Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(339,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.339");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.49843600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} + 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 339.4 | ||
Root | \(0.330837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.339 |
Dual form | 845.2.b.d.339.3 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.330837i | 0.233937i | 0.993136 | + | 0.116968i | \(0.0373176\pi\) | ||||
−0.993136 | + | 0.116968i | \(0.962682\pi\) | |||||||
\(3\) | 2.69180i | 1.55411i | 0.629430 | + | 0.777057i | \(0.283288\pi\) | ||||
−0.629430 | + | 0.777057i | \(0.716712\pi\) | |||||||
\(4\) | 1.89055 | 0.945274 | ||||||||
\(5\) | −2.12291 | + | 0.702335i | −0.949392 | + | 0.314094i | ||||
\(6\) | −0.890547 | −0.363564 | ||||||||
\(7\) | 3.35348i | 1.26750i | 0.773540 | + | 0.633748i | \(0.218484\pi\) | ||||
−0.773540 | + | 0.633748i | \(0.781516\pi\) | |||||||
\(8\) | 1.28714i | 0.455071i | ||||||||
\(9\) | −4.24581 | −1.41527 | ||||||||
\(10\) | −0.232358 | − | 0.702335i | −0.0734780 | − | 0.222098i | ||||
\(11\) | −3.24581 | −0.978649 | −0.489324 | − | 0.872102i | \(-0.662757\pi\) | ||||
−0.489324 | + | 0.872102i | \(0.662757\pi\) | |||||||
\(12\) | 5.08898i | 1.46906i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.10945 | −0.296514 | ||||||||
\(15\) | −1.89055 | − | 5.71445i | −0.488137 | − | 1.47546i | ||||
\(16\) | 3.35526 | 0.838816 | ||||||||
\(17\) | − | 1.94881i | − | 0.472655i | −0.971673 | − | 0.236328i | \(-0.924056\pi\) | ||
0.971673 | − | 0.236328i | \(-0.0759439\pi\) | |||||||
\(18\) | − | 1.40467i | − | 0.331084i | ||||||
\(19\) | 1.24581 | 0.285808 | 0.142904 | − | 0.989737i | \(-0.454356\pi\) | ||||
0.142904 | + | 0.989737i | \(0.454356\pi\) | |||||||
\(20\) | −4.01345 | + | 1.32780i | −0.897435 | + | 0.296904i | ||||
\(21\) | −9.02690 | −1.96983 | ||||||||
\(22\) | − | 1.07383i | − | 0.228942i | ||||||
\(23\) | − | 2.69180i | − | 0.561280i | −0.959813 | − | 0.280640i | \(-0.909453\pi\) | ||
0.959813 | − | 0.280640i | \(-0.0905467\pi\) | |||||||
\(24\) | −3.46472 | −0.707232 | ||||||||
\(25\) | 4.01345 | − | 2.98198i | 0.802690 | − | 0.596396i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.35348i | − | 0.645377i | ||||||
\(28\) | 6.33991i | 1.19813i | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 1.89055 | − | 0.625462i | 0.345165 | − | 0.114193i | ||||
\(31\) | 3.78109 | 0.679105 | 0.339552 | − | 0.940587i | \(-0.389724\pi\) | ||||
0.339552 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(32\) | 3.68431i | 0.651301i | ||||||||
\(33\) | − | 8.73709i | − | 1.52093i | ||||||
\(34\) | 0.644737 | 0.110571 | ||||||||
\(35\) | −2.35526 | − | 7.11911i | −0.398112 | − | 1.20335i | ||||
\(36\) | −8.02690 | −1.33782 | ||||||||
\(37\) | 1.94881i | 0.320382i | 0.987086 | + | 0.160191i | \(0.0512110\pi\) | ||||
−0.987086 | + | 0.160191i | \(0.948789\pi\) | |||||||
\(38\) | 0.412160i | 0.0668611i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.904000 | − | 2.73247i | −0.142935 | − | 0.432041i | ||||
\(41\) | 2.78109 | 0.434334 | 0.217167 | − | 0.976134i | \(-0.430318\pi\) | ||||
0.217167 | + | 0.976134i | \(0.430318\pi\) | |||||||
\(42\) | − | 2.98643i | − | 0.460816i | ||||||
\(43\) | 8.73709i | 1.33239i | 0.745776 | + | 0.666197i | \(0.232079\pi\) | ||||
−0.745776 | + | 0.666197i | \(0.767921\pi\) | |||||||
\(44\) | −6.13636 | −0.925091 | ||||||||
\(45\) | 9.01345 | − | 2.98198i | 1.34365 | − | 0.444527i | ||||
\(46\) | 0.890547 | 0.131304 | ||||||||
\(47\) | − | 6.86960i | − | 1.00203i | −0.865437 | − | 0.501017i | \(-0.832959\pi\) | ||
0.865437 | − | 0.501017i | \(-0.167041\pi\) | |||||||
\(48\) | 9.03171i | 1.30362i | ||||||||
\(49\) | −4.24581 | −0.606544 | ||||||||
\(50\) | 0.986548 | + | 1.32780i | 0.139519 | + | 0.187779i | ||||
\(51\) | 5.24581 | 0.734560 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8336i | 1.76282i | 0.472347 | + | 0.881412i | \(0.343407\pi\) | ||||
−0.472347 | + | 0.881412i | \(0.656593\pi\) | |||||||
\(54\) | 1.10945 | 0.150977 | ||||||||
\(55\) | 6.89055 | − | 2.27964i | 0.929121 | − | 0.307387i | ||||
\(56\) | −4.31638 | −0.576800 | ||||||||
\(57\) | 3.35348i | 0.444179i | ||||||||
\(58\) | − | 0.992510i | − | 0.130323i | ||||||
\(59\) | 2.53528 | 0.330066 | 0.165033 | − | 0.986288i | \(-0.447227\pi\) | ||||
0.165033 | + | 0.986288i | \(0.447227\pi\) | |||||||
\(60\) | −3.57417 | − | 10.8034i | −0.461423 | − | 1.39472i | ||||
\(61\) | −7.49162 | −0.959204 | −0.479602 | − | 0.877486i | \(-0.659219\pi\) | ||||
−0.479602 | + | 0.877486i | \(0.659219\pi\) | |||||||
\(62\) | 1.25092i | 0.158868i | ||||||||
\(63\) | − | 14.2382i | − | 1.79385i | ||||||
\(64\) | 5.49162 | 0.686453 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.89055 | 0.355802 | ||||||||
\(67\) | − | 4.01515i | − | 0.490529i | −0.969456 | − | 0.245264i | \(-0.921125\pi\) | ||
0.969456 | − | 0.245264i | \(-0.0788748\pi\) | |||||||
\(68\) | − | 3.68431i | − | 0.446789i | ||||||
\(69\) | 7.24581 | 0.872293 | ||||||||
\(70\) | 2.35526 | − | 0.779207i | 0.281508 | − | 0.0931331i | ||||
\(71\) | 5.24581 | 0.622563 | 0.311282 | − | 0.950318i | \(-0.399242\pi\) | ||||
0.311282 | + | 0.950318i | \(0.399242\pi\) | |||||||
\(72\) | − | 5.46493i | − | 0.644048i | ||||||
\(73\) | 5.46493i | 0.639622i | 0.947481 | + | 0.319811i | \(0.103619\pi\) | ||||
−0.947481 | + | 0.319811i | \(0.896381\pi\) | |||||||
\(74\) | −0.644737 | −0.0749491 | ||||||||
\(75\) | 8.02690 | + | 10.8034i | 0.926867 | + | 1.24747i | ||||
\(76\) | 2.35526 | 0.270167 | ||||||||
\(77\) | − | 10.8848i | − | 1.24043i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7811 | −1.55049 | −0.775247 | − | 0.631658i | \(-0.782375\pi\) | ||||
−0.775247 | + | 0.631658i | \(0.782375\pi\) | |||||||
\(80\) | −7.12291 | + | 2.35652i | −0.796365 | + | 0.263467i | ||||
\(81\) | −3.71053 | −0.412281 | ||||||||
\(82\) | 0.920088i | 0.101607i | ||||||||
\(83\) | − | 8.61955i | − | 0.946119i | −0.881031 | − | 0.473059i | \(-0.843150\pi\) | ||
0.881031 | − | 0.473059i | \(-0.156850\pi\) | |||||||
\(84\) | −17.0658 | −1.86203 | ||||||||
\(85\) | 1.36872 | + | 4.13713i | 0.148458 | + | 0.448735i | ||||
\(86\) | −2.89055 | −0.311696 | ||||||||
\(87\) | − | 8.07541i | − | 0.865775i | ||||||
\(88\) | − | 4.17780i | − | 0.445355i | ||||||
\(89\) | −10.3164 | −1.09353 | −0.546767 | − | 0.837285i | \(-0.684142\pi\) | ||||
−0.546767 | + | 0.837285i | \(0.684142\pi\) | |||||||
\(90\) | 0.986548 | + | 2.98198i | 0.103991 | + | 0.314328i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 5.08898i | − | 0.530563i | ||||||
\(93\) | 10.1780i | 1.05541i | ||||||||
\(94\) | 2.27271 | 0.234413 | ||||||||
\(95\) | −2.64474 | + | 0.874976i | −0.271344 | + | 0.0897706i | ||||
\(96\) | −9.91745 | −1.01220 | ||||||||
\(97\) | − | 5.26607i | − | 0.534689i | −0.963601 | − | 0.267344i | \(-0.913854\pi\) | ||
0.963601 | − | 0.267344i | \(-0.0861461\pi\) | |||||||
\(98\) | − | 1.40467i | − | 0.141893i | ||||||
\(99\) | 13.7811 | 1.38505 | ||||||||
\(100\) | 7.58762 | − | 5.63757i | 0.758762 | − | 0.563757i | ||||
\(101\) | 5.71053 | 0.568219 | 0.284109 | − | 0.958792i | \(-0.408302\pi\) | ||||
0.284109 | + | 0.958792i | \(0.408302\pi\) | |||||||
\(102\) | 1.73551i | 0.171841i | ||||||||
\(103\) | 7.36863i | 0.726052i | 0.931779 | + | 0.363026i | \(0.118256\pi\) | ||||
−0.931779 | + | 0.363026i | \(0.881744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.1633 | − | 6.33991i | 1.87014 | − | 0.618712i | ||||
\(106\) | −4.24581 | −0.412390 | ||||||||
\(107\) | 8.57444i | 0.828922i | 0.910067 | + | 0.414461i | \(0.136030\pi\) | ||||
−0.910067 | + | 0.414461i | \(0.863970\pi\) | |||||||
\(108\) | − | 6.33991i | − | 0.610058i | ||||||
\(109\) | 8.49162 | 0.813350 | 0.406675 | − | 0.913573i | \(-0.366688\pi\) | ||||
