Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 241.2 | ||
Root | \(0.403374 - 1.68443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.241 |
Dual form | 720.2.q.k.481.2 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.403374 | + | 1.68443i | 0.232888 | + | 0.972504i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.91751 | + | 3.32123i | −0.724751 | + | 1.25531i | 0.234326 | + | 0.972158i | \(0.424712\pi\) |
−0.959076 | + | 0.283147i | \(0.908621\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.67458 | + | 1.35891i | −0.891526 | + | 0.452969i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.853695 | + | 1.47864i | −0.257399 | + | 0.445828i | −0.965544 | − | 0.260239i | \(-0.916199\pi\) |
0.708146 | + | 0.706066i | \(0.249532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.85369 | − | 3.21069i | −0.514122 | − | 0.890486i | −0.999866 | − | 0.0163846i | \(-0.994784\pi\) |
0.485743 | − | 0.874101i | \(-0.338549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.25707 | + | 1.19154i | −0.324574 | + | 0.307656i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.70739 | 0.414103 | 0.207051 | − | 0.978330i | \(-0.433613\pi\) | ||||
0.207051 | + | 0.978330i | \(0.433613\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.292611 | −0.0671295 | −0.0335647 | − | 0.999437i | \(-0.510686\pi\) | ||||
−0.0335647 | + | 0.999437i | \(0.510686\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.36783 | − | 1.89021i | −1.38957 | − | 0.412477i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.91751 | − | 5.05328i | −0.608343 | − | 1.05368i | −0.991514 | − | 0.130003i | \(-0.958501\pi\) |
0.383171 | − | 0.923678i | \(-0.374832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.36783 | − | 3.95698i | −0.648139 | − | 0.761522i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.33502 | + | 7.50848i | −0.804993 | + | 1.39429i | 0.111302 | + | 0.993787i | \(0.464498\pi\) |
−0.916296 | + | 0.400503i | \(0.868836\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.146305 | + | 0.253408i | 0.0262772 | + | 0.0455135i | 0.878865 | − | 0.477071i | \(-0.158301\pi\) |
−0.852588 | + | 0.522584i | \(0.824968\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.83502 | − | 0.841540i | −0.493514 | − | 0.146493i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.83502 | −0.648237 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.9627 | 1.96665 | 0.983324 | − | 0.181862i | \(-0.0582124\pi\) | ||||
0.983324 | + | 0.181862i | \(0.0582124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.66044 | − | 4.41752i | 0.746268 | − | 0.707369i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.48133 | + | 6.02983i | 0.543692 | + | 0.941702i | 0.998688 | + | 0.0512085i | \(0.0163073\pi\) |
−0.454996 | + | 0.890493i | \(0.650359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.85369 | − | 3.21069i | 0.282686 | − | 0.489626i | −0.689360 | − | 0.724419i | \(-0.742108\pi\) |
0.972045 | + | 0.234793i | \(0.0754413\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.51414 | − | 1.63680i | −0.374785 | − | 0.244000i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.936184 | − | 1.62152i | 0.136556 | − | 0.236523i | −0.789634 | − | 0.613578i | \(-0.789730\pi\) |
0.926191 | + | 0.377055i | \(0.123063\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.85369 | − | 6.67479i | −0.550528 | − | 0.953542i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.688716 | + | 2.87597i | 0.0964395 | + | 0.402716i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6700 | −1.60300 | −0.801502 | − | 0.597992i | \(-0.795965\pi\) | ||||
−0.801502 | + | 0.597992i | \(0.795965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.70739 | −0.230224 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.118031 | − | 0.492881i | −0.0156336 | − | 0.0652837i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.83502 | + | 10.1066i | 0.759655 | + | 1.31576i | 0.943027 | + | 0.332718i | \(0.107966\pi\) |
−0.183371 | + | 0.983044i | \(0.558701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.48133 | + | 12.9580i | −0.957886 | + | 1.65911i | −0.230264 | + | 0.973128i | \(0.573959\pi\) |
−0.727622 | + | 0.685979i | \(0.759374\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.615299 | − | 11.4886i | 0.0775204 | − | 1.44743i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.85369 | − | 3.21069i | 0.229923 | − | 0.398237i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.77121 | + | 8.26397i | 0.582896 | + | 1.00960i | 0.995134 | + | 0.0985288i | \(0.0314136\pi\) |
−0.412239 | + | 0.911076i | \(0.635253\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.33502 | − | 6.95269i | 0.883033 | − | 0.837005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.9627 | −1.89442 | −0.947209 | − | 0.320616i | \(-0.896110\pi\) | ||||
−0.947209 | + | 0.320616i | \(0.896110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.66044 | − | 0.492881i | −0.191731 | − | 0.0569130i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.27394 | − | 5.67063i | −0.373100 | − | 0.646228i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | − | 1.73205i | 0.112509 | − | 0.194871i | −0.804272 | − | 0.594261i | \(-0.797445\pi\) |
0.916781 | + | 0.399390i | \(0.130778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.30675 | − | 7.26900i | 0.589639 | − | 0.807667i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.91751 | + | 10.2494i | −0.649531 | + | 1.12502i | 0.333704 | + | 0.942678i | \(0.391701\pi\) |
−0.983235 | + | 0.182343i | \(0.941632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.853695 | + | 1.47864i | 0.0925962 | + | 0.160381i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.3961 | − | 4.27330i | −1.54342 | − | 0.458146i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.2179 | 1.49044 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.367832 | + | 0.348659i | −0.0381424 | + | 0.0361542i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.146305 | − | 0.253408i | −0.0150106 | − | 0.0259991i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.83502 | − | 3.17835i | 0.186318 | − | 0.322713i | −0.757702 | − | 0.652601i | \(-0.773678\pi\) |
0.944020 | + | 0.329888i | \(0.107011\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.273937 | − | 5.11484i | 0.0275317 | − | 0.514061i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.164979 | + | 0.285751i | −0.0164160 | + | 0.0284333i | −0.874117 | − | 0.485716i | \(-0.838559\pi\) |
0.857701 | + | 0.514149i | \(0.171892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.56108 | − | 2.70388i | −0.153818 | − | 0.266421i | 0.778810 | − | 0.627260i | \(-0.215824\pi\) |
−0.932628 | + | 0.360839i | \(0.882490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.54695 | − | 6.45981i | −0.150967 | − | 0.630413i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.9198 | 1.44236 | 0.721178 | − | 0.692750i | \(-0.243601\pi\) | ||||
0.721178 | + | 0.692750i | \(0.243601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.70739 | 0.642451 | 0.321226 | − | 0.947003i | \(-0.395905\pi\) | ||||
0.321226 | + | 0.947003i | \(0.395905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.82542 | + | 20.1502i | 0.458009 | + | 1.91257i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.83502 | − | 4.91040i | −0.266696 | − | 0.461932i | 0.701310 | − | 0.712856i | \(-0.252599\pi\) |
