Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,3,Mod(271,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.271");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.o (of order \(6\), 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: | \(35.3134422611\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.703 |
Dual form | 1296.3.o.p.271.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | + | 5.19615i | 0.600000 | + | 1.03923i | 0.992820 | + | 0.119615i | \(0.0381661\pi\) |
−0.392820 | + | 0.919615i | \(0.628501\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | + | 3.46410i | 0.857143 | + | 0.494872i | 0.863054 | − | 0.505111i | \(-0.168548\pi\) |
−0.00591161 | + | 0.999983i | \(0.501882\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.0000 | + | 10.3923i | 1.63636 | + | 0.944755i | 0.982071 | + | 0.188514i | \(0.0603671\pi\) |
0.654293 | + | 0.756241i | \(0.272966\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.00000 | + | 12.1244i | 0.538462 | + | 0.932643i | 0.998987 | + | 0.0449963i | \(0.0143276\pi\) |
−0.460526 | + | 0.887646i | \(0.652339\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 0.352941 | 0.176471 | − | 0.984306i | \(-0.443532\pi\) | ||||
0.176471 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820i | 0.364642i | 0.983239 | + | 0.182321i | \(0.0583610\pi\) | ||||
−0.983239 | + | 0.182321i | \(0.941639\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.0000 | − | 25.9808i | 0.517241 | − | 0.895888i | −0.482558 | − | 0.875864i | \(-0.660292\pi\) |
0.999799 | − | 0.0200244i | \(-0.00637439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.0000 | + | 10.3923i | −0.580645 | + | 0.335236i | −0.761390 | − | 0.648294i | \(-0.775483\pi\) |
0.180745 | + | 0.983530i | \(0.442149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 41.5692i | 1.18769i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000 | 0.702703 | 0.351351 | − | 0.936244i | \(-0.385722\pi\) | ||||
0.351351 | + | 0.936244i | \(0.385722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −27.0000 | − | 46.7654i | −0.658537 | − | 1.14062i | −0.980995 | − | 0.194035i | \(-0.937842\pi\) |
0.322458 | − | 0.946584i | \(-0.395491\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18.0000 | − | 10.3923i | −0.418605 | − | 0.241682i | 0.275875 | − | 0.961193i | \(-0.411032\pi\) |
−0.694480 | + | 0.719512i | \(0.744366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −36.0000 | − | 20.7846i | −0.765957 | − | 0.442226i | 0.0654732 | − | 0.997854i | \(-0.479144\pi\) |
−0.831431 | + | 0.555629i | \(0.812478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0102041 | − | 0.0176740i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18.0000 | 0.339623 | 0.169811 | − | 0.985477i | \(-0.445684\pi\) | ||||
0.169811 | + | 0.985477i | \(0.445684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 124.708i | 2.26741i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18.0000 | − | 10.3923i | 0.305085 | − | 0.176141i | −0.339640 | − | 0.940555i | \(-0.610305\pi\) |
0.644725 | + | 0.764415i | \(0.276972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.0000 | − | 60.6218i | 0.573770 | − | 0.993800i | −0.422404 | − | 0.906408i | \(-0.638813\pi\) |
0.996174 | − | 0.0873918i | \(-0.0278532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −42.0000 | + | 72.7461i | −0.646154 | + | 1.11917i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −102.000 | + | 58.8897i | −1.52239 | + | 0.878951i | −0.522738 | + | 0.852493i | \(0.675089\pi\) |
−0.999650 | + | 0.0264578i | \(0.991577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 83.1384i | − | 1.17096i | −0.810685 | − | 0.585482i | \(-0.800905\pi\) | ||
0.810685 | − | 0.585482i | \(-0.199095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 82.0000 | 1.12329 | 0.561644 | − | 0.827379i | \(-0.310169\pi\) | ||||
0.561644 | + | 0.827379i | \(0.310169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 72.0000 | + | 124.708i | 0.935065 | + | 1.61958i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 66.0000 | + | 38.1051i | 0.835443 | + | 0.482343i | 0.855713 | − | 0.517451i | \(-0.173119\pi\) |
−0.0202696 | + | 0.999795i | \(0.506452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18.0000 | − | 10.3923i | −0.216867 | − | 0.125208i | 0.387631 | − | 0.921814i | \(-0.373293\pi\) |
−0.604499 | + | 0.796606i | \(0.706627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0000 | + | 31.1769i | 0.211765 | + | 0.366787i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −114.000 | −1.28090 | −0.640449 | − | 0.768000i | \(-0.721252\pi\) | ||||
−0.640449 | + | 0.768000i | \(0.721252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.9948i | 1.06588i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.0000 | + | 20.7846i | −0.378947 | + | 0.218785i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.0000 | + | 29.4449i | −0.175258 | + | 0.303555i | −0.940250 | − | 0.340484i | \(-0.889409\pi\) |
0.764993 | + | 0.644039i | \(0.222743\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | + | 15.5885i | −0.0891089 | + | 0.154341i | −0.907135 | − | 0.420840i | \(-0.861735\pi\) |
0.818026 | + | 0.575182i | \(0.195069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −114.000 | + | 65.8179i | −1.10680 | + | 0.639009i | −0.937998 | − | 0.346642i | \(-0.887322\pi\) |
−0.168798 | + | 0.985651i | \(0.553989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 145.492i | − | 1.35974i | −0.733332 | − | 0.679870i | \(-0.762036\pi\) | ||