0.406675 | + | 0.913573i | \(0.366688\pi\) | |||||||
\(110\) | 0.754190 | + | 2.27964i | 0.0719092 | + | 0.217356i | ||||
\(111\) | −5.24581 | −0.497910 | ||||||||
\(112\) | 11.2518i | 1.06320i | ||||||||
\(113\) | 7.33242i | 0.689776i | 0.938644 | + | 0.344888i | \(0.112083\pi\) | ||||
−0.938644 | + | 0.344888i | \(0.887917\pi\) | |||||||
\(114\) | −1.10945 | −0.103910 | ||||||||
\(115\) | 1.89055 | + | 5.71445i | 0.176294 | + | 0.532875i | ||||
\(116\) | −5.67164 | −0.526599 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.838765i | 0.0772145i | ||||||||
\(119\) | 6.53528 | 0.599089 | ||||||||
\(120\) | 7.35526 | − | 2.43339i | 0.671441 | − | 0.222137i | ||||
\(121\) | −0.464716 | −0.0422469 | ||||||||
\(122\) | − | 2.47850i | − | 0.224393i | ||||||
\(123\) | 7.48616i | 0.675004i | ||||||||
\(124\) | 7.14834 | 0.641940 | ||||||||
\(125\) | −6.42583 | + | 9.14925i | −0.574744 | + | 0.818333i | ||||
\(126\) | 4.71053 | 0.419647 | ||||||||
\(127\) | − | 9.16369i | − | 0.813146i | −0.913618 | − | 0.406573i | \(-0.866724\pi\) | ||
0.913618 | − | 0.406573i | \(-0.133276\pi\) | |||||||
\(128\) | 9.18546i | 0.811887i | ||||||||
\(129\) | −23.5185 | −2.07069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | − | 16.5179i | − | 1.43770i | ||||||
\(133\) | 4.17780i | 0.362261i | ||||||||
\(134\) | 1.32836 | 0.114753 | ||||||||
\(135\) | 2.35526 | + | 7.11911i | 0.202709 | + | 0.612716i | ||||
\(136\) | 2.50838 | 0.215092 | ||||||||
\(137\) | 16.8487i | 1.43948i | 0.694242 | + | 0.719741i | \(0.255740\pi\) | ||||
−0.694242 | + | 0.719741i | \(0.744260\pi\) | |||||||
\(138\) | 2.39718i | 0.204061i | ||||||||
\(139\) | 1.02690 | 0.0871009 | 0.0435505 | − | 0.999051i | \(-0.486133\pi\) | ||||
0.0435505 | + | 0.999051i | \(0.486133\pi\) | |||||||
\(140\) | −4.45274 | − | 13.4590i | −0.376325 | − | 1.13749i | ||||
\(141\) | 18.4916 | 1.55728 | ||||||||
\(142\) | 1.73551i | 0.145640i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −14.2458 | −1.18715 | ||||||||
\(145\) | 6.36872 | − | 2.10700i | 0.528893 | − | 0.174977i | ||||
\(146\) | −1.80800 | −0.149631 | ||||||||
\(147\) | − | 11.4289i | − | 0.942639i | ||||||
\(148\) | 3.68431i | 0.302849i | ||||||||
\(149\) | −15.8517 | −1.29862 | −0.649309 | − | 0.760524i | \(-0.724942\pi\) | ||||
−0.649309 | + | 0.760524i | \(0.724942\pi\) | |||||||
\(150\) | −3.57417 | + | 2.65559i | −0.291830 | + | 0.216828i | ||||
\(151\) | 14.5454 | 1.18369 | 0.591845 | − | 0.806052i | \(-0.298400\pi\) | ||||
0.591845 | + | 0.806052i | \(0.298400\pi\) | |||||||
\(152\) | 1.60353i | 0.130063i | ||||||||
\(153\) | 8.27427i | 0.668935i | ||||||||
\(154\) | 3.60107 | 0.290183 | ||||||||
\(155\) | −8.02690 | + | 2.65559i | −0.644736 | + | 0.213302i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9210i | 0.871588i | 0.900047 | + | 0.435794i | \(0.143532\pi\) | ||||
−0.900047 | + | 0.435794i | \(0.856468\pi\) | |||||||
\(158\) | − | 4.55929i | − | 0.362718i | ||||||
\(159\) | −34.5454 | −2.73963 | ||||||||
\(160\) | −2.58762 | − | 7.82145i | −0.204569 | − | 0.618340i | ||||
\(161\) | 9.02690 | 0.711420 | ||||||||
\(162\) | − | 1.22758i | − | 0.0964476i | ||||||
\(163\) | 4.17780i | 0.327230i | 0.986524 | + | 0.163615i | \(0.0523155\pi\) | ||||
−0.986524 | + | 0.163615i | \(0.947684\pi\) | |||||||
\(164\) | 5.25779 | 0.410564 | ||||||||
\(165\) | 6.13636 | + | 18.5480i | 0.477715 | + | 1.44396i | ||||
\(166\) | 2.85166 | 0.221332 | ||||||||
\(167\) | − | 3.35348i | − | 0.259500i | −0.991547 | − | 0.129750i | \(-0.958583\pi\) | ||
0.991547 | − | 0.129750i | \(-0.0414175\pi\) | |||||||
\(168\) | − | 11.6188i | − | 0.896413i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.36872 | + | 0.452821i | −0.104976 | + | 0.0347298i | ||||
\(171\) | −5.28947 | −0.404496 | ||||||||
\(172\) | 16.5179i | 1.25948i | ||||||||
\(173\) | − | 8.73709i | − | 0.664268i | −0.943232 | − | 0.332134i | \(-0.892231\pi\) | ||
0.943232 | − | 0.332134i | \(-0.107769\pi\) | |||||||
\(174\) | 2.67164 | 0.202537 | ||||||||
\(175\) | 10.0000 | + | 13.4590i | 0.755929 | + | 1.01741i | ||||
\(176\) | −10.8905 | −0.820906 | ||||||||
\(177\) | 6.82449i | 0.512960i | ||||||||
\(178\) | − | 3.41303i | − | 0.255818i | ||||||
\(179\) | 18.0101 | 1.34614 | 0.673071 | − | 0.739578i | \(-0.264975\pi\) | ||||
0.673071 | + | 0.739578i | \(0.264975\pi\) | |||||||
\(180\) | 17.0404 | − | 5.63757i | 1.27011 | − | 0.420200i | ||||
\(181\) | 1.04366 | 0.0775749 | 0.0387875 | − | 0.999247i | \(-0.487650\pi\) | ||||
0.0387875 | + | 0.999247i | \(0.487650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 20.1660i | − | 1.49071i | ||||||
\(184\) | 3.46472 | 0.255422 | ||||||||
\(185\) | −1.36872 | − | 4.13713i | −0.100630 | − | 0.304168i | ||||
\(186\) | −3.36724 | −0.246898 | ||||||||
\(187\) | 6.32546i | 0.462564i | ||||||||
\(188\) | − | 12.9873i | − | 0.947197i | ||||||
\(189\) | 11.2458 | 0.818012 | ||||||||
\(190\) | −0.289474 | − | 0.874976i | −0.0210006 | − | 0.0634774i | ||||
\(191\) | 25.5185 | 1.84646 | 0.923228 | − | 0.384253i | \(-0.125541\pi\) | ||||
0.923228 | + | 0.384253i | \(0.125541\pi\) | |||||||
\(192\) | 14.7824i | 1.06683i | ||||||||
\(193\) | 19.8207i | 1.42672i | 0.700795 | + | 0.713362i | \(0.252829\pi\) | ||||
−0.700795 | + | 0.713362i | \(0.747171\pi\) | |||||||
\(194\) | 1.74221 | 0.125083 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.02690 | −0.573350 | ||||||||
\(197\) | 21.6520i | 1.54264i | 0.636448 | + | 0.771319i | \(0.280403\pi\) | ||||
−0.636448 | + | 0.771319i | \(0.719597\pi\) | |||||||
\(198\) | 4.55929i | 0.324015i | ||||||||
\(199\) | −18.2291 | −1.29222 | −0.646112 | − | 0.763243i | \(-0.723606\pi\) | ||||
−0.646112 | + | 0.763243i | \(0.723606\pi\) | |||||||
\(200\) | 3.83821 | + | 5.16586i | 0.271402 | + | 0.365281i | ||||
\(201\) | 10.8080 | 0.762337 | ||||||||
\(202\) | 1.88925i | 0.132927i | ||||||||
\(203\) | − | 10.0604i | − | 0.706104i | ||||||
\(204\) | 9.91745 | 0.694361 | ||||||||
\(205\) | −5.90400 | + | 1.95326i | −0.412353 | + | 0.136422i | ||||
\(206\) | −2.43781 | −0.169850 | ||||||||
\(207\) | 11.4289i | 0.794363i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.04366 | −0.279706 | ||||||||
\(210\) | 2.09747 | + | 6.33991i | 0.144739 | + | 0.437495i | ||||
\(211\) | 19.2996 | 1.32864 | 0.664320 | − | 0.747448i | \(-0.268721\pi\) | ||||
0.664320 | + | 0.747448i | \(0.268721\pi\) | |||||||
\(212\) | 24.2624i | 1.66635i | ||||||||
\(213\) | 14.1207i | 0.967534i | ||||||||
\(214\) | −2.83674 | −0.193915 | ||||||||
\(215\) | −6.13636 | − | 18.5480i | −0.418496 | − | 1.26496i | ||||
\(216\) | 4.31638 | 0.293692 | ||||||||
\(217\) | 12.6798i | 0.860762i | ||||||||
\(218\) | 2.80934i | 0.190272i | ||||||||
\(219\) | −14.7105 | −0.994045 | ||||||||
\(220\) | 13.0269 | − | 4.30978i | 0.878274 | − | 0.290565i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 1.73551i | − | 0.116480i | ||||||
\(223\) | − | 12.3707i | − | 0.828406i | −0.910184 | − | 0.414203i | \(-0.864060\pi\) | ||
0.910184 | − | 0.414203i | \(-0.135940\pi\) | |||||||
\(224\) | −12.3553 | −0.825521 | ||||||||
\(225\) | −17.0404 | + | 12.6609i | −1.13602 | + | 0.844061i | ||||
\(226\) | −2.42583 | −0.161364 | ||||||||
\(227\) | − | 6.16282i | − | 0.409040i | −0.978862 | − | 0.204520i | \(-0.934437\pi\) | ||
0.978862 | − | 0.204520i | \(-0.0655634\pi\) | |||||||
\(228\) | 6.33991i | 0.419871i | ||||||||
\(229\) | 26.9832 | 1.78310 | 0.891551 | − | 0.452920i | \(-0.149618\pi\) | ||||
0.891551 | + | 0.452920i | \(0.149618\pi\) | |||||||
\(230\) | −1.89055 | + | 0.625462i | −0.124659 | + | 0.0412417i | ||||
\(231\) | 29.2996 | 1.92777 | ||||||||
\(232\) | − | 3.86141i | − | 0.253514i | ||||||
\(233\) | − | 0.824319i | − | 0.0540029i | −0.999635 | − | 0.0270015i | \(-0.991404\pi\) | ||