−0.968007 | + | 0.250924i | \(0.919265\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.91751 | − | 5.05328i | 0.272059 | − | 0.471220i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.32088 | + | 6.06826i | 0.861716 | + | 0.561010i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.27394 | + | 5.67063i | −0.300121 | + | 0.519825i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.04241 | + | 7.00166i | 0.367492 | + | 0.636515i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.75253 | + | 8.29631i | −0.789189 | + | 0.748053i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.54241 | 0.491809 | 0.245905 | − | 0.969294i | \(-0.420915\pi\) | ||||
0.245905 | + | 0.969294i | \(0.420915\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.15591 | + | 1.82730i | 0.541997 | + | 0.160885i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.41478 | + | 11.1107i | 0.560462 | + | 0.970748i | 0.997456 | + | 0.0712840i | \(0.0227097\pi\) |
−0.436994 | + | 0.899464i | \(0.643957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.561084 | − | 0.971826i | 0.0486522 | − | 0.0842680i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.74293 | − | 4.89512i | 0.150008 | − | 0.421305i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.54241 | + | 7.86769i | −0.388084 | + | 0.672182i | −0.992192 | − | 0.124721i | \(-0.960196\pi\) |
0.604108 | + | 0.796903i | \(0.293530\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 3.46410i | −0.169638 | − | 0.293821i | 0.768655 | − | 0.639664i | \(-0.220926\pi\) |
−0.938293 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.10896 | + | 0.922854i | 0.261822 | + | 0.0777184i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.32996 | 0.529338 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.67004 | −0.720008 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.68872 | − | 9.18370i | 0.799112 | − | 0.757459i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.06108 | + | 7.03400i | 0.332697 | + | 0.576248i | 0.983040 | − | 0.183393i | \(-0.0587080\pi\) |
−0.650343 | + | 0.759641i | \(0.725375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5237 | − | 18.2276i | 0.856410 | − | 1.48334i | −0.0189215 | − | 0.999821i | \(-0.506023\pi\) |
0.875331 | − | 0.483524i | \(-0.160643\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.56655 | + | 2.32018i | −0.369184 | + | 0.187576i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.146305 | + | 0.253408i | −0.0117515 | + | 0.0203542i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.127632 | + | 0.221065i | 0.0101861 | + | 0.0176429i | 0.871074 | − | 0.491153i | \(-0.163424\pi\) |
−0.860887 | + | 0.508796i | \(0.830091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.70739 | − | 19.6573i | −0.373320 | − | 1.55893i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.3774 | 1.76359 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7074 | 0.916994 | 0.458497 | − | 0.888696i | \(-0.348388\pi\) | ||||
0.458497 | + | 0.888696i | \(0.348388\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.688716 | − | 2.87597i | −0.0536165 | − | 0.223894i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.06382 | + | 13.9669i | 0.623997 | + | 1.08079i | 0.988734 | + | 0.149684i | \(0.0478255\pi\) |
−0.364737 | + | 0.931111i | \(0.618841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.372368 | + | 0.644960i | −0.0286437 | + | 0.0496123i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.782610 | − | 0.397630i | 0.0598477 | − | 0.0304076i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.29261 | − | 7.43502i | 0.326361 | − | 0.565274i | −0.655426 | − | 0.755260i | \(-0.727511\pi\) |
0.981787 | + | 0.189986i | \(0.0608441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.91751 | − | 3.32123i | −0.144950 | − | 0.251061i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.6700 | + | 13.9054i | −1.10267 | + | 1.04519i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.37743 | 0.551415 | 0.275708 | − | 0.961242i | \(-0.411088\pi\) | ||||
0.275708 | + | 0.961242i | \(0.411088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4996 | 1.30074 | 0.650368 | − | 0.759620i | \(-0.274615\pi\) | ||||
0.650368 | + | 0.759620i | \(0.274615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.8446 | − | 7.37481i | −1.83657 | − | 0.545161i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.98133 | + | 10.3600i | 0.439756 | + | 0.761680i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.45759 | + | 2.52462i | −0.106589 | + | 0.184618i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.5999 | − | 3.59777i | 1.42568 | − | 0.261700i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.27394 | − | 5.67063i | 0.236894 | − | 0.410312i | −0.722928 | − | 0.690924i | \(-0.757204\pi\) |
0.959821 | + | 0.280612i | \(0.0905373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.56108 | − | 6.16798i | −0.256332 | − | 0.443981i | 0.708924 | − | 0.705285i | \(-0.249181\pi\) |
−0.965257 | + | 0.261304i | \(0.915848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.15591 | + | 1.82730i | 0.440834 | + | 0.130856i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.6700 | −1.25894 | −0.629469 | − | 0.777025i | \(-0.716728\pi\) | ||||
−0.629469 | + | 0.777025i | \(0.716728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6327 | −0.824620 | −0.412310 | − | 0.911044i | \(-0.635278\pi\) | ||||
−0.412310 | + | 0.911044i | \(0.635278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9955 | + | 11.3702i | −0.846095 | + | 0.801993i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.6249 | − | 28.7952i | −1.16684 | − | 2.02102i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.48133 | + | 6.02983i | −0.243146 | + | 0.421142i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.6700 | + | 9.55077i | 1.01964 | + | 0.663824i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.249800 | − | 0.432667i | 0.0172790 | − | 0.0299282i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.81635 | + | 4.87806i | 0.193885 | + | 0.335819i | 0.946535 | − | 0.322602i | \(-0.104558\pi\) |
−0.752649 | + | 0.658422i | \(0.771224\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.43892 | − | 26.8879i | −0.441187 | − | 1.84233i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.70739 | 0.252842 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.12217 | −0.0761777 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.22699 | + | 13.4754i | 0.218060 | + | 0.910583i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.16498 | − | 5.48190i | −0.212899 | − | 0.368753i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.06382 | + | 7.03874i | −0.272133 | + | 0.471349i | −0.969408 | − | 0.245455i | \(-0.921062\pi\) |
0.697275 | + | 0.716804i | \(0.254396\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.160442 | − | 2.99571i | 0.0106961 | − | 0.199714i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.98133 | − | 8.62791i | 0.330622 | − | 0.572655i | −0.652012 | − | 0.758209i | \(-0.726075\pi\) |
0.982634 | + | 0.185554i | \(0.0594081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.627632 | − | 1.08709i | −0.0414751 | − | 0.0718370i | 0.844543 | − | 0.535488i | \(-0.179872\pi\) |
−0.886018 | + | 0.463651i | \(0.846539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.23113 | − | 7.80209i | 0.541568 | − | 0.513340i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.96265 | 0.259602 | 0.129801 | − | 0.991540i | \(-0.458566\pi\) | ||||
0.129801 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.87237 | 0.122140 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.32088 | + | 0.985762i | 0.215715 | + | 0.0640321i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.83502 | − | 4.91040i | −0.183382 | − | 0.317627i | 0.759648 | − | 0.650335i | \(-0.225371\pi\) |
−0.943030 | + | 0.332707i | \(0.892038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.31635 | − | 14.4043i | 0.535703 | − | 0.927865i | −0.463426 | − | 0.886136i | \(-0.653380\pi\) |