0.733332 | − | 0.679870i | \(-0.237964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 34.0000 | 0.311927 | 0.155963 | − | 0.987763i | \(-0.450152\pi\) | ||||
0.155963 | + | 0.987763i | \(0.450152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −39.0000 | − | 67.5500i | −0.345133 | − | 0.597787i | 0.640245 | − | 0.768171i | \(-0.278833\pi\) |
−0.985378 | + | 0.170383i | \(0.945499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 36.0000 | + | 20.7846i | 0.302521 | + | 0.174661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 155.500 | + | 269.334i | 1.28512 | + | 2.22590i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 84.0000 | 0.672000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 103.923i | 0.818292i | 0.912469 | + | 0.409146i | \(0.134173\pi\) | ||||
−0.912469 | + | 0.409146i | \(0.865827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −90.0000 | + | 51.9615i | −0.687023 | + | 0.396653i | −0.802496 | − | 0.596658i | \(-0.796495\pi\) |
0.115473 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | + | 41.5692i | −0.180451 | + | 0.312551i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 93.0000 | − | 161.081i | 0.678832 | − | 1.17577i | −0.296501 | − | 0.955033i | \(-0.595820\pi\) |
0.975333 | − | 0.220739i | \(-0.0708469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −42.0000 | + | 24.2487i | −0.302158 | + | 0.174451i | −0.643412 | − | 0.765520i | \(-0.722482\pi\) |
0.341254 | + | 0.939971i | \(0.389148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 290.985i | 2.03486i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 180.000 | 1.24138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −93.0000 | − | 161.081i | −0.624161 | − | 1.08108i | −0.988702 | − | 0.149892i | \(-0.952108\pi\) |
0.364541 | − | 0.931187i | \(-0.381226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.0000 | + | 17.3205i | 0.198675 | + | 0.114705i | 0.596038 | − | 0.802957i | \(-0.296741\pi\) |
−0.397362 | + | 0.917662i | \(0.630074\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −108.000 | − | 62.3538i | −0.696774 | − | 0.402283i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −85.0000 | − | 147.224i | −0.541401 | − | 0.937735i | −0.998824 | − | 0.0484851i | \(-0.984561\pi\) |
0.457423 | − | 0.889249i | \(-0.348773\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 284.056i | 1.74268i | 0.490683 | + | 0.871338i | \(0.336747\pi\) | ||||
−0.490683 | + | 0.871338i | \(0.663253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 180.000 | − | 103.923i | 1.07784 | − | 0.622294i | 0.147530 | − | 0.989058i | \(-0.452868\pi\) |
0.930314 | + | 0.366764i | \(0.119534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.5000 | + | 23.3827i | −0.0798817 | + | 0.138359i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.0000 | + | 36.3731i | −0.121387 | + | 0.210249i | −0.920315 | − | 0.391178i | \(-0.872068\pi\) |
0.798928 | + | 0.601427i | \(0.205401\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −66.0000 | + | 38.1051i | −0.377143 | + | 0.217744i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 145.492i | 0.812806i | 0.913694 | + | 0.406403i | \(0.133217\pi\) | ||||
−0.913694 | + | 0.406403i | \(0.866783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 82.0000 | 0.453039 | 0.226519 | − | 0.974007i | \(-0.427265\pi\) | ||||
0.226519 | + | 0.974007i | \(0.427265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 78.0000 | + | 135.100i | 0.421622 | + | 0.730270i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 108.000 | + | 62.3538i | 0.577540 | + | 0.333443i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 288.000 | + | 166.277i | 1.50785 | + | 0.870560i | 0.999958 | + | 0.00914069i | \(0.00290961\pi\) |
0.507895 | + | 0.861419i | \(0.330424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 47.0000 | + | 81.4064i | 0.243523 | + | 0.421795i | 0.961715 | − | 0.274050i | \(-0.0883634\pi\) |
−0.718192 | + | 0.695845i | \(0.755030\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 258.000 | 1.30964 | 0.654822 | − | 0.755783i | \(-0.272743\pi\) | ||||
0.654822 | + | 0.755783i | \(0.272743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 117.779i | 0.591857i | 0.955210 | + | 0.295928i | \(0.0956289\pi\) | ||||
−0.955210 | + | 0.295928i | \(0.904371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 180.000 | − | 103.923i | 0.886700 | − | 0.511936i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 162.000 | − | 280.592i | 0.790244 | − | 1.36874i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −72.0000 | + | 124.708i | −0.344498 | + | 0.596687i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −78.0000 | + | 45.0333i | −0.369668 | + | 0.213428i | −0.673314 | − | 0.739357i | \(-0.735130\pi\) |
0.303645 | + | 0.952785i | \(0.401796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 124.708i | − | 0.580036i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −144.000 | −0.663594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.0000 | + | 72.7461i | 0.190045 | + | 0.329168i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −306.000 | − | 176.669i | −1.37220 | − | 0.792238i | −0.380993 | − | 0.924578i | \(-0.624418\pi\) |
−0.991204 | + | 0.132339i | \(0.957751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 126.000 | + | 72.7461i | 0.555066 | + | 0.320468i | 0.751163 | − | 0.660117i | \(-0.229493\pi\) |
−0.196097 | + | 0.980585i | \(0.562827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −113.000 | − | 195.722i | −0.493450 | − | 0.854680i | 0.506522 | − | 0.862227i | \(-0.330931\pi\) |