0.999635 | − | 0.0270015i | \(-0.00859588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.82476 | + | 14.5835i | 0.314733 | + | 0.951323i | ||||
\(236\) | 4.79307 | 0.312003 | ||||||||
\(237\) | − | 37.0960i | − | 2.40964i | ||||||
\(238\) | 2.16211i | 0.140149i | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | −6.34328 | − | 19.1735i | −0.409457 | − | 1.23764i | ||||
\(241\) | 22.6938 | 1.46183 | 0.730917 | − | 0.682466i | \(-0.239093\pi\) | ||||
0.730917 | + | 0.682466i | \(0.239093\pi\) | |||||||
\(242\) | − | 0.153745i | − | 0.00988310i | ||||||
\(243\) | − | 20.0484i | − | 1.28611i | ||||||
\(244\) | −14.1633 | −0.906710 | ||||||||
\(245\) | 9.01345 | − | 2.98198i | 0.575848 | − | 0.190512i | ||||
\(246\) | −2.47670 | −0.157908 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.86678i | 0.309041i | ||||||||
\(249\) | 23.2021 | 1.47038 | ||||||||
\(250\) | −3.02690 | − | 2.12590i | −0.191438 | − | 0.134454i | ||||
\(251\) | 19.0269 | 1.20097 | 0.600484 | − | 0.799637i | \(-0.294975\pi\) | ||||
0.600484 | + | 0.799637i | \(0.294975\pi\) | |||||||
\(252\) | − | 26.9180i | − | 1.69568i | ||||||
\(253\) | 8.73709i | 0.549296i | ||||||||
\(254\) | 3.03168 | 0.190225 | ||||||||
\(255\) | −11.1364 | + | 3.68431i | −0.697386 | + | 0.230721i | ||||
\(256\) | 7.94436 | 0.496522 | ||||||||
\(257\) | − | 2.11145i | − | 0.131709i | −0.997829 | − | 0.0658544i | \(-0.979023\pi\) | ||
0.997829 | − | 0.0658544i | \(-0.0209773\pi\) | |||||||
\(258\) | − | 7.78079i | − | 0.484411i | ||||||
\(259\) | −6.53528 | −0.406083 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.7374 | 0.788427 | ||||||||
\(262\) | 3.30837i | 0.204391i | ||||||||
\(263\) | − | 29.9173i | − | 1.84478i | −0.386257 | − | 0.922391i | \(-0.626232\pi\) | ||
0.386257 | − | 0.922391i | \(-0.373768\pi\) | |||||||
\(264\) | 11.2458 | 0.692132 | ||||||||
\(265\) | −9.01345 | − | 27.2444i | −0.553692 | − | 1.67361i | ||||
\(266\) | −1.38217 | −0.0847461 | ||||||||
\(267\) | − | 27.7697i | − | 1.69948i | ||||||
\(268\) | − | 7.59083i | − | 0.463684i | ||||||
\(269\) | −18.5891 | −1.13340 | −0.566699 | − | 0.823925i | \(-0.691780\pi\) | ||||
−0.566699 | + | 0.823925i | \(0.691780\pi\) | |||||||
\(270\) | −2.35526 | + | 0.779207i | −0.143337 | + | 0.0474210i | ||||
\(271\) | 5.82476 | 0.353829 | 0.176914 | − | 0.984226i | \(-0.443388\pi\) | ||||
0.176914 | + | 0.984226i | \(0.443388\pi\) | |||||||
\(272\) | − | 6.53876i | − | 0.396471i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.57417 | −0.336748 | ||||||||
\(275\) | −13.0269 | + | 9.67894i | −0.785552 | + | 0.583662i | ||||
\(276\) | 13.6985 | 0.824556 | ||||||||
\(277\) | − | 13.5403i | − | 0.813560i | −0.913526 | − | 0.406780i | \(-0.866651\pi\) | ||
0.913526 | − | 0.406780i | \(-0.133349\pi\) | |||||||
\(278\) | 0.339738i | 0.0203761i | ||||||||
\(279\) | −16.0538 | −0.961116 | ||||||||
\(280\) | 9.16326 | − | 3.03154i | 0.547610 | − | 0.181169i | ||||
\(281\) | −0.464716 | −0.0277226 | −0.0138613 | − | 0.999904i | \(-0.504412\pi\) | ||||
−0.0138613 | + | 0.999904i | \(0.504412\pi\) | |||||||
\(282\) | 6.11770i | 0.364304i | ||||||||
\(283\) | 10.0604i | 0.598031i | 0.954248 | + | 0.299015i | \(0.0966582\pi\) | ||||
−0.954248 | + | 0.299015i | \(0.903342\pi\) | |||||||
\(284\) | 9.91745 | 0.588492 | ||||||||
\(285\) | −2.35526 | − | 7.11911i | −0.139514 | − | 0.421700i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.32634i | 0.550516i | ||||||||
\(288\) | − | 15.6429i | − | 0.921767i | ||||||
\(289\) | 13.2021 | 0.776597 | ||||||||
\(290\) | 0.697074 | + | 2.10700i | 0.0409336 | + | 0.123728i | ||||
\(291\) | 14.1752 | 0.830967 | ||||||||
\(292\) | 10.3317i | 0.604618i | ||||||||
\(293\) | 13.4501i | 0.785764i | 0.919589 | + | 0.392882i | \(0.128522\pi\) | ||||
−0.919589 | + | 0.392882i | \(0.871478\pi\) | |||||||
\(294\) | 3.78109 | 0.220518 | ||||||||
\(295\) | −5.38217 | + | 1.78062i | −0.313362 | + | 0.103672i | ||||
\(296\) | −2.50838 | −0.145797 | ||||||||
\(297\) | 10.8848i | 0.631597i | ||||||||
\(298\) | − | 5.24431i | − | 0.303795i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 15.1752 | + | 20.4244i | 0.876143 | + | 1.17920i | ||||
\(301\) | −29.2996 | −1.68880 | ||||||||
\(302\) | 4.81216i | 0.276909i | ||||||||
\(303\) | 15.3716i | 0.883076i | ||||||||
\(304\) | 4.18002 | 0.239741 | ||||||||
\(305\) | 15.9040 | − | 5.26162i | 0.910660 | − | 0.301280i | ||||
\(306\) | −2.73743 | −0.156488 | ||||||||
\(307\) | − | 24.6077i | − | 1.40444i | −0.711961 | − | 0.702219i | \(-0.752193\pi\) | ||
0.711961 | − | 0.702219i | \(-0.247807\pi\) | |||||||
\(308\) | − | 20.5781i | − | 1.17255i | ||||||
\(309\) | −19.8349 | −1.12837 | ||||||||
\(310\) | −0.878567 | − | 2.65559i | −0.0498993 | − | 0.150828i | ||||
\(311\) | 2.43781 | 0.138236 | 0.0691178 | − | 0.997609i | \(-0.477982\pi\) | ||||
0.0691178 | + | 0.997609i | \(0.477982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.2965i | − | 1.09071i | −0.838207 | − | 0.545353i | \(-0.816396\pi\) | ||
0.838207 | − | 0.545353i | \(-0.183604\pi\) | |||||||
\(314\) | −3.61305 | −0.203896 | ||||||||
\(315\) | 10.0000 | + | 30.2264i | 0.563436 | + | 1.70307i | ||||
\(316\) | −26.0538 | −1.46564 | ||||||||
\(317\) | 28.8217i | 1.61879i | 0.587265 | + | 0.809395i | \(0.300205\pi\) | ||||
−0.587265 | + | 0.809395i | \(0.699795\pi\) | |||||||
\(318\) | − | 11.4289i | − | 0.640900i | ||||||
\(319\) | 9.73743 | 0.545191 | ||||||||
\(320\) | −11.6582 | + | 3.85695i | −0.651713 | + | 0.215610i | ||||
\(321\) | −23.0807 | −1.28824 | ||||||||
\(322\) | 2.98643i | 0.166427i | ||||||||
\(323\) | − | 2.42785i | − | 0.135089i | ||||||
\(324\) | −7.01492 | −0.389718 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.38217 | −0.0765512 | ||||||||
\(327\) | 22.8578i | 1.26404i | ||||||||
\(328\) | 3.57964i | 0.197653i | ||||||||
\(329\) | 23.0371 | 1.27007 | ||||||||
\(330\) | −6.13636 | + | 2.03013i | −0.337795 | + | 0.111755i | ||||
\(331\) | −2.97310 | −0.163416 | −0.0817081 | − | 0.996656i | \(-0.526038\pi\) | ||||
−0.0817081 | + | 0.996656i | \(0.526038\pi\) | |||||||
\(332\) | − | 16.2957i | − | 0.894341i | ||||||
\(333\) | − | 8.27427i | − | 0.453427i | ||||||
\(334\) | 1.10945 | 0.0607066 | ||||||||
\(335\) | 2.81998 | + | 8.52378i | 0.154072 | + | 0.465704i | ||||
\(336\) | −30.2876 | −1.65233 | ||||||||
\(337\) | − | 1.90370i | − | 0.103701i | −0.998655 | − | 0.0518505i | \(-0.983488\pi\) | ||
0.998655 | − | 0.0518505i | \(-0.0165119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.7374 | −1.07199 | ||||||||
\(340\) | 2.58762 | + | 7.82145i | 0.140333 | + | 0.424178i | ||||
\(341\) | −12.2727 | −0.664605 | ||||||||
\(342\) | − | 1.74995i | − | 0.0946265i | ||||||
\(343\) | 9.23611i | 0.498703i | ||||||||
\(344\) | −11.2458 | −0.606333 | ||||||||
\(345\) | −15.3822 | + | 5.08898i | −0.828148 | + | 0.273982i | ||||
\(346\) | 2.89055 | 0.155397 | ||||||||
\(347\) | 12.6347i | 0.678266i | 0.940738 | + | 0.339133i | \(0.110134\pi\) | ||||
−0.940738 | + | 0.339133i | \(0.889866\pi\) | |||||||
\(348\) | − | 15.2669i | − | 0.818394i | ||||||
\(349\) | −8.97310 | −0.480319 | −0.240159 | − | 0.970733i | \(-0.577200\pi\) | ||||
−0.240159 | + | 0.970733i | \(0.577200\pi\) | |||||||
\(350\) | −4.45274 | + | 3.30837i | −0.238009 | + | 0.176840i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 11.9586i | − | 0.637395i | ||||||
\(353\) | − | 34.2505i | − | 1.82297i | −0.411336 | − | 0.911484i | \(-0.634938\pi\) | ||
0.411336 | − | 0.911484i | \(-0.365062\pi\) | |||||||
\(354\) | −2.25779 | −0.120000 | ||||||||
\(355\) | −11.1364 | + | 3.68431i | −0.591056 | + | 0.195543i | ||||
\(356\) | −19.5036 | −1.03369 | ||||||||
\(357\) | 17.5917i | 0.931052i | ||||||||
\(358\) | 5.95841i | 0.314912i | ||||||||
\(359\) | −22.4043 | −1.18245 | −0.591227 | − | 0.806505i | \(-0.701356\pi\) | ||||
−0.591227 | + | 0.806505i | \(0.701356\pi\) | |||||||