0.999129 | − | 0.0417293i | \(-0.0132867\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3847 | + | 6.00670i | 0.922779 | + | 0.385330i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.85369 | − | 6.67479i | 0.246204 | − | 0.426437i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.542411 | + | 0.939483i | 0.0345128 | + | 0.0597779i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.6514 | − | 5.83326i | −1.24535 | − | 0.369668i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3774 | −0.844376 | −0.422188 | − | 0.906508i | \(-0.638738\pi\) | ||||
−0.422188 | + | 0.906508i | \(0.638738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.96265 | 0.626347 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.14631 | + | 2.03443i | −0.134407 | + | 0.127401i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.414779 | − | 0.718418i | −0.0258732 | − | 0.0448137i | 0.852799 | − | 0.522239i | \(-0.174903\pi\) |
−0.878672 | + | 0.477426i | \(0.841570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.9385 | + | 39.7307i | −1.42533 | + | 2.46874i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.39104 | − | 25.9729i | 0.0861033 | − | 1.60768i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.10896 | − | 10.5810i | 0.376695 | − | 0.652454i | −0.613885 | − | 0.789396i | \(-0.710394\pi\) |
0.990579 | + | 0.136942i | \(0.0437273\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.83502 | − | 10.1066i | −0.358443 | − | 0.620841i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.21012 | − | 5.05328i | −0.0740582 | − | 0.309256i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.5369 | 1.06925 | 0.534623 | − | 0.845091i | \(-0.320454\pi\) | ||||
0.534623 | + | 0.845091i | \(0.320454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1222 | 0.918606 | 0.459303 | − | 0.888280i | \(-0.348099\pi\) | ||||
0.459303 | + | 0.888280i | \(0.348099\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.73514 | + | 23.9490i | 0.347106 | + | 1.44946i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.853695 | − | 1.47864i | −0.0514797 | − | 0.0891655i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.85369 | − | 4.94274i | 0.171462 | − | 0.296981i | −0.767469 | − | 0.641086i | \(-0.778484\pi\) |
0.938931 | + | 0.344105i | \(0.111818\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.735663 | − | 0.478945i | −0.0440430 | − | 0.0286737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.64631 | + | 6.31559i | −0.217520 | + | 0.376756i | −0.954049 | − | 0.299650i | \(-0.903130\pi\) |
0.736529 | + | 0.676406i | \(0.236464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.08249 | − | 8.80313i | −0.302123 | − | 0.523292i | 0.674494 | − | 0.738280i | \(-0.264362\pi\) |
−0.976617 | + | 0.214989i | \(0.931029\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.367832 | − | 0.348659i | 0.0217885 | − | 0.0206528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.7019 | −1.57616 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0848 | −0.828519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.09389 | + | 1.80889i | 0.357230 | + | 0.106039i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.52374 | − | 11.2994i | −0.381121 | − | 0.660121i | 0.610102 | − | 0.792323i | \(-0.291128\pi\) |
−0.991223 | + | 0.132202i | \(0.957795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.83502 | + | 10.1066i | −0.339728 | + | 0.588426i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.72606 | − | 1.60176i | 0.506338 | − | 0.0929438i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.8163 | + | 18.7345i | −0.625526 | + | 1.08344i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.10896 | + | 12.3131i | 0.409754 | + | 0.709714i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.547875 | − | 0.162630i | −0.0314746 | − | 0.00934282i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.9627 | −0.856759 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.50506 | −0.0858986 | −0.0429493 | − | 0.999077i | \(-0.513675\pi\) | ||||
−0.0429493 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.92478 | − | 3.72020i | 0.223273 | − | 0.211635i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.72606 | − | 4.72168i | −0.154581 | − | 0.267742i | 0.778325 | − | 0.627861i | \(-0.216069\pi\) |
−0.932906 | + | 0.360119i | \(0.882736\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.27394 | − | 9.13473i | 0.298101 | − | 0.516325i | −0.677601 | − | 0.735430i | \(-0.736980\pi\) |
0.975701 | + | 0.219105i | \(0.0703136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.2571 | − | 5.21143i | 0.577920 | − | 0.293631i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6887 | + | 21.9775i | −0.712669 | + | 1.23438i | 0.251182 | + | 0.967940i | \(0.419181\pi\) |
−0.963852 | + | 0.266440i | \(0.914153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.40157 | − | 12.8199i | −0.414408 | − | 0.717776i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.01827 | + | 25.1314i | 0.335907 | + | 1.40270i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.499600 | −0.0277985 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.70739 | 0.205649 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.70559 | + | 11.2981i | 0.149619 | + | 0.624786i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.59029 | + | 6.21856i | 0.197939 | + | 0.342840i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5424 | + | 26.9202i | −0.854288 | + | 1.47967i | 0.0230157 | + | 0.999735i | \(0.492673\pi\) |
−0.877304 | + | 0.479935i | \(0.840660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −31.9951 | + | 16.2561i | −1.75332 | + | 0.890830i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.77121 | + | 8.26397i | −0.260679 | + | 0.451509i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.12763 | − | 8.88132i | −0.279320 | − | 0.483796i | 0.691896 | − | 0.721997i | \(-0.256776\pi\) |
−0.971216 | + | 0.238201i | \(0.923442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.12763 | − | 6.75611i | 0.387120 | − | 0.366942i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.499600 | −0.0270549 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.71285 | 0.146480 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.68872 | + | 2.87597i | 0.521623 | + | 0.154837i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.52374 | − | 6.10329i | −0.189164 | − | 0.327642i | 0.755808 | − | 0.654794i | \(-0.227244\pi\) |
−0.944972 | + | 0.327152i | \(0.893911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5848 | + | 25.2617i | −0.780708 | + | 1.35223i | 0.150822 | + | 0.988561i | \(0.451808\pi\) |
−0.931530 | + | 0.363664i | \(0.881526\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.46173 | + | 18.1481i | −0.344901 | + | 0.968675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.98133 | − | 13.8241i | −0.423605 | − | 0.733705i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.8724 | − | 3.22732i | −0.575427 | − | 0.170808i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7922 | 1.51959 | 0.759797 | − | 0.650160i | \(-0.225298\pi\) | ||||
0.759797 | + | 0.650160i | \(0.225298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9144 | −0.995494 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.1632 | + | 9.63343i | −0.533428 | + | 0.505624i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | + | 6.92820i | 0.209370 | + | 0.362639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.52374 | + | 9.56739i | −0.288337 | + | 0.499414i | −0.973413 | − | 0.229058i | \(-0.926436\pi\) |