−0.999972 | + | 0.00754710i | \(0.997598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −114.000 | −0.489270 | −0.244635 | − | 0.969615i | \(-0.578668\pi\) | ||||
−0.244635 | + | 0.969615i | \(0.578668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 249.415i | − | 1.06134i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −288.000 | + | 166.277i | −1.20502 | + | 0.695719i | −0.961667 | − | 0.274219i | \(-0.911581\pi\) |
−0.243354 | + | 0.969938i | \(0.578248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −89.0000 | + | 154.153i | −0.369295 | + | 0.639637i | −0.989455 | − | 0.144838i | \(-0.953734\pi\) |
0.620161 | + | 0.784475i | \(0.287067\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | − | 5.19615i | 0.0122449 | − | 0.0212088i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −84.0000 | + | 48.4974i | −0.340081 | + | 0.196346i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 103.923i | − | 0.414036i | −0.978337 | − | 0.207018i | \(-0.933624\pi\) | ||
0.978337 | − | 0.207018i | \(-0.0663759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 129.000 | + | 223.435i | 0.501946 | + | 0.869395i | 0.999997 | + | 0.00224796i | \(0.000715548\pi\) |
−0.498052 | + | 0.867147i | \(0.665951\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 156.000 | + | 90.0666i | 0.602317 | + | 0.347748i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −324.000 | − | 187.061i | −1.23194 | − | 0.711260i | −0.264505 | − | 0.964384i | \(-0.585209\pi\) |
−0.967434 | + | 0.253124i | \(0.918542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 54.0000 | + | 93.5307i | 0.203774 | + | 0.352946i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −510.000 | −1.89591 | −0.947955 | − | 0.318403i | \(-0.896853\pi\) | ||||
−0.947955 | + | 0.318403i | \(0.896853\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 450.333i | − | 1.66175i | −0.556462 | − | 0.830873i | \(-0.687842\pi\) | ||
0.556462 | − | 0.830873i | \(-0.312158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −198.000 | + | 114.315i | −0.720000 | + | 0.415692i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | − | 12.1244i | 0.0252708 | − | 0.0437702i | −0.853113 | − | 0.521725i | \(-0.825289\pi\) |
0.878384 | + | 0.477955i | \(0.158622\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 177.000 | − | 306.573i | 0.629893 | − | 1.09101i | −0.357679 | − | 0.933844i | \(-0.616432\pi\) |
0.987573 | − | 0.157163i | \(-0.0502347\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 126.000 | − | 72.7461i | 0.445230 | − | 0.257053i | −0.260584 | − | 0.965451i | \(-0.583915\pi\) |
0.705813 | + | 0.708398i | \(0.250582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 374.123i | − | 1.30356i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −253.000 | −0.875433 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −249.000 | − | 431.281i | −0.849829 | − | 1.47195i | −0.881360 | − | 0.472445i | \(-0.843372\pi\) |
0.0315309 | − | 0.999503i | \(-0.489962\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 108.000 | + | 62.3538i | 0.366102 | + | 0.211369i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.0000 | − | 124.708i | −0.239203 | − | 0.414311i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 420.000 | 1.37705 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 187.061i | 0.609321i | 0.952461 | + | 0.304660i | \(0.0985430\pi\) | ||||
−0.952461 | + | 0.304660i | \(0.901457\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 36.0000 | − | 20.7846i | 0.115756 | − | 0.0668315i | −0.441004 | − | 0.897505i | \(-0.645378\pi\) |
0.556760 | + | 0.830673i | \(0.312044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −145.000 | + | 251.147i | −0.463259 | + | 0.802388i | −0.999121 | − | 0.0419176i | \(-0.986653\pi\) |
0.535862 | + | 0.844305i | \(0.319987\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −105.000 | + | 181.865i | −0.331230 | + | 0.573708i | −0.982753 | − | 0.184921i | \(-0.940797\pi\) |
0.651523 | + | 0.758629i | \(0.274130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 540.000 | − | 311.769i | 1.69279 | − | 0.977333i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.5692i | 0.128697i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −154.000 | −0.473846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −144.000 | − | 249.415i | −0.437690 | − | 0.758101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −174.000 | − | 100.459i | −0.525680 | − | 0.303501i | 0.213576 | − | 0.976927i | \(-0.431489\pi\) |
−0.739255 | + | 0.673425i | \(0.764822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −612.000 | − | 353.338i | −1.82687 | − | 1.05474i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 151.000 | + | 261.540i | 0.448071 | + | 0.776082i | 0.998260 | − | 0.0589579i | \(-0.0187778\pi\) |
−0.550189 | + | 0.835040i | \(0.685444\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −432.000 | −1.26686 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 346.410i | − | 1.00994i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 54.0000 | − | 31.1769i | 0.155620 | − | 0.0898470i | −0.420168 | − | 0.907446i | \(-0.638029\pi\) |
0.575788 | + | 0.817599i | \(0.304696\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 179.000 | − | 310.037i | 0.512894 | − | 0.888358i | −0.486994 | − | 0.873405i | \(-0.661907\pi\) |
0.999888 | − | 0.0149532i | \(-0.00475994\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −279.000 | + | 483.242i | −0.790368 | + | 1.36896i | 0.135371 | + | 0.990795i | \(0.456777\pi\) |