\(360\) | 3.83821 | + | 11.6015i | 0.202291 | + | 0.611454i | ||||
\(361\) | −17.4480 | −0.918314 | ||||||||
\(362\) | 0.345282i | 0.0181476i | ||||||||
\(363\) | − | 1.25092i | − | 0.0656565i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.83821 | − | 11.6015i | −0.200901 | − | 0.607252i | ||||
\(366\) | 6.67164 | 0.348732 | ||||||||
\(367\) | 13.1951i | 0.688777i | 0.938827 | + | 0.344388i | \(0.111914\pi\) | ||||
−0.938827 | + | 0.344388i | \(0.888086\pi\) | |||||||
\(368\) | − | 9.03171i | − | 0.470811i | ||||||
\(369\) | −11.8080 | −0.614700 | ||||||||
\(370\) | 1.36872 | − | 0.452821i | 0.0711561 | − | 0.0235410i | ||||
\(371\) | −43.0371 | −2.23437 | ||||||||
\(372\) | 19.2419i | 0.997647i | ||||||||
\(373\) | − | 15.2614i | − | 0.790206i | −0.918637 | − | 0.395103i | \(-0.870709\pi\) | ||
0.918637 | − | 0.395103i | \(-0.129291\pi\) | |||||||
\(374\) | −2.09269 | −0.108211 | ||||||||
\(375\) | −24.6280 | − | 17.2971i | −1.27178 | − | 0.893217i | ||||
\(376\) | 8.84210 | 0.455997 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.72052i | 0.191363i | ||||||||
\(379\) | −18.2291 | −0.936363 | −0.468182 | − | 0.883632i | \(-0.655091\pi\) | ||||
−0.468182 | + | 0.883632i | \(0.655091\pi\) | |||||||
\(380\) | −5.00000 | + | 1.65418i | −0.256495 | + | 0.0848578i | ||||
\(381\) | 24.6669 | 1.26372 | ||||||||
\(382\) | 8.44246i | 0.431954i | ||||||||
\(383\) | 1.44088i | 0.0736255i | 0.999322 | + | 0.0368128i | \(0.0117205\pi\) | ||||
−0.999322 | + | 0.0368128i | \(0.988279\pi\) | |||||||
\(384\) | −24.7255 | −1.26177 | ||||||||
\(385\) | 7.64474 | + | 23.1073i | 0.389612 | + | 1.17766i | ||||
\(386\) | −6.55741 | −0.333763 | ||||||||
\(387\) | − | 37.0960i | − | 1.88570i | ||||||
\(388\) | − | 9.95576i | − | 0.505427i | ||||||
\(389\) | 18.7912 | 0.952754 | 0.476377 | − | 0.879241i | \(-0.341950\pi\) | ||||
0.476377 | + | 0.879241i | \(0.341950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.24581 | −0.265292 | ||||||||
\(392\) | − | 5.46493i | − | 0.276021i | ||||||
\(393\) | 26.9180i | 1.35784i | ||||||||
\(394\) | −7.16326 | −0.360880 | ||||||||
\(395\) | 29.2560 | − | 9.67894i | 1.47203 | − | 0.487000i | ||||
\(396\) | 26.0538 | 1.30925 | ||||||||
\(397\) | 17.0927i | 0.857857i | 0.903338 | + | 0.428928i | \(0.141109\pi\) | ||||
−0.903338 | + | 0.428928i | \(0.858891\pi\) | |||||||
\(398\) | − | 6.03084i | − | 0.302298i | ||||||
\(399\) | −11.2458 | −0.562995 | ||||||||
\(400\) | 13.4662 | − | 10.0053i | 0.673309 | − | 0.500266i | ||||
\(401\) | 22.2021 | 1.10872 | 0.554361 | − | 0.832276i | \(-0.312963\pi\) | ||||
0.554361 | + | 0.832276i | \(0.312963\pi\) | |||||||
\(402\) | 3.57568i | 0.178339i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.7960 | 0.537122 | ||||||||
\(405\) | 7.87709 | − | 2.60603i | 0.391416 | − | 0.129495i | ||||
\(406\) | 3.32836 | 0.165184 | ||||||||
\(407\) | − | 6.32546i | − | 0.313541i | ||||||
\(408\) | 6.75207i | 0.334277i | ||||||||
\(409\) | 9.63276 | 0.476309 | 0.238155 | − | 0.971227i | \(-0.423458\pi\) | ||||
0.238155 | + | 0.971227i | \(0.423458\pi\) | |||||||
\(410\) | −0.646209 | − | 1.95326i | −0.0319140 | − | 0.0964646i | ||||
\(411\) | −45.3534 | −2.23712 | ||||||||
\(412\) | 13.9307i | 0.686318i | ||||||||
\(413\) | 8.50202i | 0.418357i | ||||||||
\(414\) | −3.78109 | −0.185831 | ||||||||
\(415\) | 6.05381 | + | 18.2985i | 0.297170 | + | 0.898238i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.76423i | 0.135365i | ||||||||
\(418\) | − | 1.33779i | − | 0.0654335i | ||||||
\(419\) | 1.95634 | 0.0955733 | 0.0477866 | − | 0.998858i | \(-0.484783\pi\) | ||||
0.0477866 | + | 0.998858i | \(0.484783\pi\) | |||||||
\(420\) | 36.2291 | − | 11.9859i | 1.76780 | − | 0.584852i | ||||
\(421\) | −12.0807 | −0.588778 | −0.294389 | − | 0.955686i | \(-0.595116\pi\) | ||||
−0.294389 | + | 0.955686i | \(0.595116\pi\) | |||||||
\(422\) | 6.38502i | 0.310818i | ||||||||
\(423\) | 29.1670i | 1.41815i | ||||||||
\(424\) | −16.5185 | −0.802210 | ||||||||
\(425\) | −5.81131 | − | 7.82145i | −0.281890 | − | 0.379396i | ||||
\(426\) | −4.67164 | −0.226342 | ||||||||
\(427\) | − | 25.1230i | − | 1.21579i | ||||||
\(428\) | 16.2104i | 0.783558i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.13636 | − | 2.03013i | 0.295921 | − | 0.0979016i | ||||
\(431\) | 24.5891 | 1.18441 | 0.592207 | − | 0.805786i | \(-0.298257\pi\) | ||||
0.592207 | + | 0.805786i | \(0.298257\pi\) | |||||||
\(432\) | − | 11.2518i | − | 0.541352i | ||||||
\(433\) | − | 36.0728i | − | 1.73355i | −0.498700 | − | 0.866775i | \(-0.666189\pi\) | ||
0.498700 | − | 0.866775i | \(-0.333811\pi\) | |||||||
\(434\) | −4.19495 | −0.201364 | ||||||||
\(435\) | 5.67164 | + | 17.1433i | 0.271934 | + | 0.821960i | ||||
\(436\) | 16.0538 | 0.768838 | ||||||||
\(437\) | − | 3.35348i | − | 0.160419i | ||||||
\(438\) | − | 4.86678i | − | 0.232544i | ||||||
\(439\) | −2.53528 | −0.121003 | −0.0605013 | − | 0.998168i | \(-0.519270\pi\) | ||||
−0.0605013 | + | 0.998168i | \(0.519270\pi\) | |||||||
\(440\) | 2.93421 | + | 8.86907i | 0.139883 | + | 0.422816i | ||||
\(441\) | 18.0269 | 0.858424 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 19.3579i | − | 0.919721i | −0.887991 | − | 0.459860i | \(-0.847899\pi\) | ||
0.887991 | − | 0.459860i | \(-0.152101\pi\) | |||||||
\(444\) | −9.91745 | −0.470661 | ||||||||
\(445\) | 21.9007 | − | 7.24555i | 1.03819 | − | 0.343472i | ||||
\(446\) | 4.09269 | 0.193795 | ||||||||
\(447\) | − | 42.6696i | − | 2.01820i | ||||||
\(448\) | 18.4160i | 0.870075i | ||||||||
\(449\) | 24.8080 | 1.17076 | 0.585381 | − | 0.810758i | \(-0.300945\pi\) | ||||
0.585381 | + | 0.810758i | \(0.300945\pi\) | |||||||
\(450\) | −4.18869 | − | 5.63757i | −0.197457 | − | 0.265758i | ||||
\(451\) | −9.02690 | −0.425060 | ||||||||
\(452\) | 13.8623i | 0.652027i | ||||||||
\(453\) | 39.1534i | 1.83959i | ||||||||
\(454\) | 2.03888 | 0.0956896 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.31638 | −0.202133 | ||||||||
\(457\) | − | 7.56748i | − | 0.353992i | −0.984212 | − | 0.176996i | \(-0.943362\pi\) | ||
0.984212 | − | 0.176996i | \(-0.0566380\pi\) | |||||||
\(458\) | 8.92704i | 0.417133i | ||||||||
\(459\) | −6.53528 | −0.305041 | ||||||||
\(460\) | 3.57417 | + | 10.8034i | 0.166646 | + | 0.503712i | ||||
\(461\) | −12.3433 | −0.574884 | −0.287442 | − | 0.957798i | \(-0.592805\pi\) | ||||
−0.287442 | + | 0.957798i | \(0.592805\pi\) | |||||||
\(462\) | 9.69338i | 0.450977i | ||||||||
\(463\) | 22.8578i | 1.06229i | 0.847281 | + | 0.531146i | \(0.178238\pi\) | ||||
−0.847281 | + | 0.531146i | \(0.821762\pi\) | |||||||
\(464\) | −10.0658 | −0.467293 | ||||||||
\(465\) | −7.14834 | − | 21.6069i | −0.331496 | − | 1.00199i | ||||
\(466\) | 0.272715 | 0.0126333 | ||||||||
\(467\) | 15.2976i | 0.707889i | 0.935266 | + | 0.353945i | \(0.115160\pi\) | ||||
−0.935266 | + | 0.353945i | \(0.884840\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4647 | 0.621743 | ||||||||
\(470\) | −4.82476 | + | 1.59621i | −0.222549 | + | 0.0736275i | ||||
\(471\) | −29.3971 | −1.35455 | ||||||||
\(472\) | 3.26325i | 0.150203i | ||||||||
\(473\) | − | 28.3589i | − | 1.30394i | ||||||
\(474\) | 12.2727 | 0.563704 | ||||||||
\(475\) | 5.00000 | − | 3.71498i | 0.229416 | − | 0.170455i | ||||
\(476\) | 12.3553 | 0.566303 | ||||||||
\(477\) | − | 54.4889i | − | 2.49487i | ||||||
\(478\) | − | 1.32335i | − | 0.0605284i | ||||||
\(479\) | −24.2829 | −1.10951 | −0.554756 | − | 0.832013i | \(-0.687188\pi\) | ||||
−0.554756 | + | 0.832013i | \(0.687188\pi\) | |||||||
\(480\) | 21.0538 | − | 6.96537i | 0.960971 | − | 0.317924i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.50793i | 0.341977i | ||||||||
\(483\) | 24.2987i | 1.10563i | ||||||||
\(484\) | −0.878567 | −0.0399349 | ||||||||
\(485\) | 3.69855 | + | 11.1794i | 0.167942 | + | 0.507629i | ||||
\(486\) | 6.63276 | 0.300868 | ||||||||