0.685076 | + | 0.728471i | \(0.259769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.5051 | − | 11.3965i | −0.911277 | − | 0.593277i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.3774 | − | 38.7588i | 1.16178 | − | 2.01226i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.83502 | + | 13.5707i | 0.405682 | + | 0.702662i | 0.994401 | − | 0.105676i | \(-0.0337007\pi\) |
−0.588719 | + | 0.808338i | \(0.700367\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.403374 | − | 1.68443i | −0.0208301 | − | 0.0869834i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.1432 | 1.65546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.58522 | 0.338260 | 0.169130 | − | 0.985594i | \(-0.445904\pi\) | ||||
0.169130 | + | 0.985594i | \(0.445904\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.23566 | + | 9.33578i | 0.114536 | + | 0.478286i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.10896 | − | 10.5810i | −0.312153 | − | 0.540665i | 0.666675 | − | 0.745348i | \(-0.267717\pi\) |
−0.978828 | + | 0.204683i | \(0.934384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.27394 | − | 5.67063i | 0.166855 | − | 0.289002i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.594822 | + | 11.1063i | −0.0302365 | + | 0.564562i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.8588 | + | 24.0041i | −0.702667 | + | 1.21705i | 0.264860 | + | 0.964287i | \(0.414674\pi\) |
−0.967527 | + | 0.252768i | \(0.918659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.98133 | − | 8.62791i | −0.251917 | − | 0.436332i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.1276 | + | 15.2870i | −0.813531 | + | 0.771127i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.5105 | −1.33053 | −0.665263 | − | 0.746609i | \(-0.731680\pi\) | ||||
−0.665263 | + | 0.746609i | \(0.731680\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.86330 | + | 0.553095i | 0.0932814 | + | 0.0276894i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.42024 | − | 14.5843i | −0.420487 | − | 0.728305i | 0.575500 | − | 0.817802i | \(-0.304807\pi\) |
−0.995987 | + | 0.0894970i | \(0.971474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.542411 | − | 0.939483i | 0.0270194 | − | 0.0467990i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.94852 | + | 0.961276i | 0.444655 | + | 0.0477662i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2125 | + | 17.6885i | −0.506213 | + | 0.876786i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.54787 | − | 13.0733i | −0.373218 | − | 0.646433i | 0.616840 | − | 0.787088i | \(-0.288412\pi\) |
−0.990059 | + | 0.140655i | \(0.955079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.0848 | − | 4.47773i | −0.744079 | − | 0.220870i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.7549 | −2.20224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.8350 | −0.580958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.02827 | − | 4.76618i | 0.246236 | − | 0.233401i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.18365 | − | 2.05015i | −0.0578252 | − | 0.100156i | 0.835664 | − | 0.549241i | \(-0.185083\pi\) |
−0.893489 | + | 0.449085i | \(0.851750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.96265 | + | 8.59557i | −0.241865 | + | 0.418922i | −0.961246 | − | 0.275694i | \(-0.911092\pi\) |
0.719381 | + | 0.694616i | \(0.244426\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.300407 | + | 5.60907i | −0.0146063 | + | 0.272722i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.853695 | + | 1.47864i | −0.0414103 | + | 0.0717247i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.6910 | − | 49.6944i | −1.38846 | − | 2.40488i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.55334 | + | 10.6623i | 0.123276 | + | 0.514783i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.9253 | 0.670758 | 0.335379 | − | 0.942083i | \(-0.391136\pi\) | ||||
0.335379 | + | 0.942083i | \(0.391136\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.29261 | −0.110176 | −0.0550879 | − | 0.998482i | \(-0.517544\pi\) | ||||
−0.0550879 | + | 0.998482i | \(0.517544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.49727 | − | 14.6040i | −0.167681 | − | 0.700210i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.853695 | + | 1.47864i | 0.0408378 | + | 0.0707331i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5051 | − | 21.6594i | 0.596834 | − | 1.03375i | −0.396451 | − | 0.918056i | \(-0.629758\pi\) |
0.993285 | − | 0.115691i | \(-0.0369083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3774 | + | 12.6155i | 0.922735 | + | 0.600736i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.93618 | + | 17.2100i | −0.472082 | + | 0.817671i | −0.999490 | − | 0.0319419i | \(-0.989831\pi\) |
0.527407 | + | 0.849613i | \(0.323164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.50000 | − | 2.59808i | −0.0711068 | − | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.2101 | + | 9.67793i | −0.482922 | + | 0.457750i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.2553 | 1.52222 | 0.761110 | − | 0.648623i | \(-0.224655\pi\) | ||||
0.761110 | + | 0.648623i | \(0.224655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.8880 | −0.559782 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 34.9481 | + | 10.3739i | 1.64201 | + | 0.487408i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.10896 | + | 12.3131i | 0.333273 | + | 0.577246i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.94398 | + | 17.2235i | −0.465160 | + | 0.805680i | −0.999209 | − | 0.0397732i | \(-0.987336\pi\) |
0.534049 | + | 0.845454i | \(0.320670\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.75020 | − | 6.75611i | −0.268396 | − | 0.315348i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8829 | − | 18.8497i | 0.506867 | − | 0.877919i | −0.493101 | − | 0.869972i | \(-0.664137\pi\) |
0.999968 | − | 0.00794757i | \(-0.00252982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.98133 | + | 15.5561i | 0.417398 | + | 0.722954i | 0.995677 | − | 0.0928850i | \(-0.0296089\pi\) |
−0.578279 | + | 0.815839i | \(0.696276\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.485863 | − | 0.144222i | −0.0225314 | − | 0.00668814i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.0475 | −0.881412 | −0.440706 | − | 0.897651i | \(-0.645272\pi\) | ||||
−0.440706 | + | 0.897651i | \(0.645272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.5953 | −1.68982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.320884 | + | 0.304159i | −0.0147856 | + | 0.0140149i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.16498 | + | 5.48190i | 0.145526 | + | 0.252058i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.146305 | − | 0.253408i | 0.00671295 | − | 0.0116272i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.2125 | − | 15.8585i | 1.42912 | − | 0.726111i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3774 | − | 17.9742i | 0.474157 | − | 0.821264i | −0.525405 | − | 0.850852i | \(-0.676086\pi\) |
0.999562 | + | 0.0295882i | \(0.00941958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.1751 | − | 38.4084i | −1.01110 | − | 1.75127i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.02647 | + | 37.6931i | 0.410719 | + | 1.71510i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.67004 | 0.166648 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.86690 | −0.220540 | −0.110270 | − | 0.993902i | \(-0.535172\pi\) | ||||
−0.110270 | + | 0.993902i | \(0.535172\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.72245 | + | 19.7202i | 0.213557 | + | 0.891779i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.1276 | + | 33.1300i | 0.863218 | + | 1.49514i | 0.868806 | + | 0.495153i | \(0.164888\pi\) |
