.8625 | + | 8.31256i | −1.28822 | + | 0.298596i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 20.7999i | − | 0.746193i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 61.8260 | 2.21515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1797 | 0.364257 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.18513i | − | 0.0780903i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0328135 | − | 0.286885i | −0.00117116 | − | 0.0102394i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 52.9997i | − | 1.88924i | −0.328171 | − | 0.944618i | \(-0.606432\pi\) | ||
0.328171 | − | 0.944618i | \(-0.393568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.4256 | −0.655970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.2088 | 1.35855 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 13.9391i | − | 0.494993i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.0153 | + | 1.14554i | −0.355208 | + | 0.0406282i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5738i | 0.587075i | 0.955948 | + | 0.293538i | \(0.0948326\pi\) | ||||
−0.955948 | + | 0.293538i | \(0.905167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.4835 | 0.830785 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.7581 | −0.521453 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 23.4835i | − | 0.828713i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.3433 | + | 3.24186i | −0.998969 | + | 0.114261i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.86940i | 0.136209i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.5491 | −1.32016 | −0.660078 | − | 0.751197i | \(-0.729477\pi\) | ||||
−0.660078 | + | 0.751197i | \(0.729477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.1102 | −1.12754 | −0.563771 | − | 0.825931i | \(-0.690650\pi\) | ||||
−0.563771 | + | 0.825931i | \(0.690650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 17.3955i | − | 0.610086i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.95078 | + | 43.2841i | 0.173418 | + | 1.51618i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.20207i | 0.251969i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.2293 | 0.357442 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.3809 | −1.02540 | −0.512699 | − | 0.858568i | \(-0.671354\pi\) | ||||
−0.512699 | + | 0.858568i | \(0.671354\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.3866i | − | 0.989495i | −0.869037 | − | 0.494748i | \(-0.835260\pi\) | ||
0.869037 | − | 0.494748i | \(-0.164740\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.70892 | + | 7.37270i | 0.0594968 | + | 0.256684i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.45065i | 0.0504439i | 0.999682 | + | 0.0252219i | \(0.00802924\pi\) | ||||
−0.999682 | + | 0.0252219i | \(0.991971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.4621 | −1.30111 | −0.650556 | − | 0.759458i | \(-0.725464\pi\) | ||||
−0.650556 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.887271 | 0.0307791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.0543744i | − | 0.00188396i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.457515 | − | 4.00000i | −0.0158329 | − | 0.138426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.36266i | 0.254491i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.7581 | −1.68332 | −0.841659 | − | 0.540010i | \(-0.818421\pi\) | ||||
−0.841659 | + | 0.540010i | \(0.818421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2252 | −0.835351 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.4835i | 0.464395i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.40672 | − | 0.504034i | 0.151596 | − | 0.0173393i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 23.0146i | − | 0.790791i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.4342 | −0.975861 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.9988 | 1.30258 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.37073i | 0.149651i | 0.997197 | + | 0.0748255i | \(0.0238400\pi\) | ||||
−0.997197 | + | 0.0748255i | \(0.976160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.7417 | + | 1.80052i | −0.538356 | + | 0.0615764i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5130i | 0.700712i | 0.936617 | + | 0.350356i | \(0.113939\pi\) | ||||
−0.936617 | + | 0.350356i | \(0.886061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1131 | −0.345054 | −0.172527 | − | 0.985005i | \(-0.555193\pi\) | ||||
−0.172527 | + | 0.985005i | \(0.555193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.0580 | 0.785813 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.2861i | 0.452266i | 0.974096 | + | 0.226133i | \(0.0726083\pi\) | ||||
−0.974096 | + | 0.226133i | \(0.927392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.90368 | + | 51.6152i | 0.200731 | + | 1.75497i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.01641i | 0.204328i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1444 | 0.378047 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.93437 | 0.133311 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.1444i | 0.377180i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.89909 | − | 27.8381i | −0.334650 | − | 0.941098i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.6454i | 1.13612i | 0.822986 | + | 0.568062i | \(0.192307\pi\) | ||||
−0.822986 | + | 0.568062i | \(0.807693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.99166 | −0.269552 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.7909 | −1.10476 | −0.552378 | − | 0.833594i | \(-0.686279\pi\) | ||||
−0.552378 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4506i | 1.12570i | 0.826558 | + | 0.562852i | \(0.190296\pi\) | ||||