\(487\) | − | 36.8883i | − | 1.67157i | −0.549060 | − | 0.835783i | \(-0.685014\pi\) | ||
0.549060 | − | 0.835783i | \(-0.314986\pi\) | |||||||
\(488\) | − | 9.64273i | − | 0.436506i | ||||||
\(489\) | −11.2458 | −0.508553 | ||||||||
\(490\) | 0.986548 | + | 2.98198i | 0.0445677 | + | 0.134712i | ||||
\(491\) | −35.3534 | −1.59548 | −0.797739 | − | 0.603003i | \(-0.793971\pi\) | ||||
−0.797739 | + | 0.603003i | \(0.793971\pi\) | |||||||
\(492\) | 14.1529i | 0.638064i | ||||||||
\(493\) | 5.84642i | 0.263310i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.2560 | + | 9.67894i | −1.31496 | + | 0.435036i | ||||
\(496\) | 12.6866 | 0.569644 | ||||||||
\(497\) | 17.5917i | 0.789096i | ||||||||
\(498\) | 7.67612i | 0.343975i | ||||||||
\(499\) | −16.2189 | −0.726058 | −0.363029 | − | 0.931778i | \(-0.618257\pi\) | ||||
−0.363029 | + | 0.931778i | \(0.618257\pi\) | |||||||
\(500\) | −12.1483 | + | 17.2971i | −0.543290 | + | 0.773549i | ||||
\(501\) | 9.02690 | 0.403292 | ||||||||
\(502\) | 6.29480i | 0.280950i | ||||||||
\(503\) | 20.2384i | 0.902386i | 0.892427 | + | 0.451193i | \(0.149001\pi\) | ||||
−0.892427 | + | 0.451193i | \(0.850999\pi\) | |||||||
\(504\) | 18.3265 | 0.816328 | ||||||||
\(505\) | −12.1229 | + | 4.01070i | −0.539462 | + | 0.178474i | ||||
\(506\) | −2.89055 | −0.128500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 17.3244i | − | 0.768646i | ||||||
\(509\) | 20.0371 | 0.888127 | 0.444063 | − | 0.895995i | \(-0.353537\pi\) | ||||
0.444063 | + | 0.895995i | \(0.353537\pi\) | |||||||
\(510\) | −1.21891 | − | 3.68431i | −0.0539740 | − | 0.163144i | ||||
\(511\) | −18.3265 | −0.810718 | ||||||||
\(512\) | 20.9992i | 0.928042i | ||||||||
\(513\) | − | 4.17780i | − | 0.184454i | ||||||
\(514\) | 0.698546 | 0.0308116 | ||||||||
\(515\) | −5.17524 | − | 15.6429i | −0.228048 | − | 0.689308i | ||||
\(516\) | −44.4629 | −1.95737 | ||||||||
\(517\) | 22.2974i | 0.980639i | ||||||||
\(518\) | − | 2.16211i | − | 0.0949977i | ||||||
\(519\) | 23.5185 | 1.03235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0269 | 0.702151 | 0.351076 | − | 0.936347i | \(-0.385816\pi\) | ||||
0.351076 | + | 0.936347i | \(0.385816\pi\) | |||||||
\(522\) | 4.21401i | 0.184442i | ||||||||
\(523\) | − | 11.7380i | − | 0.513265i | −0.966509 | − | 0.256633i | \(-0.917387\pi\) | ||
0.966509 | − | 0.256633i | \(-0.0826130\pi\) | |||||||
\(524\) | 18.9055 | 0.825889 | ||||||||
\(525\) | −36.2291 | + | 26.9180i | −1.58117 | + | 1.17480i | ||||
\(526\) | 9.89775 | 0.431562 | ||||||||
\(527\) | − | 7.36863i | − | 0.320982i | ||||||
\(528\) | − | 29.3152i | − | 1.27578i | ||||||
\(529\) | 15.7542 | 0.684965 | ||||||||
\(530\) | 9.01345 | − | 2.98198i | 0.391519 | − | 0.129529i | ||||
\(531\) | −10.7643 | −0.467132 | ||||||||
\(532\) | 7.89832i | 0.342436i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.18722 | 0.397570 | ||||||||
\(535\) | −6.02213 | − | 18.2027i | −0.260359 | − | 0.786972i | ||||
\(536\) | 5.16804 | 0.223225 | ||||||||
\(537\) | 48.4798i | 2.09206i | ||||||||
\(538\) | − | 6.14995i | − | 0.265143i | ||||||
\(539\) | 13.7811 | 0.593594 | ||||||||
\(540\) | 4.45274 | + | 13.4590i | 0.191615 | + | 0.579184i | ||||
\(541\) | −21.8080 | −0.937599 | −0.468800 | − | 0.883305i | \(-0.655313\pi\) | ||||
−0.468800 | + | 0.883305i | \(0.655313\pi\) | |||||||
\(542\) | 1.92704i | 0.0827736i | ||||||||
\(543\) | 2.80934i | 0.120560i | ||||||||
\(544\) | 7.18002 | 0.307841 | ||||||||
\(545\) | −18.0269 | + | 5.96396i | −0.772188 | + | 0.255468i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.30924i | 0.269764i | 0.990862 | + | 0.134882i | \(0.0430655\pi\) | ||||
−0.990862 | + | 0.134882i | \(0.956935\pi\) | |||||||
\(548\) | 31.8533i | 1.36070i | ||||||||
\(549\) | 31.8080 | 1.35753 | ||||||||
\(550\) | −3.20215 | − | 4.30978i | −0.136540 | − | 0.183769i | ||||
\(551\) | −3.73743 | −0.159220 | ||||||||
\(552\) | 9.32634i | 0.396955i | ||||||||
\(553\) | − | 46.2146i | − | 1.96524i | ||||||
\(554\) | 4.47964 | 0.190322 | ||||||||
\(555\) | 11.1364 | − | 3.68431i | 0.472712 | − | 0.156390i | ||||
\(556\) | 1.94141 | 0.0823342 | ||||||||
\(557\) | − | 35.8378i | − | 1.51849i | −0.650802 | − | 0.759247i | \(-0.725567\pi\) | ||
0.650802 | − | 0.759247i | \(-0.274433\pi\) | |||||||
\(558\) | − | 5.31119i | − | 0.224840i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.90253 | − | 23.8865i | −0.333943 | − | 1.00939i | ||||
\(561\) | −17.0269 | −0.718876 | ||||||||
\(562\) | − | 0.153745i | − | 0.00648534i | ||||||
\(563\) | 5.00212i | 0.210814i | 0.994429 | + | 0.105407i | \(0.0336145\pi\) | ||||
−0.994429 | + | 0.105407i | \(0.966385\pi\) | |||||||
\(564\) | 34.9593 | 1.47205 | ||||||||
\(565\) | −5.14981 | − | 15.5660i | −0.216654 | − | 0.654868i | ||||
\(566\) | −3.32836 | −0.139901 | ||||||||
\(567\) | − | 12.4432i | − | 0.522564i | ||||||
\(568\) | 6.75207i | 0.283310i | ||||||||
\(569\) | 13.1680 | 0.552033 | 0.276017 | − | 0.961153i | \(-0.410986\pi\) | ||||
0.276017 | + | 0.961153i | \(0.410986\pi\) | |||||||
\(570\) | 2.35526 | − | 0.779207i | 0.0986511 | − | 0.0326374i | ||||
\(571\) | 19.8349 | 0.830065 | 0.415032 | − | 0.909807i | \(-0.363770\pi\) | ||||
0.415032 | + | 0.909807i | \(0.363770\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 68.6909i | 2.86960i | ||||||||
\(574\) | −3.08549 | −0.128786 | ||||||||
\(575\) | −8.02690 | − | 10.8034i | −0.334745 | − | 0.450534i | ||||
\(576\) | −23.3164 | −0.971516 | ||||||||
\(577\) | − | 10.9210i | − | 0.454646i | −0.973819 | − | 0.227323i | \(-0.927003\pi\) | ||
0.973819 | − | 0.227323i | \(-0.0729972\pi\) | |||||||
\(578\) | 4.36775i | 0.181675i | ||||||||
\(579\) | −53.3534 | −2.21729 | ||||||||
\(580\) | 12.0404 | − | 3.98339i | 0.499949 | − | 0.165401i | ||||
\(581\) | 28.9055 | 1.19920 | ||||||||
\(582\) | 4.68969i | 0.194394i | ||||||||
\(583\) | − | 41.6553i | − | 1.72519i | ||||||
\(584\) | −7.03411 | −0.291073 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.44979 | −0.183819 | ||||||||
\(587\) | − | 40.4495i | − | 1.66953i | −0.550607 | − | 0.834764i | \(-0.685604\pi\) | ||
0.550607 | − | 0.834764i | \(-0.314396\pi\) | |||||||
\(588\) | − | 21.6069i | − | 0.891052i | ||||||
\(589\) | 4.71053 | 0.194094 | ||||||||
\(590\) | −0.589093 | − | 1.78062i | −0.0242526 | − | 0.0733069i | ||||
\(591\) | −58.2829 | −2.39744 | ||||||||
\(592\) | 6.53876i | 0.268742i | ||||||||
\(593\) | 1.47709i | 0.0606569i | 0.999540 | + | 0.0303284i | \(0.00965532\pi\) | ||||
−0.999540 | + | 0.0303284i | \(0.990345\pi\) | |||||||
\(594\) | −3.60107 | −0.147754 | ||||||||
\(595\) | −13.8738 | + | 4.58996i | −0.568770 | + | 0.188170i | ||||
\(596\) | −29.9683 | −1.22755 | ||||||||
\(597\) | − | 49.0690i | − | 2.00826i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.27271 | −0.0928606 | −0.0464303 | − | 0.998922i | \(-0.514785\pi\) | ||||
−0.0464303 | + | 0.998922i | \(0.514785\pi\) | |||||||
\(600\) | −13.9055 | + | 10.3317i | −0.567689 | + | 0.421790i | ||||
\(601\) | 7.40429 | 0.302027 | 0.151014 | − | 0.988532i | \(-0.451746\pi\) | ||||
0.151014 | + | 0.988532i | \(0.451746\pi\) | |||||||
\(602\) | − | 9.69338i | − | 0.395073i | ||||||
\(603\) | 17.0476i | 0.694231i | ||||||||
\(604\) | 27.4988 | 1.11891 | ||||||||
\(605\) | 0.986548 | − | 0.326386i | 0.0401089 | − | 0.0132695i | ||||
\(606\) | −5.08549 | −0.206584 | ||||||||
\(607\) | 10.6932i | 0.434024i | 0.976169 | + | 0.217012i | \(0.0696311\pi\) | ||||
−0.976169 | + | 0.217012i | \(0.930369\pi\) | |||||||
\(608\) | 4.58996i | 0.186147i | ||||||||
\(609\) | 27.0807 | 1.09737 | ||||||||
\(610\) | 1.74074 | + | 5.26162i | 0.0704804 | + | 0.213037i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.6429i | 0.632327i | ||||||||
\(613\) | 6.08149i | 0.245629i | 0.992430 | + | 0.122815i | \(0.0391920\pi\) | ||||
−0.992430 | + | 0.122815i | \(0.960808\pi\) | |||||||
