Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.1 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1873 |
Dual form | 3024.2.t.h.289.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −1.58836 | −0.710338 | −0.355169 | − | 0.934802i | \(-0.615577\pi\) | ||||
−0.355169 | + | 0.934802i | \(0.615577\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64400 | + | 0.0963576i | 0.999337 | + | 0.0364197i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.58836 | −0.478910 | −0.239455 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239455 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40545 | − | 4.16635i | 0.667151 | − | 1.15554i | −0.311547 | − | 0.950231i | \(-0.600847\pi\) |
0.978697 | − | 0.205308i | \(-0.0658196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.69963 | − | 4.67589i | 0.654756 | − | 1.13407i | −0.327199 | − | 0.944955i | \(-0.606105\pi\) |
0.981955 | − | 0.189115i | \(-0.0605620\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.54944 | + | 6.14781i | 0.814298 | + | 1.41041i | 0.909831 | + | 0.414979i | \(0.136211\pi\) |
−0.0955331 | + | 0.995426i | \(0.530456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.300372 | 0.0626319 | 0.0313159 | − | 0.999510i | \(-0.490030\pi\) | ||||
0.0313159 | + | 0.999510i | \(0.490030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.47710 | −0.495420 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.13781 | − | 7.16689i | −0.768371 | − | 1.33086i | −0.938446 | − | 0.345427i | \(-0.887734\pi\) |
0.170074 | − | 0.985431i | \(-0.445599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35600 | − | 2.34867i | −0.243545 | − | 0.421833i | 0.718176 | − | 0.695861i | \(-0.244977\pi\) |
−0.961722 | + | 0.274028i | \(0.911644\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.19963 | − | 0.153051i | −0.709867 | − | 0.0258703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.93818 | + | 5.08907i | −0.458866 | + | 0.794780i | −0.998901 | − | 0.0468628i | \(-0.985078\pi\) |
0.540035 | + | 0.841643i | \(0.318411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.833104 | + | 1.44298i | 0.127047 | + | 0.220052i | 0.922531 | − | 0.385922i | \(-0.126117\pi\) |
−0.795484 | + | 0.605974i | \(0.792783\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.33310 | + | 2.30900i | −0.194453 | + | 0.336803i | −0.946721 | − | 0.322055i | \(-0.895627\pi\) |
0.752268 | + | 0.658857i | \(0.228960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98143 | + | 0.509538i | 0.997347 | + | 0.0727912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44437 | + | 4.23377i | −0.335760 | + | 0.581553i | −0.983630 | − | 0.180197i | \(-0.942326\pi\) |
0.647871 | + | 0.761750i | \(0.275660\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.52290 | 0.340188 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.23855 | − | 5.60933i | −0.421623 | − | 0.730273i | 0.574475 | − | 0.818522i | \(-0.305206\pi\) |
−0.996098 | + | 0.0882491i | \(0.971873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.23855 | − | 3.87728i | 0.286617 | − | 0.496435i | −0.686383 | − | 0.727240i | \(-0.740803\pi\) |
0.973000 | + | 0.230805i | \(0.0741360\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.82072 | + | 6.61769i | −0.473902 | + | 0.820823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.02654 | − | 8.70623i | −0.614090 | − | 1.06363i | −0.990543 | − | 0.137199i | \(-0.956190\pi\) |
0.376454 | − | 0.926435i | \(-0.377143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7207 | 1.50967 | 0.754833 | − | 0.655917i | \(-0.227718\pi\) | ||||
0.754833 | + | 0.655917i | \(0.227718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.02654 | − | 13.9024i | 0.939436 | − | 1.62715i | 0.172909 | − | 0.984938i | \(-0.444683\pi\) |
0.766527 | − | 0.642213i | \(-0.221983\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.19963 | − | 0.153051i | −0.478592 | − | 0.0174418i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19344 | − | 7.26325i | 0.471799 | − | 0.817179i | −0.527681 | − | 0.849443i | \(-0.676938\pi\) |