−0.925739 | + | 0.378163i | \(0.876556\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 432.000 | − | 249.415i | 1.21690 | − | 0.702578i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 83.1384i | 0.231583i | 0.993274 | + | 0.115792i | \(0.0369405\pi\) | ||||
−0.993274 | + | 0.115792i | \(0.963059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 313.000 | 0.867036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 246.000 | + | 426.084i | 0.673973 | + | 1.16735i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 186.000 | + | 107.387i | 0.506812 | + | 0.292608i | 0.731522 | − | 0.681818i | \(-0.238810\pi\) |
−0.224710 | + | 0.974426i | \(0.572144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 108.000 | + | 62.3538i | 0.291105 | + | 0.168070i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −277.000 | − | 479.778i | −0.742627 | − | 1.28627i | −0.951295 | − | 0.308282i | \(-0.900246\pi\) |
0.208668 | − | 0.977987i | \(-0.433087\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 420.000 | 1.11406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 533.472i | − | 1.40758i | −0.710410 | − | 0.703788i | \(-0.751490\pi\) | ||
0.710410 | − | 0.703788i | \(-0.248510\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 432.000 | − | 249.415i | 1.12794 | − | 0.651215i | 0.184522 | − | 0.982828i | \(-0.440926\pi\) |
0.943415 | + | 0.331613i | \(0.107593\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −432.000 | + | 748.246i | −1.12208 | + | 1.94350i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 99.0000 | − | 171.473i | 0.254499 | − | 0.440805i | −0.710261 | − | 0.703939i | \(-0.751423\pi\) |
0.964759 | + | 0.263134i | \(0.0847562\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 457.261i | 1.15762i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −646.000 | −1.62720 | −0.813602 | − | 0.581422i | \(-0.802496\pi\) | ||||
−0.813602 | + | 0.581422i | \(0.802496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 165.000 | + | 285.788i | 0.411471 | + | 0.712689i | 0.995051 | − | 0.0993667i | \(-0.0316817\pi\) |
−0.583580 | + | 0.812056i | \(0.698348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −252.000 | − | 145.492i | −0.625310 | − | 0.361023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 468.000 | + | 270.200i | 1.14988 | + | 0.663882i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −65.0000 | − | 112.583i | −0.158924 | − | 0.275265i | 0.775557 | − | 0.631278i | \(-0.217469\pi\) |
−0.934481 | + | 0.356013i | \(0.884136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 144.000 | 0.348668 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 124.708i | − | 0.300500i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 306.000 | − | 176.669i | 0.730310 | − | 0.421645i | −0.0882254 | − | 0.996101i | \(-0.528120\pi\) |
0.818536 | + | 0.574456i | \(0.194786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 199.000 | − | 344.678i | 0.472684 | − | 0.818713i | −0.526827 | − | 0.849972i | \(-0.676619\pi\) |
0.999511 | + | 0.0312596i | \(0.00995185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33.0000 | + | 57.1577i | −0.0776471 | + | 0.134489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 420.000 | − | 242.487i | 0.983607 | − | 0.567886i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 124.708i | 0.289345i | 0.989480 | + | 0.144672i | \(0.0462128\pi\) | ||||
−0.989480 | + | 0.144672i | \(0.953787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −142.000 | −0.327945 | −0.163972 | − | 0.986465i | \(-0.552431\pi\) | ||||
−0.163972 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −486.000 | − | 280.592i | −1.10706 | − | 0.639162i | −0.168995 | − | 0.985617i | \(-0.554052\pi\) |
−0.938067 | + | 0.346455i | \(0.887385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 378.000 | + | 218.238i | 0.853273 | + | 0.492637i | 0.861754 | − | 0.507327i | \(-0.169366\pi\) |
−0.00848075 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −342.000 | − | 592.361i | −0.768539 | − | 1.33115i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 198.000 | 0.440980 | 0.220490 | − | 0.975389i | \(-0.429234\pi\) | ||||
0.220490 | + | 0.975389i | \(0.429234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1122.37i | − | 2.48862i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −504.000 | + | 290.985i | −1.10769 | + | 0.639526i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 223.000 | − | 386.247i | 0.487965 | − | 0.845180i | −0.511939 | − | 0.859022i | \(-0.671073\pi\) |
0.999904 | + | 0.0138415i | \(0.00440603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 171.000 | − | 296.181i | 0.370933 | − | 0.642474i | −0.618777 | − | 0.785567i | \(-0.712371\pi\) |
0.989709 | + | 0.143093i | \(0.0457047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 138.000 | − | 79.6743i | 0.298056 | − | 0.172083i | −0.343513 | − | 0.939148i | \(-0.611617\pi\) |
0.641569 | + | 0.767065i | \(0.278284\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 394.908i | − | 0.845627i | −0.906217 | − | 0.422813i | \(-0.861043\pi\) | ||
0.906217 | − | 0.422813i | \(-0.138957\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −816.000 | −1.73987 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −216.000 | − | 374.123i | −0.456660 | − | 0.790958i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −66.0000 | − | 38.1051i | −0.138947 | − | 0.0802213i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 684.000 | + | 394.908i | 1.42797 | + | 0.824442i | 0.996961 | − | 0.0779035i | \(-0.0248226\pi\) |