−0.00558786 | + | 0.999984i | \(0.501779\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.40157 | + | 12.8199i | −0.333350 | + | 0.577379i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.56655 | − | 2.32018i | 0.205251 | − | 0.104284i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.6086 | − | 53.0156i | 1.37298 | − | 2.37807i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4202 | − | 23.2445i | −0.600773 | − | 1.04057i | −0.992704 | − | 0.120574i | \(-0.961526\pi\) |
0.391932 | − | 0.919994i | \(-0.371807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.2735 | + | 19.2168i | −0.905755 | + | 0.858543i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.8825 | 0.841929 | 0.420964 | − | 0.907077i | \(-0.361692\pi\) | ||||
0.420964 | + | 0.907077i | \(0.361692\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.329957 | −0.0146829 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.23659 | − | 0.367066i | −0.0549189 | − | 0.0163020i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.5848 | − | 28.7258i | −0.735109 | − | 1.27325i | −0.954675 | − | 0.297649i | \(-0.903797\pi\) |
0.219566 | − | 0.975598i | \(-0.429536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.3401 | + | 26.5698i | −0.678605 | + | 1.17538i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.985463 | + | 1.15786i | 0.0435093 | + | 0.0511206i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.56108 | − | 2.70388i | 0.0687896 | − | 0.119147i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.59843 | + | 2.76856i | 0.0702989 | + | 0.121761i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.2553 | + | 4.23149i | 0.625737 | + | 0.185742i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.0101 | −1.66525 | −0.832627 | − | 0.553834i | \(-0.813164\pi\) | ||||
−0.832627 | + | 0.553834i | \(0.813164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.4677 | 1.63835 | 0.819174 | − | 0.573544i | \(-0.194432\pi\) | ||||
0.819174 | + | 0.573544i | \(0.194432\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.82088 | − | 4.56960i | 0.210401 | − | 0.199434i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.249800 | + | 0.432667i | 0.0108815 | + | 0.0188473i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.52374 | + | 9.56739i | −0.240163 | + | 0.415974i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.3401 | − | 19.1015i | −1.27325 | − | 0.828936i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.9066 | − | 22.3549i | 0.559048 | − | 0.968300i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.45992 | + | 12.9210i | 0.322521 | + | 0.558622i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.97586 | + | 12.4267i | 0.128418 | + | 0.536253i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1595 | 0.566820 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7549 | 1.36525 | 0.682624 | − | 0.730770i | \(-0.260839\pi\) | ||||
0.682624 | + | 0.730770i | \(0.260839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.05888 | + | 29.4768i | 0.302926 | + | 1.26497i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.35369 | + | 5.80877i | 0.143656 | + | 0.248820i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.75253 | − | 11.6957i | 0.288717 | − | 0.500073i | −0.684786 | − | 0.728744i | \(-0.740105\pi\) |
0.973504 | + | 0.228671i | \(0.0734379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.40064 | − | 44.8237i | 0.102457 | − | 1.91303i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.26847 | − | 2.19706i | 0.0540388 | − | 0.0935979i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.83502 | + | 6.64245i | 0.163082 | + | 0.282466i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.0379 | + | 14.2540i | −0.638322 | + | 0.605050i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | 0.254228 | 0.127114 | − | 0.991888i | \(-0.459429\pi\) | ||||
0.127114 | + | 0.991888i | \(0.459429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7447 | −0.581340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.84049 | − | 1.43684i | −0.204365 | − | 0.0606632i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6062 | − | 27.0308i | −0.657724 | − | 1.13921i | −0.981203 | − | 0.192976i | \(-0.938186\pi\) |
0.323479 | − | 0.946235i | \(-0.395147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.83502 | − | 4.91040i | 0.119270 | − | 0.206582i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.9663 | + | 31.5633i | 0.586528 | + | 1.32553i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.41478 | − | 11.1107i | 0.268922 | − | 0.465786i | −0.699662 | − | 0.714474i | \(-0.746666\pi\) |
0.968584 | + | 0.248688i | \(0.0799994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.67004 | − | 13.2849i | −0.320981 | − | 0.555956i | 0.659709 | − | 0.751521i | \(-0.270679\pi\) |
−0.980691 | + | 0.195565i | \(0.937346\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8724 | + | 3.22732i | 0.454200 | + | 0.134823i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.83502 | 0.243337 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.3292 | 1.38751 | 0.693755 | − | 0.720211i | \(-0.255955\pi\) | ||||
0.693755 | + | 0.720211i | \(0.255955\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.95305 | − | 8.48638i | 0.372076 | − | 0.352682i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.6938 | − | 39.3068i | −0.941497 | − | 1.63072i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.96265 | − | 17.2558i | 0.412611 | − | 0.714663i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.594822 | + | 11.1063i | −0.0245929 | + | 0.459187i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7525 | − | 35.9444i | 0.856549 | − | 1.48359i | −0.0186522 | − | 0.999826i | \(-0.505938\pi\) |
0.875201 | − | 0.483760i | \(-0.160729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0428105 | − | 0.0741499i | −0.00176398 | − | 0.00305530i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.12763 | − | 29.7639i | −0.293192 | − | 1.22432i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.0584 | 0.700505 | 0.350252 | − | 0.936655i | \(-0.386096\pi\) | ||||
0.350252 | + | 0.936655i | \(0.386096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.54787 | −0.268437 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.69232 | − | 19.5944i | −0.192044 | − | 0.801946i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.9627 | + | 22.4520i | 0.529640 | + | 0.917363i | 0.999402 | + | 0.0345700i | \(0.0110062\pi\) |
−0.469763 | + | 0.882793i | \(0.655660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.54787 | − | 9.60920i | 0.226303 | − | 0.391967i | −0.730407 | − | 0.683012i | \(-0.760670\pi\) |
0.956709 | + | 0.291045i | \(0.0940029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.9909 | − | 15.6190i | −0.976986 | − | 0.636056i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.04241 | + | 7.00166i | −0.164347 | + | 0.284658i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1914 | + | 22.8483i | 0.535424 | + | 0.927382i | 0.999143 | + | 0.0413995i | \(0.0131816\pi\) |
−0.463718 | + | 0.885983i | \(0.653485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 41.7973 | − | 39.6186i | 1.69371 | − | 1.60543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.94160 | −0.280827 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.87783 | 0.116235 | 0.0581173 | − | 0.998310i | \(-0.481490\pi\) | ||||
0.0581173 | + | 0.998310i | \(0.481490\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.5611 | − | 3.43176i | −0.466188 | − | 0.138382i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.42024 | + | 9.38814i | 0.218211 | + | 0.377952i | 0.954261 | − | 0.298975i | \(-0.0966446\pi\) |
