Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.3 | ||
Root | \(-0.956115 + 1.65604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.k.177.3 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.956115 | − | 1.65604i | 0.552013 | − | 0.956115i | −0.446116 | − | 0.894975i | \(-0.647193\pi\) |
0.998129 | − | 0.0611395i | \(-0.0194735\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.78442 | + | 3.09071i | 0.798019 | + | 1.38221i | 0.920904 | + | 0.389789i | \(0.127452\pi\) |
−0.122885 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78442 | + | 1.95341i | −0.674449 | + | 0.738321i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.328310 | − | 0.568650i | −0.109437 | − | 0.189550i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.91223 | −1.63976 | −0.819879 | − | 0.572537i | \(-0.805959\pi\) | ||||
−0.819879 | + | 0.572537i | \(0.805959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.82446 | 1.76207 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.828310 | − | 1.43468i | 0.200895 | − | 0.347960i | −0.747922 | − | 0.663786i | \(-0.768948\pi\) |
0.948817 | + | 0.315826i | \(0.102282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.740539 | + | 1.28265i | 0.169891 | + | 0.294261i | 0.938382 | − | 0.345601i | \(-0.112325\pi\) |
−0.768490 | + | 0.639862i | \(0.778992\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.52882 | + | 4.82277i | 0.333615 | + | 1.05241i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.67169 | + | 2.89545i | 0.348571 | + | 0.603743i | 0.985996 | − | 0.166769i | \(-0.0533335\pi\) |
−0.637425 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.86834 | + | 6.70017i | −0.773669 | + | 1.34003i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.48108 | 0.862384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.08007 | 0.571954 | 0.285977 | − | 0.958236i | \(-0.407682\pi\) | ||||
0.285977 | + | 0.958236i | \(0.407682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.54003 | + | 6.13152i | −0.635809 | + | 1.10125i | 0.350534 | + | 0.936550i | \(0.386000\pi\) |
−0.986343 | + | 0.164703i | \(0.947333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.956115 | + | 1.65604i | 0.166438 | + | 0.288279i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.22162 | − | 2.02943i | −1.55874 | − | 0.343036i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.25561 | + | 3.90683i | 0.370820 | + | 0.642279i | 0.989692 | − | 0.143213i | \(-0.0457434\pi\) |
−0.618872 | + | 0.785492i | \(0.712410\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.65277 | + | 9.79088i | −0.905167 | + | 1.56780i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.28575 | −0.200800 | −0.100400 | − | 0.994947i | \(-0.532012\pi\) | ||||
−0.100400 | + | 0.994947i | \(0.532012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.59899 | −0.243843 | −0.121922 | − | 0.992540i | \(-0.538906\pi\) | ||||
−0.121922 | + | 0.992540i | \(0.538906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.17169 | − | 2.02943i | 0.174665 | − | 0.302529i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.828310 | − | 1.43468i | −0.120821 | − | 0.209269i | 0.799270 | − | 0.600972i | \(-0.205220\pi\) |
−0.920092 | + | 0.391703i | \(0.871886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.631656 | − | 6.97144i | −0.0902366 | − | 0.995920i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.58392 | − | 2.74343i | −0.221793 | − | 0.384157i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.61274 | + | 7.98949i | −0.633608 | + | 1.09744i | 0.353200 | + | 0.935548i | \(0.385093\pi\) |
−0.986808 | + | 0.161893i | \(0.948240\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.56885 | −0.481224 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.83216 | 0.375129 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.42598 | − | 7.66602i | 0.576213 | − | 0.998030i | −0.419696 | − | 0.907665i | \(-0.637863\pi\) |
0.995909 | − | 0.0903653i | \(-0.0288035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.34338 | + | 5.79090i | 0.428076 | + | 0.741449i | 0.996702 | − | 0.0811468i | \(-0.0258583\pi\) |
−0.568626 | + | 0.822596i | \(0.692525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.69665 | + | 0.373387i | 0.213758 | + | 0.0470424i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5499 | − | 18.2730i | −1.30856 | − | 2.26649i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.91223 | + | 8.50823i | −0.600124 | + | 1.03945i | 0.392677 | + | 0.919676i | \(0.371549\pi\) |
−0.992802 | + | 0.119770i | \(0.961784\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.39331 | 0.769664 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.61878 | 1.02286 | 0.511430 | − | 0.859325i | \(-0.329116\pi\) | ||||
0.511430 | + | 0.859325i | \(0.329116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.28057 | + | 3.95007i | −0.266921 | + | 0.462321i | −0.968065 | − | 0.250699i | \(-0.919340\pi\) |
0.701144 | + | 0.713019i | \(0.252673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.39716 | + | 12.8123i | 0.854150 | + | 1.47943i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.799494 | − | 2.52206i | −0.0911108 | − | 0.287416i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.19665 | − | 5.53677i | −0.359652 | − | 0.622935i | 0.628251 | − | 0.778011i | \(-0.283771\pi\) |
−0.987903 | + | 0.155076i | \(0.950438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.26936 | − | 9.12679i | 0.585484 | − | 1.01409i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.167838 | −0.0184226 | −0.00921130 | − | 0.999958i | \(-0.502932\pi\) | ||||
−0.00921130 | + | 0.999958i | \(0.502932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.91223 | 0.641271 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.94490 | − | 5.10071i | 0.315726 | − | 0.546854i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.28442 | + | 2.22469i | 0.136149 | + | 0.235817i | 0.926036 | − | 0.377436i | \(-0.123194\pi\) |
−0.789887 | + | 0.613252i | \(0.789861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5499 | − | 11.5490i | 1.10593 | − | 1.21067i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.76936 | + | 11.7249i | 0.701949 | + | 1.21581i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.64287 | + | 4.57759i | −0.271153 | + | 0.469651i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.73669 | 0.988611 | 0.494305 | − | 0.869288i | \(-0.335422\pi\) | ||||
0.494305 | + | 0.869288i | \(0.335422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.656620 | 0.0659928 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.927299 | + | 1.60613i | −0.0922697 | + | 0.159816i | −0.908466 | − | 0.417959i | \(-0.862746\pi\) |
0.816196 | + | 0.577775i | \(0.196079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.58392 | − | 2.74343i | −0.156068 | − | 0.270318i | 0.777379 | − | 0.629032i | \(-0.216549\pi\) |
−0.933447 | + | 0.358714i | \(0.883215\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.1777 | + | 13.3310i | −1.18843 | + | 1.30097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.38341 | − | 4.12819i | −0.230413 | − | 0.399087i | 0.727517 | − | 0.686090i | \(-0.240674\pi\) |
−0.957930 | + | 0.287003i | \(0.907341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.44105 | − | 12.8883i | 0.712723 | − | 1.23447i | −0.251108 | − | 0.967959i | \(-0.580795\pi\) |
0.963831 | − | 0.266513i | \(-0.0858716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.62648 | 0.818789 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4432 | 1.17056 | 0.585281 | − | 0.810831i | \(-0.300984\pi\) | ||||