0.431014 | + | 0.902345i | \(0.358156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 182.000 | + | 315.233i | 0.378378 | + | 0.655371i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −204.000 | −0.420619 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.92820i | − | 0.0142263i | −0.999975 | − | 0.00711315i | \(-0.997736\pi\) | ||
0.999975 | − | 0.00711315i | \(-0.00226420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −558.000 | + | 322.161i | −1.13646 | + | 0.656133i | −0.945551 | − | 0.325475i | \(-0.894476\pi\) |
−0.190906 | + | 0.981608i | \(0.561142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 90.0000 | − | 155.885i | 0.182556 | − | 0.316196i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 288.000 | − | 498.831i | 0.579477 | − | 1.00368i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −702.000 | + | 405.300i | −1.40681 | + | 0.812224i | −0.995079 | − | 0.0990798i | \(-0.968410\pi\) |
−0.411734 | + | 0.911304i | \(0.635077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 332.554i | 0.661141i | 0.943781 | + | 0.330570i | \(0.107241\pi\) | ||||
−0.943781 | + | 0.330570i | \(0.892759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −108.000 | −0.213861 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −153.000 | − | 265.004i | −0.300589 | − | 0.520636i | 0.675680 | − | 0.737195i | \(-0.263850\pi\) |
−0.976270 | + | 0.216559i | \(0.930517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 492.000 | + | 284.056i | 0.962818 | + | 0.555883i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −684.000 | − | 394.908i | −1.32816 | − | 0.766811i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −432.000 | − | 748.246i | −0.835590 | − | 1.44728i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −522.000 | −1.00192 | −0.500960 | − | 0.865471i | \(-0.667020\pi\) | ||||
−0.500960 | + | 0.865471i | \(0.667020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 48.4974i | 0.0927293i | 0.998925 | + | 0.0463646i | \(0.0147636\pi\) | ||||
−0.998925 | + | 0.0463646i | \(0.985236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −108.000 | + | 62.3538i | −0.204934 | + | 0.118318i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −264.500 | + | 458.127i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 378.000 | − | 654.715i | 0.709193 | − | 1.22836i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 756.000 | − | 436.477i | 1.41308 | − | 0.815844i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 20.7846i | − | 0.0385614i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 802.000 | 1.48244 | 0.741220 | − | 0.671262i | \(-0.234248\pi\) | ||||
0.741220 | + | 0.671262i | \(0.234248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 102.000 | + | 176.669i | 0.187156 | + | 0.324164i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0000 | − | 17.3205i | −0.0548446 | − | 0.0316645i | 0.472327 | − | 0.881423i | \(-0.343414\pi\) |
−0.527172 | + | 0.849759i | \(0.676747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 180.000 | + | 103.923i | 0.326679 | + | 0.188608i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 264.000 | + | 457.261i | 0.477396 | + | 0.826874i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 474.000 | 0.850987 | 0.425494 | − | 0.904961i | \(-0.360100\pi\) | ||||
0.425494 | + | 0.904961i | \(0.360100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 290.985i | − | 0.520545i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 594.000 | − | 342.946i | 1.05506 | − | 0.609140i | 0.131000 | − | 0.991382i | \(-0.458181\pi\) |
0.924062 | + | 0.382242i | \(0.124848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 234.000 | − | 405.300i | 0.414159 | − | 0.717345i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −75.0000 | + | 129.904i | −0.131810 | + | 0.228302i | −0.924374 | − | 0.381487i | \(-0.875412\pi\) |
0.792564 | + | 0.609788i | \(0.208746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 582.000 | − | 336.018i | 1.01926 | − | 0.588473i | 0.105374 | − | 0.994433i | \(-0.466396\pi\) |
0.913891 | + | 0.405960i | \(0.133063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.0000 | −0.0797227 | −0.0398614 | − | 0.999205i | \(-0.512692\pi\) | ||||
−0.0398614 | + | 0.999205i | \(0.512692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −72.0000 | − | 124.708i | −0.123924 | − | 0.214643i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 324.000 | + | 187.061i | 0.555746 | + | 0.320860i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −306.000 | − | 176.669i | −0.521295 | − | 0.300970i | 0.216170 | − | 0.976356i | \(-0.430644\pi\) |
−0.737464 | + | 0.675386i | \(0.763977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −72.0000 | − | 124.708i | −0.122241 | − | 0.211728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −114.000 | −0.192243 | −0.0961214 | − | 0.995370i | \(-0.530644\pi\) | ||||
−0.0961214 | + | 0.995370i | \(0.530644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 249.415i | 0.419185i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 216.000 | − | 124.708i | 0.360601 | − | 0.208193i | −0.308743 | − | 0.951145i | \(-0.599908\pi\) |
0.669344 | + | 0.742952i | \(0.266575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −313.000 | + | 542.132i | −0.520799 | + | 0.902050i | 0.478909 | + | 0.877865i | \(0.341032\pi\) |
−0.999707 | + | 0.0241851i | \(0.992301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −933.000 | + | 1616.00i | −1.54215 | + | 2.67108i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −582.000 | + | 336.018i | −0.958814 | + | 0.553571i | −0.895808 | − | 0.444442i | \(-0.853402\pi\) |