\(614\) | 8.14114 | 0.328550 | ||||||||
\(615\) | −5.25779 | − | 15.8924i | −0.212015 | − | 0.640844i | ||||
\(616\) | 14.0101 | 0.564485 | ||||||||
\(617\) | − | 31.8388i | − | 1.28178i | −0.767631 | − | 0.640892i | \(-0.778565\pi\) | ||
0.767631 | − | 0.640892i | \(-0.221435\pi\) | |||||||
\(618\) | − | 6.56211i | − | 0.263967i | ||||||
\(619\) | 26.4043 | 1.06128 | 0.530639 | − | 0.847598i | \(-0.321952\pi\) | ||||
0.530639 | + | 0.847598i | \(0.321952\pi\) | |||||||
\(620\) | −15.1752 | + | 5.02052i | −0.609452 | + | 0.201629i | ||||
\(621\) | −9.02690 | −0.362237 | ||||||||
\(622\) | 0.806517i | 0.0323384i | ||||||||
\(623\) | − | 34.5957i | − | 1.38605i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.21560 | − | 23.9361i | 0.288624 | − | 0.957443i | ||||
\(626\) | 6.38400 | 0.255156 | ||||||||
\(627\) | − | 10.8848i | − | 0.434695i | ||||||
\(628\) | 20.6466i | 0.823889i | ||||||||
\(629\) | 3.79785 | 0.151430 | ||||||||
\(630\) | −10.0000 | + | 3.30837i | −0.398410 | + | 0.131808i | ||||
\(631\) | 35.1680 | 1.40002 | 0.700009 | − | 0.714134i | \(-0.253179\pi\) | ||||
0.700009 | + | 0.714134i | \(0.253179\pi\) | |||||||
\(632\) | − | 17.7381i | − | 0.705585i | ||||||
\(633\) | 51.9508i | 2.06486i | ||||||||
\(634\) | −9.53528 | −0.378695 | ||||||||
\(635\) | 6.43598 | + | 19.4536i | 0.255404 | + | 0.771994i | ||||
\(636\) | −65.3098 | −2.58970 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.22150i | 0.127540i | ||||||||
\(639\) | −22.2727 | −0.881095 | ||||||||
\(640\) | −6.45126 | − | 19.4999i | −0.255009 | − | 0.770799i | ||||
\(641\) | 5.52514 | 0.218230 | 0.109115 | − | 0.994029i | \(-0.465198\pi\) | ||||
0.109115 | + | 0.994029i | \(0.465198\pi\) | |||||||
\(642\) | − | 7.63594i | − | 0.301367i | ||||||
\(643\) | − | 32.1552i | − | 1.26808i | −0.773301 | − | 0.634039i | \(-0.781396\pi\) | ||
0.773301 | − | 0.634039i | \(-0.218604\pi\) | |||||||
\(644\) | 17.0658 | 0.672486 | ||||||||
\(645\) | 49.9276 | − | 16.5179i | 1.96590 | − | 0.650391i | ||||
\(646\) | 0.803220 | 0.0316023 | ||||||||
\(647\) | 13.7843i | 0.541917i | 0.962591 | + | 0.270959i | \(0.0873407\pi\) | ||||
−0.962591 | + | 0.270959i | \(0.912659\pi\) | |||||||
\(648\) | − | 4.77595i | − | 0.187617i | ||||||
\(649\) | −8.22905 | −0.323019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.1316 | −1.33772 | ||||||||
\(652\) | 7.89832i | 0.309322i | ||||||||
\(653\) | 8.50202i | 0.332710i | 0.986066 | + | 0.166355i | \(0.0531997\pi\) | ||||
−0.986066 | + | 0.166355i | \(0.946800\pi\) | |||||||
\(654\) | −7.56219 | −0.295705 | ||||||||
\(655\) | −21.2291 | + | 7.02335i | −0.829488 | + | 0.274425i | ||||
\(656\) | 9.33130 | 0.364326 | ||||||||
\(657\) | − | 23.2031i | − | 0.905238i | ||||||
\(658\) | 7.62150i | 0.297117i | ||||||||
\(659\) | −4.04366 | −0.157519 | −0.0787594 | − | 0.996894i | \(-0.525096\pi\) | ||||
−0.0787594 | + | 0.996894i | \(0.525096\pi\) | |||||||
\(660\) | 11.6011 | + | 35.0659i | 0.451571 | + | 1.36494i | ||||
\(661\) | 31.2727 | 1.21637 | 0.608184 | − | 0.793796i | \(-0.291898\pi\) | ||||
0.608184 | + | 0.793796i | \(0.291898\pi\) | |||||||
\(662\) | − | 0.983609i | − | 0.0382290i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.0945 | 0.430551 | ||||||||
\(665\) | −2.93421 | − | 8.86907i | −0.113784 | − | 0.343928i | ||||
\(666\) | 2.73743 | 0.106073 | ||||||||
\(667\) | 8.07541i | 0.312681i | ||||||||
\(668\) | − | 6.33991i | − | 0.245298i | ||||||
\(669\) | 33.2996 | 1.28744 | ||||||||
\(670\) | −2.81998 | + | 0.932952i | −0.108945 | + | 0.0360431i | ||||
\(671\) | 24.3164 | 0.938723 | ||||||||
\(672\) | − | 33.2579i | − | 1.28295i | ||||||
\(673\) | − | 32.0739i | − | 1.23636i | −0.786037 | − | 0.618179i | \(-0.787871\pi\) | ||
0.786037 | − | 0.618179i | \(-0.212129\pi\) | |||||||
\(674\) | 0.629812 | 0.0242595 | ||||||||
\(675\) | −10.0000 | − | 13.4590i | −0.384900 | − | 0.518038i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.2382i | − | 0.547220i | −0.961841 | − | 0.273610i | \(-0.911782\pi\) | ||
0.961841 | − | 0.273610i | \(-0.0882177\pi\) | |||||||
\(678\) | − | 6.52986i | − | 0.250778i | ||||||
\(679\) | 17.6597 | 0.677716 | ||||||||
\(680\) | −5.32505 | + | 1.76172i | −0.204206 | + | 0.0675589i | ||||
\(681\) | 16.5891 | 0.635695 | ||||||||
\(682\) | − | 4.06026i | − | 0.155475i | ||||||
\(683\) | − | 25.7847i | − | 0.986622i | −0.869853 | − | 0.493311i | \(-0.835786\pi\) | ||
0.869853 | − | 0.493311i | \(-0.164214\pi\) | |||||||
\(684\) | −10.0000 | −0.382360 | ||||||||
\(685\) | −11.8334 | − | 35.7682i | −0.452132 | − | 1.36663i | ||||
\(686\) | −3.05564 | −0.116665 | ||||||||
\(687\) | 72.6336i | 2.77114i | ||||||||
\(688\) | 29.3152i | 1.11763i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.68362 | − | 5.08898i | −0.0640944 | − | 0.193734i | ||||
\(691\) | −0.0436636 | −0.00166104 | −0.000830522 | − | 1.00000i | \(-0.500264\pi\) | ||||
−0.000830522 | 1.00000i | \(0.500264\pi\) | ||||||||
\(692\) | − | 16.5179i | − | 0.627915i | ||||||
\(693\) | 46.2146i | 1.75555i | ||||||||
\(694\) | −4.18002 | −0.158671 | ||||||||
\(695\) | −2.18002 | + | 0.721231i | −0.0826929 | + | 0.0273578i | ||||
\(696\) | 10.3941 | 0.393989 | ||||||||
\(697\) | − | 5.41982i | − | 0.205290i | ||||||
\(698\) | − | 2.96863i | − | 0.112364i | ||||||
\(699\) | 2.21891 | 0.0839267 | ||||||||
\(700\) | 18.9055 | + | 25.4449i | 0.714560 | + | 0.961727i | ||||
\(701\) | −14.5454 | −0.549373 | −0.274687 | − | 0.961534i | \(-0.588574\pi\) | ||||
−0.274687 | + | 0.961534i | \(0.588574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.42785i | 0.0915679i | ||||||||
\(704\) | −17.8248 | −0.671796 | ||||||||
\(705\) | −39.2560 | + | 12.9873i | −1.47846 | + | 0.489130i | ||||
\(706\) | 11.3313 | 0.426459 | ||||||||
\(707\) | 19.1501i | 0.720214i | ||||||||
\(708\) | 12.9020i | 0.484888i | ||||||||
\(709\) | −19.6328 | −0.737324 | −0.368662 | − | 0.929564i | \(-0.620184\pi\) | ||||
−0.368662 | + | 0.929564i | \(0.620184\pi\) | |||||||
\(710\) | −1.21891 | − | 3.68431i | −0.0457447 | − | 0.138270i | ||||
\(711\) | 58.5119 | 2.19437 | ||||||||
\(712\) | − | 13.2786i | − | 0.497636i | ||||||
\(713\) | − | 10.1780i | − | 0.381168i | ||||||
\(714\) | −5.81998 | −0.217807 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 34.0490 | 1.27247 | ||||||||
\(717\) | − | 10.7672i | − | 0.402109i | ||||||
\(718\) | − | 7.41216i | − | 0.276619i | ||||||
\(719\) | −47.4312 | −1.76889 | −0.884443 | − | 0.466649i | \(-0.845461\pi\) | ||||
−0.884443 | + | 0.466649i | \(0.845461\pi\) | |||||||
\(720\) | 30.2425 | − | 10.0053i | 1.12707 | − | 0.372876i | ||||
\(721\) | −24.7105 | −0.920268 | ||||||||
\(722\) | − | 5.77242i | − | 0.214827i | ||||||
\(723\) | 61.0872i | 2.27186i | ||||||||
\(724\) | 1.97310 | 0.0733295 | ||||||||
\(725\) | −12.0404 | + | 8.94594i | −0.447168 | + | 0.332244i | ||||
\(726\) | 0.413851 | 0.0153595 | ||||||||
\(727\) | − | 34.0951i | − | 1.26452i | −0.774757 | − | 0.632259i | \(-0.782128\pi\) | ||
0.774757 | − | 0.632259i | \(-0.217872\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 42.8349 | 1.58648 | ||||||||
\(730\) | 3.83821 | − | 1.26982i | 0.142059 | − | 0.0469982i | ||||
\(731\) | 17.0269 | 0.629763 | ||||||||
\(732\) | − | 38.1247i | − | 1.40913i | ||||||
\(733\) | − | 14.3920i | − | 0.531580i | −0.964031 | − | 0.265790i | \(-0.914367\pi\) | ||
0.964031 | − | 0.265790i | \(-0.0856327\pi\) | |||||||
\(734\) | −4.36541 | −0.161130 | ||||||||
\(735\) | 8.02690 | + | 24.2624i | 0.296077 | + | 0.894934i | ||||
\(736\) | 9.91745 | 0.365562 | ||||||||
\(737\) | 13.0324i | 0.480055i | ||||||||
\(738\) | − | 3.90652i | − | 0.143801i | ||||||
\(739\) | 34.4480 | 1.26719 | 0.633594 | − | 0.773665i | \(-0.281579\pi\) | ||||
0.633594 | + | 0.773665i | \(0.281579\pi\) | |||||||