0.585281 | + | 0.810831i | \(0.300984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.96601 | + | 10.3334i | −0.556333 | + | 0.963597i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.94105 | + | 3.36199i | 0.179450 | + | 0.310816i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.32446 | + | 4.17810i | 0.121413 | + | 0.383006i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.22932 | + | 2.12925i | −0.110844 | + | 0.191988i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.76683 | −0.873571 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.62142 | 0.587556 | 0.293778 | − | 0.955874i | \(-0.405087\pi\) | ||||
0.293778 | + | 0.955874i | \(0.405087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.52882 | + | 2.64799i | −0.134605 | + | 0.233142i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.02882 | − | 5.24606i | −0.264629 | − | 0.458351i | 0.702837 | − | 0.711351i | \(-0.251916\pi\) |
−0.967466 | + | 0.253000i | \(0.918583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.82699 | − | 0.842215i | −0.331842 | − | 0.0730293i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.99615 | + | 13.8497i | 0.688199 | + | 1.19200i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.71172 | − | 6.42889i | 0.317114 | − | 0.549257i | −0.662771 | − | 0.748822i | \(-0.730620\pi\) |
0.979885 | + | 0.199565i | \(0.0639529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8245 | 0.918119 | 0.459059 | − | 0.888406i | \(-0.348187\pi\) | ||||
0.459059 | + | 0.888406i | \(0.348187\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.16784 | −0.266780 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.95611 | − | 5.12014i | 0.247203 | − | 0.428168i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.49615 | + | 9.51961i | 0.456430 | + | 0.790560i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1489 | − | 5.61945i | −1.00203 | − | 0.463484i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | + | 0.866025i | 0.0409616 | + | 0.0709476i | 0.885779 | − | 0.464107i | \(-0.153625\pi\) |
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.21172 | − | 14.2231i | 0.668261 | − | 1.15746i | −0.310130 | − | 0.950694i | \(-0.600372\pi\) |
0.978390 | − | 0.206767i | \(-0.0662942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.08777 | −0.0879411 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.2677 | −2.02955 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.72547 | − | 9.91681i | 0.456942 | − | 0.791447i | −0.541855 | − | 0.840472i | \(-0.682278\pi\) |
0.998798 | + | 0.0490246i | \(0.0156113\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.82061 | + | 15.2777i | 0.699520 | + | 1.21160i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.63902 | − | 1.90121i | −0.680850 | − | 0.149837i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.46986 | − | 7.74203i | −0.350107 | − | 0.606402i | 0.636161 | − | 0.771556i | \(-0.280521\pi\) |
−0.986268 | + | 0.165154i | \(0.947188\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.41223 | + | 5.91015i | −0.265642 | + | 0.460105i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2178 | 1.40973 | 0.704867 | − | 0.709340i | \(-0.251007\pi\) | ||||
0.704867 | + | 0.709340i | \(0.251007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.9545 | 1.68880 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.486253 | − | 0.842215i | 0.0371847 | − | 0.0644058i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.78057 | − | 16.9404i | −0.743603 | − | 1.28796i | −0.950845 | − | 0.309669i | \(-0.899782\pi\) |
0.207241 | − | 0.978290i | \(-0.433551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.18544 | − | 19.5124i | −0.467575 | − | 1.47500i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.46348 | − | 14.6592i | −0.636154 | − | 1.10185i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.62395 | − | 2.81277i | 0.121380 | − | 0.210236i | −0.798932 | − | 0.601421i | \(-0.794601\pi\) |
0.920312 | + | 0.391185i | \(0.127935\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3407 | −0.768621 | −0.384310 | − | 0.923204i | \(-0.625561\pi\) | ||||
−0.384310 | + | 0.923204i | \(0.625561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.7866 | 0.945214 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.04993 | + | 13.9429i | −0.591843 | + | 1.02510i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.828310 | + | 1.43468i | 0.0605720 | + | 0.104914i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.99615 | + | 8.75340i | −0.581634 | + | 0.636716i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.01122 | + | 8.67968i | 0.362599 | + | 0.628040i | 0.988388 | − | 0.151953i | \(-0.0485561\pi\) |
−0.625789 | + | 0.779993i | \(0.715223\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6627 | + | 21.9324i | −0.911478 | + | 1.57873i | −0.0995016 | + | 0.995037i | \(0.531725\pi\) |
−0.811977 | + | 0.583690i | \(0.801609\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40.3478 | −2.88936 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.5809 | −1.75132 | −0.875660 | − | 0.482929i | \(-0.839573\pi\) | ||||
−0.875660 | + | 0.482929i | \(0.839573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.79564 | − | 4.84219i | 0.198178 | − | 0.343254i | −0.749760 | − | 0.661710i | \(-0.769831\pi\) |
0.947938 | + | 0.318456i | \(0.103164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.39331 | + | 16.2697i | 0.662553 | + | 1.14758i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.49615 | + | 6.01665i | −0.385754 | + | 0.422286i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.29432 | − | 3.97388i | −0.160242 | − | 0.277548i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.09767 | − | 1.90121i | 0.0762930 | − | 0.132143i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.48108 | −0.102448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0999 | −0.832988 | −0.416494 | − | 0.909138i | \(-0.636741\pi\) | ||||
−0.416494 | + | 0.909138i | \(0.636741\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.24054 | − | 14.2730i | 0.564632 | − | 0.977972i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.85327 | − | 4.94202i | −0.194592 | − | 0.337043i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.66047 | − | 17.8564i | −0.384258 | − | 1.21217i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.36098 | + | 7.55344i | 0.294688 | + | 0.510414i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.89716 | + | 8.48213i | −0.329419 | + | 0.570570i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.6265 | −1.04643 | −0.523213 | − | 0.852202i | \(-0.675267\pi\) | ||||
−0.523213 | + | 0.852202i | \(0.675267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.08007 | 0.338671 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.83435 | + | 13.5695i | −0.519984 | + | 0.900639i | 0.479746 | + | 0.877408i | \(0.340729\pi\) |
−0.999730 | + | 0.0232317i | \(0.992604\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.78575 | + | 4.82506i | 0.184087 | + | 0.318849i | 0.943269 | − | 0.332031i | \(-0.107734\pi\) |
−0.759181 | + | 0.650879i | \(0.774400\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.94105 | − | 1.08739i | −0.325097 | − | 0.0715449i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.63770 | + | 16.6930i | 0.631387 | + | 1.09359i | 0.987268 | + | 0.159063i | \(0.0508472\pi\) |
−0.355882 | + | 0.934531i | \(0.615819\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.95611 | − | 5.12014i | 0.192836 | − | 0.334001i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.2255 | −0.794130 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.1575 | 1.43325 | 0.716624 | − | 0.697459i | \(-0.245686\pi\) | ||||