−0.736050 | + | 0.676927i | \(0.763311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.43892 | − | 7.68843i | 0.178415 | − | 0.309024i | −0.762923 | − | 0.646490i | \(-0.776236\pi\) |
0.941338 | + | 0.337466i | \(0.109570\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.1700 | + | 28.5631i | −0.408110 | + | 1.14620i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.75253 | − | 9.96368i | 0.230470 | − | 0.399186i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.829557 | + | 0.246243i | 0.0331293 | + | 0.00983401i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.4249 | 0.814394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.3300 | −0.570467 | −0.285233 | − | 0.958458i | \(-0.592071\pi\) | ||||
−0.285233 | + | 0.958458i | \(0.592071\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.08068 | + | 6.71161i | −0.281432 | + | 0.266763i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.77121 | + | 4.79987i | 0.109972 | + | 0.190477i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.2871 | + | 24.7461i | −0.566077 | + | 0.980475i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 42.6934 | − | 21.6917i | 1.68892 | − | 0.858112i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.0237 | + | 39.8783i | −0.909383 | + | 1.57510i | −0.0944596 | + | 0.995529i | \(0.530112\pi\) |
−0.814923 | + | 0.579569i | \(0.803221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.77121 | + | 3.06782i | 0.0698495 | + | 0.120983i | 0.898835 | − | 0.438287i | \(-0.144415\pi\) |
−0.828985 | + | 0.559270i | \(0.811081\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.49546 | + | 6.24482i | 0.0588838 | + | 0.245890i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.1276 | −0.634043 | −0.317021 | − | 0.948418i | \(-0.602683\pi\) | ||||
−0.317021 | + | 0.948418i | \(0.602683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.9253 | −0.782137 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.452653 | − | 1.89021i | −0.0177409 | − | 0.0740831i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.7735 | + | 22.1244i | 0.499867 | + | 0.865795i | 1.00000 | 0.000153387i | \(-4.88247e-5\pi\) | |
−0.500133 | + | 0.865949i | \(0.666715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.41478 | + | 11.1107i | −0.250646 | + | 0.434132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.3966 | + | 10.8713i | −0.834762 | + | 0.424128i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2498 | + | 31.6096i | −0.710911 | + | 1.23133i | 0.253604 | + | 0.967308i | \(0.418384\pi\) |
−0.964515 | + | 0.264026i | \(0.914949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.84049 | + | 6.65192i | 0.149378 | + | 0.258730i | 0.930998 | − | 0.365025i | \(-0.118940\pi\) |
−0.781620 | + | 0.623755i | \(0.785606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.95719 | − | 7.54243i | 0.309032 | − | 0.292924i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.12217 | 0.0435158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.5899 | 1.95885 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.4955 | − | 4.00595i | −0.521765 | − | 0.154879i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.7735 | − | 22.1244i | −0.493117 | − | 0.854104i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.01867 | + | 8.69260i | −0.193456 | + | 0.335075i | −0.946393 | − | 0.323017i | \(-0.895303\pi\) |
0.752938 | + | 0.658092i | \(0.228636\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.11076 | − | 0.938136i | 0.196713 | − | 0.0361089i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.7261 | − | 25.5063i | 0.565969 | − | 0.980286i | −0.430990 | − | 0.902357i | \(-0.641836\pi\) |
0.996959 | − | 0.0779297i | \(-0.0248310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.03735 | + | 12.1890i | 0.270069 | + | 0.467772i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.5424 | + | 4.91040i | 0.633907 | + | 0.188167i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.2179 | 0.926673 | 0.463336 | − | 0.886182i | \(-0.346652\pi\) | ||||
0.463336 | + | 0.886182i | \(0.346652\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.08482 | −0.347113 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.57795 | − | 1.49570i | 0.0602027 | − | 0.0570646i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.6327 | + | 37.4689i | 0.824140 | + | 1.42745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.122168 | − | 0.211601i | 0.00464749 | − | 0.00804969i | −0.863692 | − | 0.504019i | \(-0.831854\pi\) |
0.868340 | + | 0.495970i | \(0.165187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.4623 | + | 10.7176i | 0.625349 | + | 0.407127i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | − | 3.46410i | 0.0758643 | − | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.94398 | + | 10.2953i | 0.225144 | + | 0.389961i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.59843 | + | 6.67479i | 0.0604582 | + | 0.252464i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.79221 | −0.294308 | −0.147154 | − | 0.989114i | \(-0.547011\pi\) | ||||
−0.147154 | + | 0.989114i | \(0.547011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.50040 | −0.132020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.755264 | + | 3.15386i | 0.0284449 | + | 0.118781i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.632696 | − | 1.09586i | −0.0237950 | − | 0.0412141i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4198 | − | 21.5118i | 0.466437 | − | 0.807893i | −0.532828 | − | 0.846223i | \(-0.678871\pi\) |
0.999265 | + | 0.0383309i | \(0.0122041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.320884 | + | 5.99141i | −0.0120341 | + | 0.224696i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.853695 | − | 1.47864i | 0.0319711 | − | 0.0553756i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.16498 | + | 5.48190i | 0.118363 | + | 0.205012i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.12763 | − | 6.75611i | 0.266186 | − | 0.252312i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.0101 | −1.30566 | −0.652829 | − | 0.757506i | \(-0.726418\pi\) | ||||
−0.652829 | + | 0.757506i | \(0.726418\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.9736 | 0.445919 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.6176 | + | 8.19794i | 1.02711 | + | 0.304885i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.33502 | − | 7.50848i | −0.160999 | − | 0.278858i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.1541 | − | 19.3195i | 0.413683 | − | 0.716520i | −0.581606 | − | 0.813470i | \(-0.697576\pi\) |
0.995289 | + | 0.0969508i | \(0.0309089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.31542 | + | 26.6529i | −0.159830 | + | 0.987144i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.16498 | − | 5.48190i | 0.117061 | − | 0.202756i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.08482 | + | 14.0033i | 0.298620 | + | 0.517224i | 0.975820 | − | 0.218574i | \(-0.0701405\pi\) |
−0.677201 | + | 0.735798i | \(0.736807\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.7977 | + | 3.79882i | 0.472049 | + | 0.140122i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.2926 | −0.600146 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.9354 | −1.43226 | −0.716132 | − | 0.697965i | \(-0.754089\pi\) | ||||
−0.716132 | + | 0.697965i | \(0.754089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.36369 | + | 1.29261i | −0.0500966 | + | 0.0474853i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.66771 | − | 4.62061i | −0.0978688 | − | 0.169514i | 0.812933 | − | 0.582357i | \(-0.197869\pi\) |