−0.0630061 | + | 0.998013i | \(0.520069\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 581.969i | − | 0.952486i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −694.000 | −1.13214 | −0.566069 | − | 0.824358i | \(-0.691536\pi\) | ||||
−0.566069 | + | 0.824358i | \(0.691536\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0000 | − | 25.9808i | −0.0243112 | − | 0.0421082i | 0.853614 | − | 0.520906i | \(-0.174406\pi\) |
−0.877925 | + | 0.478798i | \(0.841073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −294.000 | − | 169.741i | −0.474960 | − | 0.274218i | 0.243354 | − | 0.969938i | \(-0.421752\pi\) |
−0.718314 | + | 0.695719i | \(0.755086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −684.000 | − | 394.908i | −1.09791 | − | 0.633881i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 389.500 | + | 674.634i | 0.623200 | + | 1.07941i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 156.000 | 0.248013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 464.190i | 0.735641i | 0.929897 | + | 0.367821i | \(0.119896\pi\) | ||||
−0.929897 | + | 0.367821i | \(0.880104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −540.000 | + | 311.769i | −0.850394 | + | 0.490975i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000 | − | 12.1244i | 0.0109890 | − | 0.0190335i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −195.000 | + | 337.750i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931727\pi\) |
0.672873 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 702.000 | − | 405.300i | 1.09176 | − | 0.630326i | 0.157714 | − | 0.987485i | \(-0.449588\pi\) |
0.934044 | + | 0.357158i | \(0.116254\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 581.969i | 0.899489i | 0.893157 | + | 0.449744i | \(0.148485\pi\) | ||||
−0.893157 | + | 0.449744i | \(0.851515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 432.000 | 0.665639 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 387.000 | + | 670.304i | 0.592649 | + | 1.02650i | 0.993874 | + | 0.110519i | \(0.0352513\pi\) |
−0.401225 | + | 0.915980i | \(0.631415\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −540.000 | − | 311.769i | −0.824427 | − | 0.475983i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −198.000 | − | 114.315i | −0.300455 | − | 0.173468i | 0.342192 | − | 0.939630i | \(-0.388831\pi\) |
−0.642647 | + | 0.766162i | \(0.722164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 227.000 | + | 393.176i | 0.343419 | + | 0.594819i | 0.985065 | − | 0.172182i | \(-0.0550816\pi\) |
−0.641646 | + | 0.767001i | \(0.721748\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −288.000 | −0.433083 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1260.00 | − | 727.461i | 1.87779 | − | 1.08415i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −217.000 | + | 375.855i | −0.322437 | + | 0.558477i | −0.980990 | − | 0.194057i | \(-0.937835\pi\) |
0.658553 | + | 0.752534i | \(0.271169\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −117.000 | + | 202.650i | −0.172821 | + | 0.299335i | −0.939405 | − | 0.342809i | \(-0.888622\pi\) |
0.766584 | + | 0.642144i | \(0.221955\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −204.000 | + | 117.779i | −0.300442 | + | 0.173460i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 270.200i | − | 0.395608i | −0.980242 | − | 0.197804i | \(-0.936619\pi\) | ||
0.980242 | − | 0.197804i | \(-0.0633809\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1116.00 | 1.62920 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 126.000 | + | 218.238i | 0.182874 | + | 0.316747i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0000 | + | 10.3923i | 0.0260492 | + | 0.0150395i | 0.512968 | − | 0.858408i | \(-0.328546\pi\) |
−0.486919 | + | 0.873447i | \(0.661879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −252.000 | − | 145.492i | −0.362590 | − | 0.209341i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −162.000 | − | 280.592i | −0.232425 | − | 0.402571i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1074.00 | 1.53210 | 0.766049 | − | 0.642783i | \(-0.222220\pi\) | ||||
0.766049 | + | 0.642783i | \(0.222220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 180.133i | 0.256235i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −108.000 | + | 62.3538i | −0.152758 | + | 0.0881949i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −449.000 | + | 777.691i | −0.633286 | + | 1.09688i | 0.353589 | + | 0.935401i | \(0.384961\pi\) |
−0.986875 | + | 0.161483i | \(0.948372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1512.00 | + | 872.954i | −2.11469 | + | 1.22091i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 956.092i | − | 1.32975i | −0.746954 | − | 0.664876i | \(-0.768484\pi\) | ||
0.746954 | − | 0.664876i | \(-0.231516\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −912.000 | −1.26491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 165.000 | + | 285.788i | 0.227586 | + | 0.394191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 702.000 | + | 405.300i | 0.965612 | + | 0.557496i | 0.897896 | − | 0.440208i | \(-0.145095\pi\) |
0.0677164 | + | 0.997705i | \(0.478429\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −108.000 | − | 62.3538i | −0.147743 | − | 0.0852994i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −185.000 | − | 320.429i | −0.252387 | − | 0.437148i | 0.711795 | − | 0.702387i | \(-0.247882\pi\) |
−0.964183 | + | 0.265239i | \(0.914549\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2448.00 | −3.32157 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 852.169i | 1.15314i | 0.817048 | + | 0.576569i | \(0.195609\pi\) | ||||