0.716624 | + | 0.697459i | \(0.245686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.93719 | − | 17.2117i | 0.640111 | − | 1.10870i | −0.345297 | − | 0.938494i | \(-0.612222\pi\) |
0.985408 | − | 0.170211i | \(-0.0544449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.35460 | − | 5.81033i | −0.215198 | − | 0.372733i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.4196 | − | 14.3923i | 1.30456 | − | 0.919489i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.37824 | − | 7.58333i | −0.278581 | − | 0.482516i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.160472 | + | 0.277946i | −0.0101695 | + | 0.0176141i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1076 | −1.39542 | −0.697708 | − | 0.716382i | \(-0.745797\pi\) | ||||
−0.697708 | + | 0.716382i | \(0.745797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.34338 | −0.210196 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.65277 | − | 9.79088i | 0.353990 | − | 0.613129i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5598 | − | 25.2184i | −0.908217 | − | 1.57308i | −0.816540 | − | 0.577289i | \(-0.804111\pi\) |
−0.0916768 | − | 0.995789i | \(-0.529223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6566 | − | 2.56530i | −0.724307 | − | 0.159400i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.01122 | − | 1.75148i | −0.0625928 | − | 0.108414i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.75176 | + | 13.4264i | −0.477994 | + | 0.827910i | −0.999682 | − | 0.0252268i | \(-0.991969\pi\) |
0.521688 | + | 0.853136i | \(0.325303\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.9243 | −2.02252 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.91223 | 0.300624 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.853274 | + | 1.47791i | −0.0520251 | + | 0.0901100i | −0.890865 | − | 0.454268i | \(-0.849901\pi\) |
0.838840 | + | 0.544378i | \(0.183234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2642 | − | 17.7781i | −0.623505 | − | 1.07994i | −0.988828 | − | 0.149061i | \(-0.952375\pi\) |
0.365323 | − | 0.930881i | \(-0.380958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.03871 | − | 28.5133i | −0.547048 | − | 1.72570i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.86834 | − | 6.70017i | −0.233270 | − | 0.404035i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.3305 | − | 23.0891i | 0.800952 | − | 1.38729i | −0.118038 | − | 0.993009i | \(-0.537660\pi\) |
0.918990 | − | 0.394281i | \(-0.129006\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.64892 | 0.278323 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7444 | 0.939232 | 0.469616 | − | 0.882871i | \(-0.344392\pi\) | ||||
0.469616 | + | 0.882871i | \(0.344392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.03486 | + | 13.9168i | −0.477623 | + | 0.827267i | −0.999671 | − | 0.0256490i | \(-0.991835\pi\) |
0.522048 | + | 0.852916i | \(0.325168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.05378 | + | 8.75340i | 0.299360 | + | 0.518507i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.29432 | − | 2.51160i | 0.135429 | − | 0.148255i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.12780 | + | 12.3457i | 0.419283 | + | 0.726219i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.30939 | − | 16.1243i | 0.545726 | − | 0.945225i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3357 | 0.895920 | 0.447960 | − | 0.894054i | \(-0.352151\pi\) | ||||
0.447960 | + | 0.894054i | \(0.352151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.5913 | 1.83932 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.24054 | + | 3.88073i | −0.130009 | + | 0.225183i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.88341 | − | 17.1186i | −0.571573 | − | 0.989993i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.85327 | − | 3.12349i | 0.164460 | − | 0.180035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.77321 | + | 3.07129i | 0.101868 | + | 0.176441i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.9320 | + | 20.6669i | −0.683225 | + | 1.18338i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.4707 | 0.940034 | 0.470017 | − | 0.882657i | \(-0.344248\pi\) | ||||
0.470017 | + | 0.882657i | \(0.344248\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.05763 | −0.344607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.8146 | − | 18.7314i | 0.613238 | − | 1.06216i | −0.377453 | − | 0.926029i | \(-0.623200\pi\) |
0.990691 | − | 0.136130i | \(-0.0434665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.19412 | − | 14.1926i | −0.463159 | − | 0.802215i | 0.535957 | − | 0.844245i | \(-0.319951\pi\) |
−0.999116 | + | 0.0420298i | \(0.986618\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.87352 | + | 5.91015i | 0.105561 | + | 0.332999i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.23064 | − | 3.86359i | −0.125285 | − | 0.217001i | 0.796559 | − | 0.604561i | \(-0.206651\pi\) |
−0.921844 | + | 0.387560i | \(0.873318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.54003 | + | 2.66742i | −0.0862253 | + | 0.149347i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.11526 | −0.508764 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.45359 | 0.136521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8705 | − | 39.6129i | 1.26863 | − | 2.19733i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2290 | − | 24.6453i | −0.786865 | − | 1.36289i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.28057 | + | 0.942037i | 0.235996 | + | 0.0519362i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.51979 | + | 16.4888i | 0.523255 | + | 0.906304i | 0.999634 | + | 0.0270640i | \(0.00861579\pi\) |
−0.476379 | + | 0.879240i | \(0.658051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.48108 | − | 2.56530i | 0.0811626 | − | 0.140578i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −35.0620 | −1.91564 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0147 | 1.47159 | 0.735793 | − | 0.677206i | \(-0.236810\pi\) | ||||
0.735793 | + | 0.677206i | \(0.236810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.8972 | − | 20.6065i | 0.646165 | − | 1.11919i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.54003 | − | 6.13152i | −0.191704 | − | 0.332040i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.7453 | + | 11.2061i | 0.796169 | + | 0.605074i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.4084 | + | 19.7599i | 0.614206 | + | 1.06384i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1089 | + | 17.5091i | −0.542673 | + | 0.939938i | 0.456076 | + | 0.889941i | \(0.349254\pi\) |
−0.998749 | + | 0.0499969i | \(0.984079\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0224 | −0.643546 | −0.321773 | − | 0.946817i | \(-0.604279\pi\) | ||||
−0.321773 | + | 0.946817i | \(0.604279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.4932 | −1.41410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.37956 | − | 9.31767i | 0.286325 | − | 0.495930i | −0.686605 | − | 0.727031i | \(-0.740900\pi\) |
0.972930 | + | 0.231101i | \(0.0742329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3796 | + | 26.6382i | 0.816262 | + | 1.41381i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.18544 | + | 1.80139i | 0.433219 | + | 0.0953397i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1451 | + | 21.0359i | 0.640992 | + | 1.11023i | 0.985212 | + | 0.171342i | \(0.0548102\pi\) |
−0.344220 | + | 0.938889i | \(0.611856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.40320 | − | 14.5548i | 0.442274 | − | 0.766041i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.91223 | −0.100366 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.2780 | −0.852032 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.42212 | − | 9.39139i | 0.283033 | − | 0.490227i | −0.689098 | − | 0.724669i | \(-0.741993\pi\) |