−0.826558 | + | 0.562852i | \(0.809704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.72762 | + | 15.1044i | 0.0580733 | + | 0.507729i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 34.8924i | − | 1.17157i | −0.810466 | − | 0.585785i | \(-0.800786\pi\) | ||
0.810466 | − | 0.585785i | \(-0.199214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.4671 | 1.02183 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.51363 | 0.0507086 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 50.2088i | − | 1.68017i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.34625 | + | 0.725876i | −0.212132 | + | 0.0242634i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.6877i | 0.623964i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.0884 | −0.536578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.9409 | −0.497752 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.68601i | 0.0893847i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7417 | − | 1.34300i | 0.390308 | − | 0.0446429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.9836i | 1.02879i | 0.857552 | + | 0.514397i | \(0.171984\pi\) | ||||
−0.857552 | + | 0.514397i | \(0.828016\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.3295 | −0.442112 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7181i | 0.387814i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.915029 | + | 8.00000i | 0.0302499 | + | 0.264472i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.4835i | 0.643400i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.6043 | −0.514737 | −0.257368 | − | 0.966313i | \(-0.582855\pi\) | ||||
−0.257368 | + | 0.966313i | \(0.582855\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.4506 | −0.575018 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.0328i | 0.856880i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.88633 | + | 38.3379i | 0.292181 | + | 1.26054i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.958386i | − | 0.0314775i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.9341 | 1.27739 | 0.638693 | − | 0.769461i | \(-0.279475\pi\) | ||||
0.638693 | + | 0.769461i | \(0.279475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.116255 | −0.00381011 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 21.4506i | − | 0.702263i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.27468 | + | 11.1444i | 0.0416864 | + | 0.364460i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.6027i | 0.640393i | 0.947351 | + | 0.320197i | \(0.103749\pi\) | ||||
−0.947351 | + | 0.320197i | \(0.896251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.73879 | −0.252546 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.0476 | −0.816530 | −0.408265 | − | 0.912864i | \(-0.633866\pi\) | ||||
−0.408265 | + | 0.912864i | \(0.633866\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.1240i | 1.37175i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.87086 | + | 0.671502i | −0.190979 | + | 0.0218439i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 7.93437i | − | 0.257832i | −0.991655 | − | 0.128916i | \(-0.958850\pi\) | ||
0.991655 | − | 0.128916i | \(-0.0411498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0550 | 1.94947 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.2335 | −0.364272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4809i | 0.371903i | 0.982559 | + | 0.185952i | \(0.0595368\pi\) | ||||
−0.982559 | + | 0.185952i | \(0.940463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.2566 | − | 1.51627i | 0.428974 | − | 0.0490654i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.30749i | 0.106916i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.2744 | 0.331778 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.2088 | 0.748670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 4.00000i | − | 0.128898i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.79650 | + | 33.1924i | 0.122214 | + | 1.06850i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8993i | 0.511285i | 0.966771 | + | 0.255643i | \(0.0822871\pi\) | ||||
−0.966771 | + | 0.255643i | \(0.917713\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.4835 | −0.754397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.6600 | −1.30484 | −0.652421 | − | 0.757857i | \(-0.726246\pi\) | ||||
−0.652421 | + | 0.757857i | \(0.726246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 38.6597i | − | 1.23937i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.8545 | + | 4.37027i | −0.603826 | + | 0.139961i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.5676i | 0.849972i | 0.905200 | + | 0.424986i | \(0.139721\pi\) | ||||
−0.905200 | + | 0.424986i | \(0.860279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.3384 | 0.713938 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.769233 | 0.0245597 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9.88057i | − | 0.315141i | −0.987508 | − | 0.157571i | \(-0.949634\pi\) | ||
0.987508 | − | 0.157571i | \(-0.0503662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.821644 | + | 7.18355i | 0.0261798 | + | 0.228887i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 18.7253i | − | 0.596034i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.90699 | −0.156033 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.0549 | −1.68534 | −0.842672 | − | 0.538427i | \(-0.819019\pi\) | ||||
−0.842672 | + | 0.538427i | \(0.819019\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.00084i | − | 0.253899i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0410 | − | 2.06351i | 0.571939 | − | 0.0654176i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.3051i | 1.02311i | 0.859250 | + | 0.511556i | \(0.170931\pi\) | ||||
−0.859250 | + | 0.511556i | \(0.829069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.87086 | 0.249023 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))