\(740\) | −2.58762 | − | 7.82145i | −0.0951228 | − | 0.287522i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 14.2382i | − | 0.522702i | ||||||
\(743\) | 40.7134i | 1.49363i | 0.665031 | + | 0.746816i | \(0.268418\pi\) | ||||
−0.665031 | + | 0.746816i | \(0.731582\pi\) | |||||||
\(744\) | −13.1004 | −0.480285 | ||||||||
\(745\) | 33.6516 | − | 11.1332i | 1.23290 | − | 0.407888i | ||||
\(746\) | 5.04903 | 0.184858 | ||||||||
\(747\) | 36.5970i | 1.33901i | ||||||||
\(748\) | 11.9586i | 0.437249i | ||||||||
\(749\) | −28.7542 | −1.05066 | ||||||||
\(750\) | 5.72251 | − | 8.14783i | 0.208956 | − | 0.297517i | ||||
\(751\) | 32.5018 | 1.18601 | 0.593003 | − | 0.805200i | \(-0.297942\pi\) | ||||
0.593003 | + | 0.805200i | \(0.297942\pi\) | |||||||
\(752\) | − | 23.0493i | − | 0.840522i | ||||||
\(753\) | 51.2167i | 1.86644i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.8786 | + | 10.2158i | −1.12379 | + | 0.371790i | ||||
\(756\) | 21.2607 | 0.773245 | ||||||||
\(757\) | 13.0324i | 0.473671i | 0.971550 | + | 0.236836i | \(0.0761103\pi\) | ||||
−0.971550 | + | 0.236836i | \(0.923890\pi\) | |||||||
\(758\) | − | 6.03084i | − | 0.219050i | ||||||
\(759\) | −23.5185 | −0.853668 | ||||||||
\(760\) | −1.12621 | − | 3.40413i | −0.0408520 | − | 0.123481i | ||||
\(761\) | −3.98985 | −0.144632 | −0.0723161 | − | 0.997382i | \(-0.523039\pi\) | ||||
−0.0723161 | + | 0.997382i | \(0.523039\pi\) | |||||||
\(762\) | 8.16070i | 0.295631i | ||||||||
\(763\) | 28.4765i | 1.03092i | ||||||||
\(764\) | 48.2440 | 1.74541 | ||||||||
\(765\) | −5.81131 | − | 17.5655i | −0.210108 | − | 0.635082i | ||||
\(766\) | −0.476696 | −0.0172237 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 21.3847i | 0.771652i | ||||||||
\(769\) | −6.66686 | −0.240413 | −0.120207 | − | 0.992749i | \(-0.538356\pi\) | ||||
−0.120207 | + | 0.992749i | \(0.538356\pi\) | |||||||
\(770\) | −7.64474 | + | 2.52916i | −0.275497 | + | 0.0911445i | ||||
\(771\) | 5.68362 | 0.204691 | ||||||||
\(772\) | 37.4720i | 1.34865i | ||||||||
\(773\) | 48.3349i | 1.73849i | 0.494384 | + | 0.869244i | \(0.335394\pi\) | ||||
−0.494384 | + | 0.869244i | \(0.664606\pi\) | |||||||
\(774\) | 12.2727 | 0.441134 | ||||||||
\(775\) | 15.1752 | − | 11.2751i | 0.545111 | − | 0.405015i | ||||
\(776\) | 6.77815 | 0.243321 | ||||||||
\(777\) | − | 17.5917i | − | 0.631099i | ||||||
\(778\) | 6.21683i | 0.222884i | ||||||||
\(779\) | 3.46472 | 0.124136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0269 | −0.609271 | ||||||||
\(782\) | − | 1.73551i | − | 0.0620616i | ||||||
\(783\) | 10.0604i | 0.359531i | ||||||||
\(784\) | −14.2458 | −0.508779 | ||||||||
\(785\) | −7.67017 | − | 23.1842i | −0.273760 | − | 0.827478i | ||||
\(786\) | −8.90547 | −0.317648 | ||||||||
\(787\) | 27.9612i | 0.996709i | 0.866973 | + | 0.498355i | \(0.166062\pi\) | ||||
−0.866973 | + | 0.498355i | \(0.833938\pi\) | |||||||
\(788\) | 40.9341i | 1.45822i | ||||||||
\(789\) | 80.5316 | 2.86700 | ||||||||
\(790\) | 3.20215 | + | 9.67894i | 0.113927 | + | 0.344361i | ||||
\(791\) | −24.5891 | −0.874288 | ||||||||
\(792\) | 17.7381i | 0.630297i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.65488 | −0.200684 | ||||||||
\(795\) | 73.3367 | − | 24.2624i | 2.60098 | − | 0.860500i | ||||
\(796\) | −34.4629 | −1.22150 | ||||||||
\(797\) | − | 37.2424i | − | 1.31919i | −0.751619 | − | 0.659597i | \(-0.770727\pi\) | ||
0.751619 | − | 0.659597i | \(-0.229273\pi\) | |||||||
\(798\) | − | 3.72052i | − | 0.131705i | ||||||
\(799\) | −13.3875 | −0.473617 | ||||||||
\(800\) | 10.9865 | + | 14.7868i | 0.388433 | + | 0.522793i | ||||
\(801\) | 43.8014 | 1.54765 | ||||||||
\(802\) | 7.34528i | 0.259371i | ||||||||
\(803\) | − | 17.7381i | − | 0.625965i | ||||||
\(804\) | 20.4330 | 0.720617 | ||||||||
\(805\) | −19.1633 | + | 6.33991i | −0.675416 | + | 0.223452i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 50.0382i | − | 1.76143i | ||||||
\(808\) | 7.35022i | 0.258580i | ||||||||
\(809\) | −14.5287 | −0.510801 | −0.255400 | − | 0.966835i | \(-0.582207\pi\) | ||||
−0.255400 | + | 0.966835i | \(0.582207\pi\) | |||||||
\(810\) | 0.862170 | + | 2.60603i | 0.0302936 | + | 0.0915666i | ||||
\(811\) | 44.0538 | 1.54694 | 0.773469 | − | 0.633834i | \(-0.218520\pi\) | ||||
0.773469 | + | 0.633834i | \(0.218520\pi\) | |||||||
\(812\) | − | 19.0197i | − | 0.667461i | ||||||
\(813\) | 15.6791i | 0.549890i | ||||||||
\(814\) | 2.09269 | 0.0733489 | ||||||||
\(815\) | −2.93421 | − | 8.86907i | −0.102781 | − | 0.310670i | ||||
\(816\) | 17.6011 | 0.616161 | ||||||||
\(817\) | 10.8848i | 0.380809i | ||||||||
\(818\) | 3.18687i | 0.111426i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.1618 | + | 3.69273i | −0.389787 | + | 0.128956i | ||||
\(821\) | 27.0269 | 0.943245 | 0.471623 | − | 0.881800i | \(-0.343668\pi\) | ||||
0.471623 | + | 0.881800i | \(0.343668\pi\) | |||||||
\(822\) | − | 15.0046i | − | 0.523345i | ||||||
\(823\) | − | 39.5963i | − | 1.38024i | −0.723695 | − | 0.690120i | \(-0.757558\pi\) | ||
0.723695 | − | 0.690120i | \(-0.242442\pi\) | |||||||
\(824\) | −9.48442 | −0.330405 | ||||||||
\(825\) | −26.0538 | − | 35.0659i | −0.907077 | − | 1.22084i | ||||
\(826\) | −2.81278 | −0.0978691 | ||||||||
\(827\) | 26.5639i | 0.923716i | 0.886954 | + | 0.461858i | \(0.152817\pi\) | ||||
−0.886954 | + | 0.461858i | \(0.847183\pi\) | |||||||
\(828\) | 21.6069i | 0.750890i | ||||||||
\(829\) | −13.9832 | −0.485658 | −0.242829 | − | 0.970069i | \(-0.578075\pi\) | ||||
−0.242829 | + | 0.970069i | \(0.578075\pi\) | |||||||
\(830\) | −6.05381 | + | 2.00282i | −0.210131 | + | 0.0695189i | ||||
\(831\) | 36.4480 | 1.26437 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.27427i | 0.286686i | ||||||||
\(834\) | −0.914507 | −0.0316668 | ||||||||
\(835\) | 2.35526 | + | 7.11911i | 0.0815072 | + | 0.246367i | ||||
\(836\) | −7.64474 | −0.264399 | ||||||||
\(837\) | − | 12.6798i | − | 0.438278i | ||||||
\(838\) | 0.647228i | 0.0223581i | ||||||||
\(839\) | −14.3941 | −0.496941 | −0.248471 | − | 0.968639i | \(-0.579928\pi\) | ||||
−0.248471 | + | 0.968639i | \(0.579928\pi\) | |||||||
\(840\) | 8.16032 | + | 24.6657i | 0.281558 | + | 0.851048i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | − | 3.99674i | − | 0.137737i | ||||||
\(843\) | − | 1.25092i | − | 0.0430841i | ||||||
\(844\) | 36.4868 | 1.25593 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.64952 | −0.331757 | ||||||||
\(847\) | − | 1.55841i | − | 0.0535477i | ||||||
\(848\) | 43.0600i | 1.47869i | ||||||||
\(849\) | −27.0807 | −0.929408 | ||||||||
\(850\) | 2.58762 | − | 1.92259i | 0.0887547 | − | 0.0659444i | ||||
\(851\) | 5.24581 | 0.179824 | ||||||||
\(852\) | 26.6958i | 0.914584i | ||||||||
\(853\) | − | 27.2633i | − | 0.933478i | −0.884395 | − | 0.466739i | \(-0.845429\pi\) | ||
0.884395 | − | 0.466739i | \(-0.154571\pi\) | |||||||
\(854\) | 8.31160 | 0.284417 | ||||||||
\(855\) | 11.2291 | − | 3.71498i | 0.384025 | − | 0.127050i | ||||
\(856\) | −11.0365 | −0.377219 | ||||||||
\(857\) | 50.6201i | 1.72915i | 0.502503 | + | 0.864575i | \(0.332413\pi\) | ||||
−0.502503 | + | 0.864575i | \(0.667587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.27992 | −0.0436702 | −0.0218351 | − | 0.999762i | \(-0.506951\pi\) | ||||
−0.0218351 | + | 0.999762i | \(0.506951\pi\) | |||||||
\(860\) | −11.6011 | − | 35.0659i | −0.395593 | − | 1.19574i | ||||
\(861\) | −25.1047 | −0.855565 | ||||||||
\(862\) | 8.13497i | 0.277078i | ||||||||
\(863\) | 8.38448i | 0.285411i | 0.989765 | + | 0.142706i | \(0.0455802\pi\) | ||||
−0.989765 | + | 0.142706i | \(0.954420\pi\) | |||||||
\(864\) | 12.3553 | 0.420335 | ||||||||
\(865\) | 6.13636 | + | 18.5480i | 0.208642 | + | 0.630651i | ||||
\(866\) | 11.9342 | 0.405541 | ||||||||
\(867\) | 35.5376i | 1.20692i | ||||||||
\(868\) | 23.9718i | 0.813655i | ||||||||
\(869\) | 44.7308 | 1.51739 | ||||||||