0.972130 | + | 0.234442i | \(0.0753262\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.422124 | + | 0.731140i | 0.0219749 | + | 0.0380616i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.37571 | − | 23.2672i | −0.382928 | − | 1.20797i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5121 | + | 28.5998i | 0.854963 | + | 1.48084i | 0.876679 | + | 0.481076i | \(0.159754\pi\) |
−0.0217156 | + | 0.999764i | \(0.506913\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.33821 | + | 16.1742i | −0.482223 | + | 0.835234i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.2101 | −0.937866 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9320 | 1.12657 | 0.563286 | − | 0.826262i | \(-0.309537\pi\) | ||||
0.563286 | + | 0.826262i | \(0.309537\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.33084 | − | 10.9653i | 0.324339 | − | 0.561771i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.2315 | + | 31.5779i | 0.931587 | + | 1.61356i | 0.780610 | + | 0.625018i | \(0.214909\pi\) |
0.150977 | + | 0.988537i | \(0.451758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.36834 | − | 6.97144i | 0.324561 | − | 0.355298i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.524964 | + | 0.909265i | 0.0266854 | + | 0.0462205i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.73801 | + | 16.8667i | −0.493737 | + | 0.855177i | −0.999974 | − | 0.00721718i | \(-0.997703\pi\) |
0.506237 | + | 0.862394i | \(0.331036\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.53871 | 0.280105 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5836 | −0.584314 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.4084 | − | 19.7599i | 0.574018 | − | 0.994228i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.91993 | + | 6.78952i | 0.196736 | + | 0.340756i | 0.947468 | − | 0.319850i | \(-0.103633\pi\) |
−0.750732 | + | 0.660606i | \(0.770299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.05378 | + | 5.53239i | −0.253005 | + | 0.276966i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2229 | + | 21.1708i | 0.610385 | + | 1.05722i | 0.991176 | + | 0.132556i | \(0.0423184\pi\) |
−0.380791 | + | 0.924661i | \(0.624348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9295 | − | 36.2509i | 1.04257 | − | 1.80579i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 37.6111 | 1.86891 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.51122 | −0.223613 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.17686 | − | 2.03839i | 0.0581922 | − | 0.100792i | −0.835462 | − | 0.549549i | \(-0.814800\pi\) |
0.893654 | + | 0.448757i | \(0.148133\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.09767 | − | 12.2935i | −0.350102 | − | 0.606395i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.07708 | + | 22.3252i | 0.348241 | + | 1.09855i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.299494 | − | 0.518739i | −0.0147016 | − | 0.0254639i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3494 | − | 17.9257i | 0.506813 | − | 0.877827i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.29081 | −0.453886 | −0.226943 | − | 0.973908i | \(-0.572873\pi\) | ||||
−0.226943 | + | 0.973908i | \(0.572873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.0319 | −1.90230 | −0.951149 | − | 0.308733i | \(-0.900095\pi\) | ||||
−0.951149 | + | 0.308733i | \(0.900095\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.543885 | + | 0.942037i | −0.0264446 | + | 0.0458034i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.40838 | + | 11.0996i | 0.310852 | + | 0.538411i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.2780 | − | 3.80243i | −0.836143 | − | 0.184012i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65277 | − | 9.79088i | −0.272918 | − | 0.472708i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.90101 | + | 3.29265i | −0.0915685 | + | 0.158601i | −0.908171 | − | 0.418599i | \(-0.862521\pi\) |
0.816603 | + | 0.577200i | \(0.195855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.22041 | 0.395048 | 0.197524 | − | 0.980298i | \(-0.436710\pi\) | ||||
0.197524 | + | 0.980298i | \(0.436710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.0198 | 1.00782 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.47590 | + | 4.28839i | −0.118439 | + | 0.205142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.27068 | + | 3.93293i | 0.108374 | + | 0.187708i | 0.915112 | − | 0.403201i | \(-0.132102\pi\) |
−0.806738 | + | 0.590909i | \(0.798769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.75693 | + | 2.64799i | −0.178901 | + | 0.126095i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.87220 | + | 11.9030i | 0.326508 | + | 0.565528i | 0.981816 | − | 0.189833i | \(-0.0607947\pi\) |
−0.655309 | + | 0.755361i | \(0.727461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.58392 | + | 7.93958i | −0.217299 | + | 0.376372i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.91223 | 0.0904453 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5662 | 1.01777 | 0.508886 | − | 0.860834i | \(-0.330057\pi\) | ||||
0.508886 | + | 0.860834i | \(0.330057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.642874 | − | 1.11349i | 0.0302717 | − | 0.0524322i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.7027 | − | 27.1979i | −0.737777 | − | 1.27787i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 54.5203 | + | 11.9984i | 2.55595 | + | 0.562495i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.65277 | + | 2.86268i | 0.0773133 | + | 0.133910i | 0.902090 | − | 0.431548i | \(-0.142033\pi\) |
−0.824777 | + | 0.565459i | \(0.808699\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.71172 | − | 6.42889i | 0.173248 | − | 0.300075i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.1524 | −1.49749 | −0.748744 | − | 0.662859i | \(-0.769343\pi\) | ||||
−0.748744 | + | 0.662859i | \(0.769343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.82181 | −0.270563 | −0.135281 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135281 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.1588 | + | 41.8443i | −1.12034 | + | 1.94048i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.00737 | − | 5.20891i | −0.139164 | − | 0.241040i | 0.788016 | − | 0.615654i | \(-0.211108\pi\) |
−0.927181 | + | 0.374615i | \(0.877775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.85460 | − | 24.7779i | −0.362692 | − | 1.14414i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9484 | − | 18.9632i | −0.504476 | − | 0.873778i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.799494 | − | 1.38476i | 0.0367608 | − | 0.0636715i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.4586 | −0.525759 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.05763 | 0.277360 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.56753 | − | 14.8394i | 0.391460 | − | 0.678029i | −0.601182 | − | 0.799112i | \(-0.705303\pi\) |
0.992642 | + | 0.121083i | \(0.0386367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3357 | − | 23.0981i | −0.608054 | − | 1.05318i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.4084 | + | 12.4888i | −0.519099 | + | 0.568259i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.3744 | + | 30.0933i | 0.788930 | + | 1.36647i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.85713 | − | 4.94869i | 0.129469 | − | 0.224246i | −0.794002 | − | 0.607915i | \(-0.792006\pi\) |