−0.817048 | + | 0.576569i | \(0.804391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1188.00 | + | 685.892i | −1.59892 | + | 0.923139i | −0.607228 | + | 0.794527i | \(0.707719\pi\) |
−0.991695 | + | 0.128611i | \(0.958948\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 558.000 | − | 966.484i | 0.748993 | − | 1.29729i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 504.000 | − | 872.954i | 0.672897 | − | 1.16549i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −66.0000 | + | 38.1051i | −0.0878828 | + | 0.0507392i | −0.543297 | − | 0.839540i | \(-0.682824\pi\) |
0.455415 | + | 0.890279i | \(0.349491\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 207.846i | 0.275293i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 514.000 | 0.678996 | 0.339498 | − | 0.940607i | \(-0.389743\pi\) | ||||
0.339498 | + | 0.940607i | \(0.389743\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −483.000 | − | 836.581i | −0.634691 | − | 1.09932i | −0.986580 | − | 0.163276i | \(-0.947794\pi\) |
0.351889 | − | 0.936042i | \(-0.385539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 204.000 | + | 117.779i | 0.267366 | + | 0.154364i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 252.000 | + | 145.492i | 0.328553 | + | 0.189690i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 479.000 | + | 829.652i | 0.622887 | + | 1.07887i | 0.988945 | + | 0.148280i | \(0.0473736\pi\) |
−0.366059 | + | 0.930592i | \(0.619293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 546.000 | 0.706339 | 0.353169 | − | 0.935559i | \(-0.385104\pi\) | ||||
0.353169 | + | 0.935559i | \(0.385104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 228.631i | − | 0.295007i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 324.000 | − | 187.061i | 0.415918 | − | 0.240130i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 864.000 | − | 1496.49i | 1.10627 | − | 1.91612i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 510.000 | − | 883.346i | 0.649682 | − | 1.12528i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −210.000 | + | 121.244i | −0.266836 | + | 0.154058i | −0.627449 | − | 0.778658i | \(-0.715901\pi\) |
0.360613 | + | 0.932716i | \(0.382568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 540.400i | − | 0.683186i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 980.000 | 1.23581 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −669.000 | − | 1158.74i | −0.839398 | − | 1.45388i | −0.890399 | − | 0.455181i | \(-0.849575\pi\) |
0.0510012 | − | 0.998699i | \(-0.483759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −216.000 | − | 124.708i | −0.270338 | − | 0.156080i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1476.00 | + | 852.169i | 1.83811 | + | 1.06123i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 966.000 | 1.19407 | 0.597033 | − | 0.802216i | \(-0.296346\pi\) | ||||
0.597033 | + | 0.802216i | \(0.296346\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1517.28i | 1.87087i | 0.353497 | + | 0.935436i | \(0.384992\pi\) | ||||
−0.353497 | + | 0.935436i | \(0.615008\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1476.00 | + | 852.169i | −1.81104 | + | 1.04561i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 72.0000 | − | 124.708i | 0.0881273 | − | 0.152641i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 111.000 | − | 192.258i | 0.135201 | − | 0.234175i | −0.790473 | − | 0.612497i | \(-0.790165\pi\) |
0.925674 | + | 0.378322i | \(0.123499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1110.00 | + | 640.859i | −1.34872 | + | 0.778686i | −0.988069 | − | 0.154013i | \(-0.950780\pi\) |
−0.360655 | + | 0.932699i | \(0.617447\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1434.14i | 1.73415i | 0.498182 | + | 0.867073i | \(0.334001\pi\) | ||||
−0.498182 | + | 0.867073i | \(0.665999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 226.000 | 0.272618 | 0.136309 | − | 0.990666i | \(-0.456476\pi\) | ||||
0.136309 | + | 0.990666i | \(0.456476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00000 | − | 5.19615i | −0.00360144 | − | 0.00623788i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1080.00 | + | 623.538i | 1.29341 | + | 0.746752i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −432.000 | − | 249.415i | −0.514899 | − | 0.297277i | 0.219946 | − | 0.975512i | \(-0.429412\pi\) |
−0.734845 | + | 0.678235i | \(0.762745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.5000 | − | 51.0955i | −0.0350773 | − | 0.0607556i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −162.000 | −0.191716 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2154.67i | 2.54389i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0000 | − | 60.6218i | 0.0410317 | − | 0.0710689i | −0.844780 | − | 0.535113i | \(-0.820269\pi\) |
0.885812 | + | 0.464044i | \(0.153602\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.0245041 | − | 0.0424423i | −0.853513 | − | 0.521071i | \(-0.825533\pi\) |
0.878017 | + | 0.478629i | \(0.158866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −798.000 | + | 460.726i | −0.928987 | + | 0.536351i | −0.886491 | − | 0.462746i | \(-0.846864\pi\) |
−0.0424961 | + | 0.999097i | \(0.513531\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 166.277i | − | 0.192673i | −0.995349 | − | 0.0963365i | \(-0.969287\pi\) | ||