−0.910802 | + | 0.412843i | \(0.864536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.06108 | + | 7.03400i | −0.148787 | + | 0.257706i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.89884 | − | 35.4543i | 0.0694748 | − | 1.29720i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.6090 | + | 49.5522i | −1.04535 | + | 1.81060i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.1035 | + | 29.6241i | 0.624115 | + | 1.08100i | 0.988711 | + | 0.149834i | \(0.0478738\pi\) |
−0.364596 | + | 0.931166i | \(0.618793\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.39611 | − | 22.5333i | −0.196645 | − | 0.821159i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.0475 | 0.765996 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.952525 | 0.0346201 | 0.0173101 | − | 0.999850i | \(-0.494490\pi\) | ||||
0.0173101 | + | 0.999850i | \(0.494490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.01867 | + | 16.7813i | 0.145869 | + | 0.609124i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.29767 | − | 14.3720i | −0.300790 | − | 0.520984i | 0.675525 | − | 0.737337i | \(-0.263917\pi\) |
−0.976315 | + | 0.216353i | \(0.930584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8615 | + | 22.2768i | −0.465617 | + | 0.806473i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.29261 | − | 2.79466i | −0.155200 | − | 0.101041i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.6327 | − | 37.4689i | 0.781111 | − | 1.35292i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.29767 | − | 5.71174i | −0.118917 | − | 0.205971i | 0.800422 | − | 0.599437i | \(-0.204609\pi\) |
−0.919339 | + | 0.393467i | \(0.871276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.04281 | − | 0.988455i | 0.0375559 | − | 0.0355983i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8296 | 0.677252 | 0.338626 | − | 0.940921i | \(-0.390038\pi\) | ||||
0.338626 | + | 0.940921i | \(0.390038\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.292611 | −0.0105109 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −76.1762 | − | 22.6119i | −2.73280 | − | 0.811198i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.01867 | − | 1.76439i | −0.0364978 | − | 0.0632160i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6272 | − | 23.6031i | 0.487621 | − | 0.844584i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.3105 | − | 8.13368i | 1.58353 | − | 0.290674i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.127632 | + | 0.221065i | −0.00455538 | + | 0.00789016i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.56108 | + | 6.16798i | 0.126939 | + | 0.219865i | 0.922489 | − | 0.386023i | \(-0.126151\pi\) |
−0.795550 | + | 0.605888i | \(0.792818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.2871 | + | 6.02198i | 0.722242 | + | 0.214388i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.7447 | 0.773154 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.4724 | 1.96988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.6700 | − | 13.9054i | 0.520293 | − | 0.493173i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.3588 | + | 42.1906i | 0.862832 | + | 1.49447i | 0.869184 | + | 0.494488i | \(0.164644\pi\) |
−0.00635283 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.59843 | − | 2.76856i | 0.0565484 | − | 0.0979447i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.02374 | − | 4.07672i | 0.283505 | − | 0.144044i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.82956 | + | 11.8291i | −0.241010 | + | 0.417441i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.1887 | + | 19.3794i | 0.394350 | + | 0.683035i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.07394 | + | 29.5397i | 0.249015 | + | 1.03985i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.1595 | 0.673613 | 0.336806 | − | 0.941574i | \(-0.390653\pi\) | ||||
0.336806 | + | 0.941574i | \(0.390653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3401 | −0.468434 | −0.234217 | − | 0.972184i | \(-0.575253\pi\) | ||||
−0.234217 | + | 0.972184i | \(0.575253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.09989 | + | 25.4722i | 0.213932 | + | 0.893348i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.85369 | + | 10.1389i | 0.205046 | + | 0.355150i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.542411 | + | 0.939483i | −0.0189766 | + | 0.0328684i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.0269 | + | 19.3208i | −1.32877 | + | 0.675124i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.811284 | − | 1.40518i | 0.0283140 | − | 0.0490413i | −0.851521 | − | 0.524320i | \(-0.824320\pi\) |
0.879835 | + | 0.475279i | \(0.157653\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.0265 | + | 22.5625i | 0.454074 | + | 0.786480i | 0.998634 | − | 0.0522422i | \(-0.0166368\pi\) |
−0.544560 | + | 0.838722i | \(0.683303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.14631 | − | 2.03443i | 0.0747248 | − | 0.0708298i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.4786 | −1.30326 | −0.651630 | − | 0.758537i | \(-0.725915\pi\) | ||||
−0.651630 | + | 0.758537i | \(0.725915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9627 | 1.14484 | 0.572420 | − | 0.819960i | \(-0.306005\pi\) | ||||
0.572420 | + | 0.819960i | \(0.306005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.47679 | + | 2.81306i | 0.328746 | + | 0.0975841i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.57976 | − | 11.3965i | −0.227975 | − | 0.394864i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.06382 | + | 13.9669i | −0.279060 | + | 0.483346i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.510000 | − | 1.43236i | 0.0176282 | − | 0.0495097i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.43892 | + | 11.1525i | −0.222296 | + | 0.385028i | −0.955505 | − | 0.294976i | \(-0.904688\pi\) |
0.733209 | + | 0.680004i | \(0.238022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0848 | − | 39.9841i | −0.796028 | − | 1.37876i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1090 | − | 3.59439i | −0.417055 | − | 0.123797i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.744736 | −0.0256197 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.0055 | −1.06536 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.7781 | − | 12.1120i | 0.438542 | − | 0.415684i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.9012 | − | 60.4506i | −1.19640 | − | 2.07222i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0661 | − | 38.2197i | 0.755531 | − | 1.30862i | −0.189580 | − | 0.981865i | \(-0.560713\pi\) |
0.945110 | − | 0.326752i | \(-0.105954\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.735663 | + | 0.478945i | 0.0251592 | + | 0.0163796i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.81635 | − | 13.5383i | 0.267001 | − | 0.462460i | −0.701085 | − | 0.713078i | \(-0.747301\pi\) |
0.968086 | + | 0.250618i | \(0.0806338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.94398 | + | 6.83117i | 0.134567 | + | 0.233077i | 0.925432 | − | 0.378914i | \(-0.123702\pi\) |
−0.790865 | + | 0.611991i | \(0.790369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7709 | − | 44.9774i | −0.367070 | − | 1.53283i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.53148 | −0.324455 | −0.162228 | − | 0.986753i | \(-0.551868\pi\) | ||||
−0.162228 | + | 0.986753i | \(0.551868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.58522 | 0.291906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.68145 | − | 23.7248i | −0.192952 | − | 0.805738i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.70739 | + | 2.95729i | 0.0579192 | + | 0.100319i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.6887 | − | 30.6378i | 0.599359 | − | 1.03812i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.588830 | + | 10.9944i | −0.0199289 | + | 0.372103i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.91751 | − | 3.32123i | 0.0648237 | − | 0.112278i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.9759 | − | 32.8672i | −0.640769 | − | 1.10985i | −0.985261 | − | 0.171056i | \(-0.945282\pi\) |