0.923471 | + | 0.383669i | \(0.125339\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.0948 | −0.773054 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0673 | −1.08614 | −0.543071 | − | 0.839687i | \(-0.682739\pi\) | ||||
−0.543071 | + | 0.839687i | \(0.682739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.55125 | − | 4.41890i | 0.114903 | − | 0.199017i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.17169 | + | 2.02943i | 0.0526635 | + | 0.0912159i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.3796 | + | 16.8360i | −0.689868 | + | 0.755200i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.39463 | + | 9.34377i | 0.241497 | + | 0.418285i | 0.961141 | − | 0.276058i | \(-0.0890283\pi\) |
−0.719644 | + | 0.694343i | \(0.755695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.4183 | − | 30.1693i | 0.778191 | − | 1.34787i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.0121 | −1.24900 | −0.624499 | − | 0.781026i | \(-0.714697\pi\) | ||||
−0.624499 | + | 0.781026i | \(0.714697\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.61878 | −0.294532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.9910 | − | 36.3574i | 0.932242 | − | 1.61469i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.957437 | + | 1.65833i | 0.0424377 | + | 0.0735042i | 0.886464 | − | 0.462797i | \(-0.153154\pi\) |
−0.844026 | + | 0.536302i | \(0.819821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.64661 | − | 11.5035i | −0.161317 | − | 0.508885i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.31842 | + | 5.74766i | 0.146512 | + | 0.253766i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.65277 | − | 9.79088i | 0.249091 | − | 0.431438i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65662 | 0.0728581 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.4054 | −1.64191 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.789599 | + | 1.36763i | −0.0345930 | + | 0.0599168i | −0.882804 | − | 0.469742i | \(-0.844347\pi\) |
0.848211 | + | 0.529659i | \(0.177680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.48493 | − | 7.76813i | −0.196112 | − | 0.339677i | 0.751152 | − | 0.660129i | \(-0.229498\pi\) |
−0.947265 | + | 0.320452i | \(0.896165\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −38.2273 | − | 8.41279i | −1.66838 | − | 0.367164i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.86449 | + | 10.1576i | 0.255461 | + | 0.442472i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.91091 | − | 10.2380i | 0.256996 | − | 0.445130i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.81237 | −0.252235 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.60163 | 0.329263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.50604 | − | 14.7329i | 0.367748 | − | 0.636959i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.10537 | − | 5.37866i | −0.134007 | − | 0.232106i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.35327 | + | 2.93869i | 0.273655 | + | 0.126578i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.05125 | − | 15.6772i | −0.389144 | − | 0.674017i | 0.603191 | − | 0.797597i | \(-0.293896\pi\) |
−0.992335 | + | 0.123580i | \(0.960562\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.88693 | + | 17.1247i | −0.424289 | + | 0.734889i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 53.1119 | 2.27507 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6885 | −0.970090 | −0.485045 | − | 0.874489i | \(-0.661197\pi\) | ||||
−0.485045 | + | 0.874489i | \(0.661197\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.19533 | − | 3.80243i | 0.0936945 | − | 0.162284i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.28091 | + | 3.95065i | 0.0971701 | + | 0.168304i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.5198 | + | 3.63555i | 0.702493 | + | 0.154599i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.3933 | + | 26.6620i | 0.653410 | + | 1.13174i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.1777 | + | 33.2168i | −0.812587 | + | 1.40744i | 0.0984613 | + | 0.995141i | \(0.468608\pi\) |
−0.911048 | + | 0.412300i | \(0.864725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.45359 | 0.399844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.16784 | 0.133746 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.8869 | + | 36.1772i | −0.880279 | + | 1.52469i | −0.0292482 | + | 0.999572i | \(0.509311\pi\) |
−0.851031 | + | 0.525116i | \(0.824022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.2040 | + | 38.4585i | 0.934130 | + | 1.61796i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.42564 | + | 26.5793i | 0.353844 | + | 1.11623i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.93500 | + | 10.2797i | 0.248808 | + | 0.430949i | 0.963195 | − | 0.268802i | \(-0.0866278\pi\) |
−0.714387 | + | 0.699751i | \(0.753294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.90067 | − | 17.1485i | 0.414330 | − | 0.717641i | −0.581028 | − | 0.813884i | \(-0.697349\pi\) |
0.995358 | + | 0.0962427i | \(0.0306825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.1652 | 0.800637 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.8667 | −1.07872 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.3395 | + | 24.8368i | −0.596962 | + | 1.03397i | 0.396304 | + | 0.918119i | \(0.370293\pi\) |
−0.993267 | + | 0.115850i | \(0.963041\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.2139 | + | 41.9397i | 1.00630 | + | 1.74296i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.299494 | − | 0.327857i | 0.0124251 | − | 0.0136018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.61274 | − | 7.98949i | −0.191040 | − | 0.330891i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.92730 | + | 11.9984i | −0.286409 | + | 0.496074i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.01209 | −0.0417733 | −0.0208866 | − | 0.999782i | \(-0.506649\pi\) | ||||
−0.0208866 | + | 0.999782i | \(0.506649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4861 | −0.432074 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.5022 | + | 40.7070i | −0.966751 | + | 1.67446i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.11659 | − | 12.3263i | −0.292243 | − | 0.506180i | 0.682097 | − | 0.731262i | \(-0.261068\pi\) |
−0.974340 | + | 0.225082i | \(0.927735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.5499 | + | 11.5490i | −0.432505 | + | 0.473464i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.34591 | − | 9.25939i | −0.218793 | − | 0.378961i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.2729 | + | 22.9893i | −0.542315 | + | 0.939317i | 0.456456 | + | 0.889746i | \(0.349119\pi\) |
−0.998771 | + | 0.0495706i | \(0.984215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1558 | −0.495843 | −0.247922 | − | 0.968780i | \(-0.579748\pi\) | ||||
−0.247922 | + | 0.968780i | \(0.579748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.45094 | 0.262703 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.78442 | − | 3.09071i | 0.0725472 | − | 0.125655i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.98361 | + | 12.0960i | 0.283456 | + | 0.490960i | 0.972234 | − | 0.234013i | \(-0.0751857\pi\) |
−0.688778 | + | 0.724973i | \(0.741852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.70886 | + | 14.8544i | 0.190812 | + | 0.601932i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.89716 | + | 8.48213i | 0.198118 | + | 0.343150i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.32094 | + | 4.01999i | −0.0937421 | + | 0.162366i | −0.909083 | − | 0.416615i | \(-0.863216\pi\) |