0.995349 | − | 0.0963365i | \(-0.0307125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −252.000 | −0.291329 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 792.000 | + | 1371.78i | 0.911392 | + | 1.57858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1428.00 | − | 824.456i | −1.63949 | − | 0.946563i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 504.000 | + | 290.985i | 0.576000 | + | 0.332554i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 83.0000 | + | 143.760i | 0.0946408 | + | 0.163923i | 0.909459 | − | 0.415794i | \(-0.136496\pi\) |
−0.814818 | + | 0.579717i | \(0.803163\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 702.000 | 0.796822 | 0.398411 | − | 0.917207i | \(-0.369562\pi\) | ||||
0.398411 | + | 0.917207i | \(0.369562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 630.466i | − | 0.714005i | −0.934103 | − | 0.357003i | \(-0.883799\pi\) | ||
0.934103 | − | 0.357003i | \(-0.116201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1116.00 | − | 644.323i | 1.25817 | − | 0.726407i | 0.285454 | − | 0.958392i | \(-0.407856\pi\) |
0.972719 | + | 0.231985i | \(0.0745222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −360.000 | + | 623.538i | −0.404949 | + | 0.701393i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 144.000 | − | 249.415i | 0.161254 | − | 0.279300i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −756.000 | + | 436.477i | −0.844693 | + | 0.487684i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 623.538i | 0.693591i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 108.000 | 0.119867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 246.000 | + | 426.084i | 0.271823 | + | 0.470812i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1254.00 | + | 723.997i | 1.38258 | + | 0.798233i | 0.992464 | − | 0.122533i | \(-0.0391017\pi\) |
0.390115 | + | 0.920766i | \(0.372435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 288.000 | + | 166.277i | 0.316136 | + | 0.182521i | 0.649669 | − | 0.760217i | \(-0.274907\pi\) |
−0.333533 | + | 0.942738i | \(0.608241\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −216.000 | − | 374.123i | −0.236583 | − | 0.409773i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −720.000 | −0.785169 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 561.184i | − | 0.610647i | −0.952249 | − | 0.305323i | \(-0.901235\pi\) | ||
0.952249 | − | 0.305323i | \(-0.0987646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1008.00 | − | 581.969i | 1.09209 | − | 0.630519i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −143.000 | + | 247.683i | −0.154595 | + | 0.267766i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −219.000 | + | 379.319i | −0.235737 | + | 0.408309i | −0.959487 | − | 0.281754i | \(-0.909084\pi\) |
0.723749 | + | 0.690063i | \(0.242417\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | − | 3.46410i | 0.00644468 | − | 0.00372084i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 748.246i | 0.800263i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1826.00 | 1.94877 | 0.974386 | − | 0.224881i | \(-0.0721992\pi\) | ||||
0.974386 | + | 0.224881i | \(0.0721992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −165.000 | − | 285.788i | −0.175345 | − | 0.303707i | 0.764935 | − | 0.644107i | \(-0.222771\pi\) |
−0.940281 | + | 0.340400i | \(0.889438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 162.000 | + | 93.5307i | 0.171067 | + | 0.0987653i | 0.583089 | − | 0.812409i | \(-0.301844\pi\) |
−0.412022 | + | 0.911174i | \(0.635177\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 574.000 | + | 994.197i | 0.604847 | + | 1.04763i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1110.00 | 1.16474 | 0.582371 | − | 0.812923i | \(-0.302125\pi\) | ||||
0.582371 | + | 0.812923i | \(0.302125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1995.32i | 2.08934i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1116.00 | − | 644.323i | 1.16371 | − | 0.671870i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −264.500 | + | 458.127i | −0.275234 | + | 0.476719i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −282.000 | + | 488.438i | −0.292228 | + | 0.506154i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 654.000 | − | 377.587i | 0.676319 | − | 0.390473i | −0.122148 | − | 0.992512i | \(-0.538978\pi\) |
0.798467 | + | 0.602039i | \(0.205645\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 394.908i | 0.406702i | 0.979106 | + | 0.203351i | \(0.0651832\pi\) | ||||
−0.979106 | + | 0.203351i | \(0.934817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −336.000 | −0.345324 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −459.000 | − | 795.011i | −0.469806 | − | 0.813727i | 0.529598 | − | 0.848248i | \(-0.322343\pi\) |
−0.999404 | + | 0.0345214i | \(0.989009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2052.00 | − | 1184.72i | −2.09602 | − | 1.21014i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | + | 20.7846i | 0.0366226 | + | 0.0211441i | 0.518200 | − | 0.855260i | \(-0.326602\pi\) |
−0.481577 | + | 0.876404i | \(0.659936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 774.000 | + | 1340.61i | 0.785787 | + | 1.36102i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48.4974i | − | 0.0489379i | −0.999701 | − | 0.0244689i | \(-0.992211\pi\) | ||
0.999701 | − | 0.0244689i | \(-0.00778948\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −612.000 | + | 353.338i | −0.615075 | + | 0.355114i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −277.000 | + | 479.778i | −0.277834 | + | 0.481222i | −0.970846 | − | 0.239704i | \(-0.922950\pi\) |
0.693013 | + | 0.720925i | \(0.256283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))