0.344492 | − | 0.938789i | \(-0.388051\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.4016 | − | 15.5467i | 0.553211 | − | 0.524376i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.2070 | 0.781863 | 0.390932 | − | 0.920420i | \(-0.372153\pi\) | ||||
0.390932 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.9572 | −1.04179 | −0.520896 | − | 0.853620i | \(-0.674402\pi\) | ||||
−0.520896 | + | 0.853620i | \(0.674402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.3774 | − | 5.75194i | −0.651365 | − | 0.193349i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.9385 | + | 32.8025i | 0.635893 | + | 1.10140i | 0.986325 | + | 0.164811i | \(0.0527014\pi\) |
−0.350432 | + | 0.936588i | \(0.613965\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.6276 | + | 18.4076i | −0.356439 | + | 0.617371i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.21792 | + | 14.0523i | 0.208308 | + | 0.470770i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.273937 | + | 0.474473i | −0.00916697 | + | 0.0158776i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.68872 | + | 6.38904i | 0.123300 | + | 0.213562i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35.9198 | − | 10.6623i | −1.19933 | − | 0.356005i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.53695 | −0.0846119 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.9253 | −0.663808 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.8729 | + | 16.9413i | −0.594773 | + | 0.563771i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.74980 | + | 15.1551i | 0.290853 | + | 0.503773i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.1914 | − | 28.0444i | 0.537628 | − | 0.931199i | −0.461403 | − | 0.887191i | \(-0.652654\pi\) |
0.999031 | − | 0.0440087i | \(-0.0140129\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0529391 | − | 0.988455i | 0.00175588 | − | 0.0327850i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6272 | + | 39.1915i | −0.749674 | + | 1.29847i | 0.198305 | + | 0.980140i | \(0.436456\pi\) |
−0.947979 | + | 0.318333i | \(0.896877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1035 | − | 17.4998i | −0.334377 | − | 0.579158i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.03554 | − | 25.2035i | −0.199529 | − | 0.833201i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.2016 | −1.62478 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.9253 | −0.723249 | −0.361625 | − | 0.932324i | \(-0.617778\pi\) | ||||
−0.361625 | + | 0.932324i | \(0.617778\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.607103 | − | 2.53517i | −0.0200047 | − | 0.0835367i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.5899 | + | 51.2512i | 0.973963 | + | 1.68695i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.98133 | + | 10.3600i | −0.196665 | + | 0.340633i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.84956 | + | 5.11037i | 0.257813 | + | 0.167846i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.63270 | − | 11.4882i | 0.217612 | − | 0.376915i | −0.736466 | − | 0.676475i | \(-0.763507\pi\) |
0.954077 | + | 0.299560i | \(0.0968400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.12763 | + | 1.95312i | 0.0369566 | + | 0.0640108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.85369 | − | 6.49645i | 0.224380 | − | 0.212684i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.91518 | −0.0953365 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.4996 | −1.32306 | −0.661532 | − | 0.749917i | \(-0.730093\pi\) | ||||
−0.661532 | + | 0.749917i | \(0.730093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.5141 | + | 5.19885i | 0.571552 | + | 0.169658i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.33502 | − | 2.31232i | −0.0435205 | − | 0.0753796i | 0.843445 | − | 0.537216i | \(-0.180524\pi\) |
−0.886965 | + | 0.461836i | \(0.847191\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.3136 | − | 35.1842i | 0.661502 | − | 1.14576i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.9157 | + | 15.1751i | 0.420148 | + | 0.493646i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.4412 | − | 31.9412i | 0.599260 | − | 1.03795i | −0.393670 | − | 0.919252i | \(-0.628795\pi\) |
0.992930 | − | 0.118697i | \(-0.0378718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.8296 | − | 25.6855i | −0.481388 | − | 0.833788i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.1378 | − | 12.5081i | −1.36641 | − | 0.405601i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.7175 | 0.411961 | 0.205980 | − | 0.978556i | \(-0.433962\pi\) | ||||
0.205980 | + | 0.978556i | \(0.433962\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.54787 | 0.211884 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.6086 | − | 17.6386i | 0.601529 | − | 0.570175i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.4202 | − | 30.1727i | −0.562529 | − | 0.974329i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4572 | − | 26.7726i | 0.498619 | − | 0.863633i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.9043 | + | 20.2747i | −1.28590 | + | 0.653342i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.56108 | − | 6.16798i | 0.114635 | − | 0.198554i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.1728 | + | 36.6723i | 0.680871 | + | 1.17930i | 0.974716 | + | 0.223449i | \(0.0717317\pi\) |
−0.293845 | + | 0.955853i | \(0.594935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.201526 | − | 0.841540i | −0.00647394 | − | 0.0270341i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.38836 | −0.172921 | −0.0864604 | − | 0.996255i | \(-0.527556\pi\) | ||||
−0.0864604 | + | 0.996255i | \(0.527556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3401 | 0.491781 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.49546 | + | 6.24482i | 0.0478932 | + | 0.199994i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.0661 | − | 24.3633i | −0.450016 | − | 0.779450i | 0.548370 | − | 0.836236i | \(-0.315248\pi\) |
−0.998386 | + | 0.0567850i | \(0.981915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.56108 | − | 4.43593i | 0.0818526 | − | 0.141773i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.9394 | + | 9.11471i | −0.572762 | + | 0.291010i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.8802 | + | 22.3091i | −0.410813 | + | 0.711550i | −0.994979 | − | 0.100085i | \(-0.968089\pi\) |
0.584165 | + | 0.811635i | \(0.301422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.83502 | − | 15.3027i | −0.281507 | − | 0.487585i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.02647 | + | 8.55597i | −0.287316 | + | 0.272340i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.6327 | −0.687880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.0848 | −0.733314 | −0.366657 | − | 0.930356i | \(-0.619498\pi\) | ||||
−0.366657 | + | 0.930356i | \(0.619498\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −51.6146 | − | 15.3211i | −1.63794 | − | 0.486201i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.81635 | − | 10.0742i | −0.184391 | − | 0.319374i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.4202 | − | 28.4407i | 0.520034 | − | 0.900726i | −0.479694 | − | 0.877436i | \(-0.659252\pi\) |
0.999729 | − | 0.0232902i | \(-0.00741418\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.2882 | − | 47.3360i | −1.27466 | − | 1.49765i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))