0.815341 | + | 0.578981i | \(0.196550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.77453 | −0.353823 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.3960 | −1.06266 | −0.531331 | − | 0.847165i | \(-0.678308\pi\) | ||||
−0.531331 | + | 0.847165i | \(0.678308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.34073 | − | 12.7145i | 0.295049 | − | 0.511040i | −0.679947 | − | 0.733261i | \(-0.737997\pi\) |
0.974996 | + | 0.222221i | \(0.0713307\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.49097 | + | 12.9747i | 0.300602 | + | 0.520659i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.63770 | − | 1.46078i | −0.265934 | − | 0.0585248i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.91355 | + | 3.31437i | 0.0765421 | + | 0.132575i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41608 | + | 2.45272i | −0.0565528 | + | 0.0979524i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.47338 | 0.297983 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1498 | 1.20024 | 0.600122 | − | 0.799908i | \(-0.295119\pi\) | ||||
0.600122 | + | 0.799908i | \(0.295119\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.5688 | + | 20.0378i | −0.459820 | + | 0.796432i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.8154 | + | 20.4649i | 0.468881 | + | 0.812126i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.73450 | + | 41.2168i | 0.147966 | + | 1.63307i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.82963 | − | 4.90107i | −0.111939 | − | 0.193883i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.08909 | − | 14.0107i | 0.319500 | − | 0.553390i | −0.660884 | − | 0.750488i | \(-0.729818\pi\) |
0.980384 | + | 0.197098i | \(0.0631517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.33568 | 0.0921101 | 0.0460550 | − | 0.998939i | \(-0.485335\pi\) | ||||
0.0460550 | + | 0.998939i | \(0.485335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.9122 | −0.429669 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.48108 | − | 12.9576i | 0.294112 | − | 0.509416i | −0.680666 | − | 0.732594i | \(-0.738310\pi\) |
0.974778 | + | 0.223177i | \(0.0716429\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.42598 | + | 7.66602i | 0.173735 | + | 0.300917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.9829 | − | 7.69879i | −1.37109 | − | 0.301739i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.4449 | + | 19.8231i | 0.447873 | + | 0.775740i | 0.998247 | − | 0.0591787i | \(-0.0188482\pi\) |
−0.550374 | + | 0.834918i | \(0.685515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8094 | − | 18.7224i | 0.422358 | − | 0.731545i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.99494 | 0.116844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.20568 | 0.0859211 | 0.0429606 | − | 0.999077i | \(-0.486321\pi\) | ||||
0.0429606 | + | 0.999077i | \(0.486321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.341188 | − | 0.590956i | 0.0132707 | − | 0.0229855i | −0.859314 | − | 0.511449i | \(-0.829109\pi\) |
0.872584 | + | 0.488463i | \(0.162442\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.36449 | + | 16.2198i | 0.363687 | + | 0.629924i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.22592 | − | 13.3310i | −0.163874 | − | 0.516954i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.14892 | + | 8.91819i | 0.199367 | + | 0.345314i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.9407 | + | 25.8781i | −0.577641 | + | 1.00050i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.68676 | −0.258139 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8865 | −0.419643 | −0.209821 | − | 0.977740i | \(-0.567288\pi\) | ||||
−0.209821 | + | 0.977740i | \(0.567288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.3344 | + | 30.0240i | −0.667200 | + | 1.15562i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.8327 | − | 39.5474i | −0.877532 | − | 1.51993i | −0.854041 | − | 0.520205i | \(-0.825855\pi\) |
−0.0234904 | − | 0.999724i | \(-0.507478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.3744 | + | 19.0198i | −0.666768 | + | 0.729912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.9811 | + | 25.9480i | 0.574076 | + | 0.994329i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.24186 | − | 5.61507i | 0.124046 | − | 0.214855i | −0.797313 | − | 0.603566i | \(-0.793746\pi\) |
0.921360 | + | 0.388711i | \(0.127079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.4932 | 1.01225 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6540 | 0.406475 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.2715 | − | 47.2357i | 1.03896 | − | 1.79954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.47338 | + | 9.48016i | 0.208217 | + | 0.360642i | 0.951153 | − | 0.308720i | \(-0.0999006\pi\) |
−0.742936 | + | 0.669363i | \(0.766567\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.17169 | + | 1.28265i | −0.0445088 | + | 0.0487239i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.3154 | + | 33.4553i | 0.732676 | + | 1.26903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.06500 | + | 1.84463i | −0.0403397 | + | 0.0698704i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.8590 | 1.39413 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.914874 | −0.0345543 | −0.0172772 | − | 0.999851i | \(-0.505500\pi\) | ||||
−0.0172772 | + | 0.999851i | \(0.505500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.34073 | + | 5.78632i | −0.125998 | + | 0.218235i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.65277 | − | 9.79088i | −0.212896 | − | 0.368746i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.48274 | − | 4.67741i | −0.0557642 | − | 0.175912i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.1562 | − | 38.3756i | −0.832092 | − | 1.44123i | −0.896376 | − | 0.443294i | \(-0.853810\pi\) |
0.0642838 | − | 0.997932i | \(-0.479524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.09899 | + | 3.63555i | −0.0787182 | + | 0.136344i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.6714 | −0.886499 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0999 | 0.789090 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.1851 | − | 36.6937i | 0.791172 | − | 1.37035i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.60118 | − | 4.50537i | −0.0970076 | − | 0.168022i | 0.813437 | − | 0.581653i | \(-0.197594\pi\) |
−0.910445 | + | 0.413631i | \(0.864260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.18544 | + | 1.80139i | 0.304842 | + | 0.0670873i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.0022 | − | 32.9128i | −0.706699 | − | 1.22404i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.9148 | + | 20.6370i | −0.442503 | + | 0.766438i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.0871 | −1.85763 | −0.928814 | − | 0.370547i | \(-0.879170\pi\) | ||||
−0.928814 | + | 0.370547i | \(0.879170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.7866 | 0.695801 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.32446 | + | 2.29403i | −0.0489869 | + | 0.0848477i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5349 | + | 40.7636i | 0.869280 | + | 1.50564i | 0.862734 | + | 0.505658i | \(0.168750\pi\) |
0.00654601 | + | 0.999979i | \(0.497916\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.31071 | − | 47.5763i | −0.159003 | − | 1.75488i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.91223 | − | 8.50823i | −0.180944 | − | 0.313405i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4957 | − | 40.6957i | 0.864303 | − | 1.49702i | −0.00343444 | − | 0.999994i | \(-0.501093\pi\) |
0.867738 | − | 0.497023i | \(-0.165573\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.7444 | −0.615121 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.19533 | 0.190598 | 0.0952991 | − | 0.995449i | \(-0.469619\pi\) | ||||