\(870\) | −5.67164 | + | 1.87639i | −0.192287 | + | 0.0636155i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.9299i | 0.370132i | ||||||||
\(873\) | 22.3588i | 0.756729i | ||||||||
\(874\) | 1.10945 | 0.0375278 | ||||||||
\(875\) | −30.6818 | − | 21.5489i | −1.03723 | − | 0.728485i | ||||
\(876\) | −27.8109 | −0.939645 | ||||||||
\(877\) | 55.8862i | 1.88714i | 0.331169 | + | 0.943572i | \(0.392557\pi\) | ||||
−0.331169 | + | 0.943572i | \(0.607443\pi\) | |||||||
\(878\) | − | 0.838765i | − | 0.0283069i | ||||||
\(879\) | −36.2051 | −1.22117 | ||||||||
\(880\) | 23.1196 | − | 7.64881i | 0.779362 | − | 0.257841i | ||||
\(881\) | 25.1949 | 0.848839 | 0.424420 | − | 0.905466i | \(-0.360478\pi\) | ||||
0.424420 | + | 0.905466i | \(0.360478\pi\) | |||||||
\(882\) | 5.96396i | 0.200817i | ||||||||
\(883\) | − | 30.7868i | − | 1.03606i | −0.855363 | − | 0.518029i | \(-0.826666\pi\) | ||
0.855363 | − | 0.518029i | \(-0.173334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.79307 | − | 14.4877i | −0.161117 | − | 0.487000i | ||||
\(886\) | 6.40429 | 0.215156 | ||||||||
\(887\) | 12.4721i | 0.418771i | 0.977833 | + | 0.209385i | \(0.0671463\pi\) | ||||
−0.977833 | + | 0.209385i | \(0.932854\pi\) | |||||||
\(888\) | − | 6.75207i | − | 0.226585i | ||||||
\(889\) | 30.7302 | 1.03066 | ||||||||
\(890\) | 2.39709 | + | 7.24555i | 0.0803507 | + | 0.242871i | ||||
\(891\) | 12.0437 | 0.403478 | ||||||||
\(892\) | − | 23.3875i | − | 0.783071i | ||||||
\(893\) | − | 8.55822i | − | 0.286390i | ||||||
\(894\) | 14.1167 | 0.472132 | ||||||||
\(895\) | −38.2338 | + | 12.6491i | −1.27802 | + | 0.422814i | ||||
\(896\) | −30.8032 | −1.02906 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.20739i | 0.273884i | ||||||||
\(899\) | −11.3433 | −0.378320 | ||||||||
\(900\) | −32.2156 | + | 23.9361i | −1.07385 | + | 0.797869i | ||||
\(901\) | 25.0101 | 0.833209 | ||||||||
\(902\) | − | 2.98643i | − | 0.0994372i | ||||||
\(903\) | − | 78.8688i | − | 2.62459i | ||||||
\(904\) | −9.43781 | −0.313897 | ||||||||
\(905\) | −2.21560 | + | 0.733001i | −0.0736490 | + | 0.0243658i | ||||
\(906\) | −12.9534 | −0.430348 | ||||||||
\(907\) | 38.8911i | 1.29136i | 0.763609 | + | 0.645678i | \(0.223425\pi\) | ||||
−0.763609 | + | 0.645678i | \(0.776575\pi\) | |||||||
\(908\) | − | 11.6511i | − | 0.386655i | ||||||
\(909\) | −24.2458 | −0.804183 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.165096 | 0.00546989 | 0.00273494 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273494 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(912\) | 11.2518i | 0.372584i | ||||||||
\(913\) | 27.9774i | 0.925918i | ||||||||
\(914\) | 2.50360 | 0.0828117 | ||||||||
\(915\) | 14.1633 | + | 42.8105i | 0.468223 | + | 1.41527i | ||||
\(916\) | 51.0131 | 1.68552 | ||||||||
\(917\) | 33.5348i | 1.10742i | ||||||||
\(918\) | − | 2.16211i | − | 0.0713603i | ||||||
\(919\) | −0.895326 | −0.0295341 | −0.0147670 | − | 0.999891i | \(-0.504701\pi\) | ||||
−0.0147670 | + | 0.999891i | \(0.504701\pi\) | |||||||
\(920\) | −7.35526 | + | 2.43339i | −0.242496 | + | 0.0802265i | ||||
\(921\) | 66.2392 | 2.18266 | ||||||||
\(922\) | − | 4.08361i | − | 0.134486i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 55.3923 | 1.82227 | ||||||||
\(925\) | 5.81131 | + | 7.82145i | 0.191075 | + | 0.257168i | ||||
\(926\) | −7.56219 | −0.248509 | ||||||||
\(927\) | − | 31.2858i | − | 1.02756i | ||||||
\(928\) | − | 11.0529i | − | 0.362831i | ||||||
\(929\) | 12.2895 | 0.403205 | 0.201602 | − | 0.979467i | \(-0.435385\pi\) | ||||
0.201602 | + | 0.979467i | \(0.435385\pi\) | |||||||
\(930\) | 7.14834 | − | 2.36493i | 0.234403 | − | 0.0775491i | ||||
\(931\) | −5.28947 | −0.173356 | ||||||||
\(932\) | − | 1.55841i | − | 0.0510476i | ||||||
\(933\) | 6.56211i | 0.214834i | ||||||||
\(934\) | −5.06101 | −0.165601 | ||||||||
\(935\) | −4.44259 | − | 13.4284i | −0.145288 | − | 0.439154i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.77242i | 0.188577i | 0.995545 | + | 0.0942884i | \(0.0300576\pi\) | ||||
−0.995545 | + | 0.0942884i | \(0.969942\pi\) | |||||||
\(938\) | 4.45462i | 0.145448i | ||||||||
\(939\) | 51.9425 | 1.69508 | ||||||||
\(940\) | 9.12143 | + | 27.5708i | 0.297508 | + | 0.899261i | ||||
\(941\) | −55.8887 | −1.82192 | −0.910960 | − | 0.412495i | \(-0.864658\pi\) | ||||
−0.910960 | + | 0.412495i | \(0.864658\pi\) | |||||||
\(942\) | − | 9.72563i | − | 0.316878i | ||||||
\(943\) | − | 7.48616i | − | 0.243783i | ||||||
\(944\) | 8.50655 | 0.276864 | ||||||||
\(945\) | −23.8738 | + | 7.89832i | −0.776614 | + | 0.256932i | ||||
\(946\) | 9.38217 | 0.305041 | ||||||||
\(947\) | 1.89638i | 0.0616239i | 0.999525 | + | 0.0308120i | \(0.00980931\pi\) | ||||
−0.999525 | + | 0.0308120i | \(0.990191\pi\) | |||||||
\(948\) | − | 70.1318i | − | 2.27777i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.22905 | + | 1.65418i | 0.0398757 | + | 0.0536688i | ||||
\(951\) | −77.5825 | −2.51578 | ||||||||
\(952\) | 8.41179i | 0.272628i | ||||||||
\(953\) | 33.6523i | 1.09011i | 0.838402 | + | 0.545053i | \(0.183490\pi\) | ||||
−0.838402 | + | 0.545053i | \(0.816510\pi\) | |||||||
\(954\) | 18.0269 | 0.583643 | ||||||||
\(955\) | −54.1734 | + | 17.9225i | −1.75301 | + | 0.579960i | ||||
\(956\) | −7.56219 | −0.244579 | ||||||||
\(957\) | 26.2113i | 0.847290i | ||||||||
\(958\) | − | 8.03366i | − | 0.259556i | ||||||
\(959\) | −56.5018 | −1.82454 | ||||||||
\(960\) | −10.3822 | − | 31.3816i | −0.335083 | − | 1.01284i | ||||
\(961\) | −16.7033 | −0.538817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 36.4054i | − | 1.17315i | ||||||
\(964\) | 42.9036 | 1.38183 | ||||||||
\(965\) | −13.9208 | − | 42.0775i | −0.448125 | − | 1.35452i | ||||
\(966\) | −8.03888 | −0.258647 | ||||||||
\(967\) | 23.0493i | 0.741216i | 0.928789 | + | 0.370608i | \(0.120851\pi\) | ||||
−0.928789 | + | 0.370608i | \(0.879149\pi\) | |||||||
\(968\) | − | 0.598152i | − | 0.0192253i | ||||||
\(969\) | 6.53528 | 0.209944 | ||||||||
\(970\) | −3.69855 | + | 1.22361i | −0.118753 | + | 0.0392879i | ||||
\(971\) | 14.9193 | 0.478783 | 0.239391 | − | 0.970923i | \(-0.423052\pi\) | ||||
0.239391 | + | 0.970923i | \(0.423052\pi\) | |||||||
\(972\) | − | 37.9025i | − | 1.21572i | ||||||
\(973\) | 3.44370i | 0.110400i | ||||||||
\(974\) | 12.2040 | 0.391041 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.1364 | −0.804595 | ||||||||
\(977\) | 23.3641i | 0.747485i | 0.927533 | + | 0.373742i | \(0.121926\pi\) | ||||
−0.927533 | + | 0.373742i | \(0.878074\pi\) | |||||||
\(978\) | − | 3.72052i | − | 0.118969i | ||||||
\(979\) | 33.4850 | 1.07019 | ||||||||
\(980\) | 17.0404 | − | 5.63757i | 0.544334 | − | 0.180086i | ||||
\(981\) | −36.0538 | −1.15111 | ||||||||
\(982\) | − | 11.6962i | − | 0.373241i | ||||||
\(983\) | 5.31119i | 0.169401i | 0.996406 | + | 0.0847003i | \(0.0269933\pi\) | ||||
−0.996406 | + | 0.0847003i | \(0.973007\pi\) | |||||||
\(984\) | −9.63570 | −0.307175 | ||||||||
\(985\) | −15.2069 | − | 45.9651i | −0.484533 | − | 1.46457i | ||||
\(986\) | −1.93421 | −0.0615978 | ||||||||
\(987\) | 62.0112i | 1.97384i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.5185 | 0.747846 | ||||||||
\(990\) | −3.20215 | − | 9.67894i | −0.101771 | − | 0.307617i | ||||
\(991\) | −24.0879 | −0.765178 | −0.382589 | − | 0.923919i | \(-0.624967\pi\) | ||||
−0.382589 | + | 0.923919i | \(0.624967\pi\) | |||||||
\(992\) | 13.9307i | 0.442301i | ||||||||
\(993\) | − | 8.00299i | − | 0.253967i | ||||||
\(994\) | −5.81998 | −0.184599 | ||||||||
\(995\) | 38.6985 | − | 12.8029i | 1.22683 | − | 0.405879i | ||||
\(996\) | 43.8648 | 1.38991 | ||||||||
\(997\) | − | 20.4099i | − | 0.646389i | −0.946332 | − | 0.323195i | \(-0.895243\pi\) | ||
0.946332 | − | 0.323195i | \(-0.104757\pi\) | |||||||
\(998\) | − | 5.36581i | − | 0.169852i | ||||||
\(999\) | 6.53528 | 0.206767 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))