0.0952991 | + | 0.995449i | \(0.469619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.78442 | + | 3.09071i | −0.0653763 | + | 0.113235i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0551029 | + | 0.0954410i | 0.00201611 | + | 0.00349200i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.3171 | + | 2.71066i | 0.450057 | + | 0.0990452i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7268 | + | 28.9717i | 0.610369 | + | 1.05719i | 0.991178 | + | 0.132537i | \(0.0423123\pi\) |
−0.380809 | + | 0.924654i | \(0.624354\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.1374 | + | 36.6110i | −0.770288 | + | 1.33418i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 58.6128 | 2.13314 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.0440 | 1.45542 | 0.727711 | − | 0.685884i | \(-0.240584\pi\) | ||||
0.727711 | + | 0.685884i | \(0.240584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.19665 | + | 5.53677i | −0.116031 | + | 0.200972i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.77925 | + | 6.54585i | 0.136998 | + | 0.237287i | 0.926359 | − | 0.376642i | \(-0.122921\pi\) |
−0.789361 | + | 0.613929i | \(0.789588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.8981 | + | 37.5336i | 0.430742 | + | 1.35881i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.94105 | − | 3.36199i | −0.0701786 | − | 0.121553i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.1674 | + | 45.3232i | −0.944849 | + | 1.63653i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.5407 | 1.85860 | 0.929302 | − | 0.369320i | \(-0.120409\pi\) | ||||
0.929302 | + | 0.369320i | \(0.120409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.6834 | −2.00539 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.73284 | − | 13.3937i | 0.278131 | − | 0.481737i | −0.692789 | − | 0.721140i | \(-0.743618\pi\) |
0.970920 | + | 0.239403i | \(0.0769518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.3881 | − | 47.4376i | −0.983811 | − | 1.70401i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3933 | + | 16.8511i | −0.552232 | + | 0.604530i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.952147 | − | 1.64917i | −0.0341142 | − | 0.0590875i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.30939 | + | 7.46408i | −0.154202 | + | 0.267086i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.8020 | 0.493244 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.8667 | 1.45859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9759 | − | 19.0108i | 0.391249 | − | 0.677663i | −0.601366 | − | 0.798974i | \(-0.705377\pi\) |
0.992615 | + | 0.121311i | \(0.0387099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.8231 | + | 25.6744i | 0.527718 | + | 0.914034i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.2040 | + | 24.3068i | −0.789484 | + | 0.864250i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.7668 | − | 34.2371i | −0.701941 | − | 1.21580i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.4794 | + | 54.5240i | −1.11646 | + | 1.93377i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.6258 | 1.50988 | 0.754942 | − | 0.655792i | \(-0.227665\pi\) | ||||
0.754942 | + | 0.655792i | \(0.227665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.74439 | −0.0970896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.843380 | − | 1.46078i | 0.0297994 | − | 0.0516140i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.28057 | − | 3.95007i | −0.0804797 | − | 0.139395i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.53958 | − | 30.0933i | −0.336226 | − | 1.06065i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.63166 | + | 2.82611i | 0.0574370 | + | 0.0994838i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.98372 | + | 3.43591i | −0.0697440 | + | 0.120800i | −0.898789 | − | 0.438382i | \(-0.855552\pi\) |
0.829045 | + | 0.559183i | \(0.188885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.9217 | 1.64764 | 0.823821 | − | 0.566850i | \(-0.191838\pi\) | ||||
0.823821 | + | 0.566850i | \(0.191838\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.2549 | −1.37673 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9523 | − | 27.6301i | 0.558783 | − | 0.967841i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.18411 | − | 2.05095i | −0.0414269 | − | 0.0717535i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.0310 | − | 2.20755i | −0.350512 | − | 0.0771381i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.3000 | + | 43.8209i | 0.882977 | + | 1.52936i | 0.848015 | + | 0.529972i | \(0.177798\pi\) |
0.0349620 | + | 0.999389i | \(0.488869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.199299 | − | 0.345196i | 0.00694714 | − | 0.0120328i | −0.862531 | − | 0.506004i | \(-0.831122\pi\) |
0.869478 | + | 0.493972i | \(0.164455\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.7943 | −0.515072 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.4234 | 0.710193 | 0.355096 | − | 0.934830i | \(-0.384448\pi\) | ||||
0.355096 | + | 0.934830i | \(0.384448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.6317 | − | 20.1466i | 0.403984 | − | 0.699721i | −0.590219 | − | 0.807244i | \(-0.700958\pi\) |
0.994203 | + | 0.107522i | \(0.0342918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.4910 | − | 44.1517i | −0.884272 | − | 1.53160i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.5250 | − | 4.86830i | −0.364668 | − | 0.168676i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.5082 | + | 56.3059i | 1.12499 | + | 1.94855i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.8632 | + | 27.4758i | −0.548311 | + | 0.949703i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.4861 | 0.569165 | 0.284582 | − | 0.958652i | \(-0.408145\pi\) | ||||
0.284582 | + | 0.958652i | \(0.408145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5132 | −0.672869 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.0534 | − | 26.0733i | 0.518468 | − | 0.898013i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.1761 | + | 67.8549i | 1.34770 | + | 2.33428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.58392 | + | 0.568650i | 0.0887845 | + | 0.0195390i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.3645 | + | 26.6121i | 0.527308 | + | 0.913324i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.54136 | + | 13.0620i | −0.258514 | + | 0.447760i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.8315 | −0.507820 | −0.253910 | − | 0.967228i | \(-0.581717\pi\) | ||||
−0.253910 | + | 0.967228i | \(0.581717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.47073 | 0.118696 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.51594 | − | 4.35773i | 0.0859428 | − | 0.148857i | −0.819850 | − | 0.572579i | \(-0.805943\pi\) |
0.905793 | + | 0.423721i | \(0.139276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0181 | − | 48.5288i | −0.955966 | − | 1.65578i | −0.732141 | − | 0.681153i | \(-0.761479\pi\) |
−0.223825 | − | 0.974629i | \(-0.571854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.96567 | − | 6.20086i | −0.0669899 | − | 0.211325i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.2380 | − | 31.5892i | −0.620829 | − | 1.07531i | −0.989332 | − | 0.145681i | \(-0.953463\pi\) |
0.368503 | − | 0.929627i | \(-0.379871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.9054 | − | 60.4579i | 1.18682 | − | 2.05563i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.2600 | 0.925798 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.39331 | 0.216878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.0422 | − | 50.3026i | 0.984058 | − | 1.70444i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.19665 | − | 5.53677i | −0.108190 | − | 0.187391i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.4282 | − | 19.0787i | 0.589180 | − | 0.644976i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.30807 | + | 5.72974i | 0.111705 | + | 0.193480i | 0.916458 | − | 0.400131i | \(-0.131035\pi\) |
−0.804753 | + | 0.593610i | \(0.797702\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.6627 | − | 25.3965i | 0.494559 | − | 0.856602i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.5286 | −0.759008 | −0.379504 | − | 0.925190i | \(-0.623905\pi\) | ||||
−0.379504 | + | 0.925190i | \(0.623905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.1652 | 1.72185 | 0.860923 | − | 0.508735i | \(-0.169887\pi\) | ||||
0.860923 | + | 0.508735i | \(0.169887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.2049 | − | 52.3164i | 1.01533 | − | 1.75860i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.16904 | − | 5.48895i | −0.106406 | − | 0.184301i | 0.807906 | − | 0.589312i | \(-0.200601\pi\) |
−0.914312 | + | 0.405011i | \(0.867268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8154 | + | 12.9344i | −0.396277 | + | 0.433805i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.26936 | + | 9.12679i | 0.176530 | + | 0.305759i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.22679 | − | 2.12487i | 0.0410531 | − | 0.0711060i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.5913 | 0.387454 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.7987 | −1.26206 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.9035 | + | 18.8855i | −0.363653 | + | 0.629866i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.64155 | + | 13.2356i | 0.254577 | + | 0.440940i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.44456 | − | 7.71155i | −0.0813498 | − | 0.256624i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.4523 | − | 31.9603i | −0.613374 | − | 1.06239i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.44237 | + | 5.96236i | −0.114302 | + | 0.197977i | −0.917500 | − | 0.397735i | \(-0.869796\pi\) |
0.803199 | + | 0.595711i | \(0.203130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.21777 | 0.0403908 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.0818 | 1.36110 | 0.680550 | − | 0.732701i | \(-0.261741\pi\) | ||||
0.680550 | + | 0.732701i | \(0.261741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0839190 | − | 0.145352i | 0.00277731 | − | 0.00481045i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.8168 | + | 39.5198i | 0.754299 | + | 1.30648i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.6524 | + | 3.44467i | 0.516889 | + | 0.113753i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.81324 | − | 10.0688i | −0.191761 | − | 0.332140i | 0.754073 | − | 0.656791i | \(-0.228087\pi\) |
−0.945834 | + | 0.324651i | \(0.894753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.7479 | − | 27.2762i | 0.518911 | − | 0.898780i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50.9562 | −1.67724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.9019 | −1.14757 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.04003 | + | 1.80139i | −0.0341592 | + | 0.0591654i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.3834 | − | 21.4487i | −0.406287 | − | 0.703709i | 0.588184 | − | 0.808727i | \(-0.299843\pi\) |
−0.994470 | + | 0.105018i | \(0.966510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.47417 | − | 5.97282i | 0.277730 | − | 0.195751i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.6799 | − | 35.8187i | −0.677030 | − | 1.17265i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.95611 | + | 5.12014i | −0.0966753 | + | 0.167447i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.15046 | 0.0375839 | 0.0187920 | − | 0.999823i | \(-0.494018\pi\) | ||||
0.0187920 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.3381 | −1.02268 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.05510 | + | 8.75570i | −0.164792 | + | 0.285428i | −0.936581 | − | 0.350450i | \(-0.886029\pi\) |
0.771790 | + | 0.635878i | \(0.219362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.14937 | − | 3.72282i | −0.0699931 | − | 0.121232i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −41.3228 | − | 9.09402i | −1.34423 | − | 0.295828i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.2277 | − | 21.1789i | −0.397346 | − | 0.688223i | 0.596052 | − | 0.802946i | \(-0.296735\pi\) |
−0.993398 | + | 0.114723i | \(0.963402\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4833 | − | 23.3537i | 0.437685 | − | 0.758093i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.53101 | −0.276637 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1696 | −0.523784 | −0.261892 | − | 0.965097i | \(-0.584346\pi\) | ||||
−0.261892 | + | 0.965097i | \(0.584346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8843 | + | 30.9765i | −0.578722 | + | 1.00238i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.94490 | + | 5.10071i | 0.0951950 | + | 0.164883i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.93500 | + | 18.7224i | 0.191651 | + | 0.604578i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.56368 | − | 16.5648i | −0.308506 | − | 0.534347i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.56500 | + | 2.71066i | −0.0504313 | + | 0.0873497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −90.3823 | −2.90951 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55941 | 0.0501472 | 0.0250736 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250736 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.34591 | − | 4.06323i | 0.0753614 | − | 0.130530i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.52364 | − | 7.83518i | −0.145171 | − | 0.251443i | 0.784266 | − | 0.620425i | \(-0.213040\pi\) |
−0.929437 | + | 0.368982i | \(0.879706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.3154 | + | 21.1447i | −0.619224 | + | 0.677866i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −43.7337 | − | 75.7490i | −1.40060 | − | 2.42591i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.37824 | − | 5.85128i | 0.108079 | − | 0.187199i | −0.806913 | − | 0.590671i | \(-0.798863\pi\) |
0.914992 | + | 0.403472i | \(0.132197\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.56885 | −0.0821008 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.77188 | −0.311992 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.2152 | − | 22.8895i | 0.421501 | − | 0.730060i | −0.574586 | − | 0.818444i | \(-0.694837\pi\) |
0.996086 | + | 0.0883838i | \(0.0281702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.8628 | − | 75.9727i | −1.39759 | − | 2.42069i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.65277 | − | 6.18810i | 0.179930 | − | 0.196969i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.67301 | − | 4.62979i | −0.0849969 | − | 0.147219i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.317093 | + | 0.549221i | −0.0100728 | + | 0.0174466i | −0.871018 | − | 0.491251i | \(-0.836540\pi\) |
0.860945 | + | 0.508698i | \(0.169873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.4080 | 1.15537 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.9545 | 0.632599 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.06368 | + | 8.77054i | −0.160368 | + | 0.277766i | −0.935001 | − | 0.354646i | \(-0.884601\pi\) |
0.774633 | + | 0.632412i | \(0.217935\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.1076 | + | 17.5068i | 0.319789 | + | 0.553891i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))