0.999479 | + | 0.0322635i | \(0.0102716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.18292 | + | 2.04887i | 0.129842 | + | 0.224893i | 0.923615 | − | 0.383321i | \(-0.125220\pi\) |
−0.793773 | + | 0.608214i | \(0.791886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28799 | + | 7.42702i | −0.465098 | + | 0.805573i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.60507 | − | 2.78007i | −0.170138 | − | 0.294687i | 0.768330 | − | 0.640054i | \(-0.221088\pi\) |
−0.938468 | + | 0.345367i | \(0.887755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.76145 | − | 10.7840i | 0.708793 | − | 1.13047i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.63781 | − | 9.76497i | −0.578427 | − | 1.00186i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.712008 | + | 1.23323i | 0.0722934 | + | 0.125216i | 0.899906 | − | 0.436084i | \(-0.143635\pi\) |
−0.827613 | + | 0.561300i | \(0.810302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0334 | −1.19737 | −0.598685 | − | 0.800985i | \(-0.704310\pi\) | ||||
−0.598685 | + | 0.800985i | \(0.704310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.09888 | 0.600941 | 0.300470 | − | 0.953791i | \(-0.402856\pi\) | ||||
0.300470 | + | 0.953791i | \(0.402856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.54325 | − | 2.67299i | −0.149192 | − | 0.258408i | 0.781737 | − | 0.623608i | \(-0.214334\pi\) |
−0.930929 | + | 0.365200i | \(0.881001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.14400 | − | 1.98146i | 0.109575 | − | 0.189789i | −0.806023 | − | 0.591884i | \(-0.798384\pi\) |
0.915598 | + | 0.402095i | \(0.131718\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.73236 | − | 16.8569i | 0.915543 | − | 1.58577i | 0.109440 | − | 0.993993i | \(-0.465094\pi\) |
0.806104 | − | 0.591774i | \(-0.201572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.477100 | −0.0444898 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.58836 | − | 12.1029i | 0.695624 | − | 1.10947i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.47710 | −0.770645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8764 | 1.06225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4400 | 1.19260 | 0.596302 | − | 0.802760i | \(-0.296636\pi\) | ||||
0.596302 | + | 0.802760i | \(0.296636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.17673 | −0.277552 | −0.138776 | − | 0.990324i | \(-0.544317\pi\) | ||||
−0.138776 | + | 0.990324i | \(0.544317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.79232 | + | 16.5968i | 0.762391 | + | 1.43913i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.2632 | 1.81664 | 0.908320 | − | 0.418275i | \(-0.137365\pi\) | ||||
0.908320 | + | 0.418275i | \(0.137365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.52654 | + | 11.3043i | −0.553574 | + | 0.958818i | 0.444439 | + | 0.895809i | \(0.353403\pi\) |
−0.998013 | + | 0.0630092i | \(0.979930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.82072 | + | 6.61769i | −0.319505 | + | 0.553399i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.57234 | + | 11.3836i | 0.545803 | + | 0.945359i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.20877 | −0.426719 | −0.213360 | − | 0.976974i | \(-0.568441\pi\) | ||||
−0.213360 | + | 0.976974i | \(0.568441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.522900 | 0.0425530 | 0.0212765 | − | 0.999774i | \(-0.493227\pi\) | ||||
0.0212765 | + | 0.999774i | \(0.493227\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.15383 | + | 3.73054i | 0.173000 | + | 0.299644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.43199 | − | 7.67643i | −0.353711 | − | 0.612646i | 0.633185 | − | 0.774000i | \(-0.281747\pi\) |
−0.986897 | + | 0.161354i | \(0.948414\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.794182 | + | 0.0289431i | 0.0625903 | + | 0.00228104i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9814 | − | 19.0204i | −0.860132 | − | 1.48979i | −0.871801 | − | 0.489860i | \(-0.837048\pi\) |
0.0116689 | − | 0.999932i | \(-0.496286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.65019 | − | 2.85821i | 0.127695 | − | 0.221175i | −0.795088 | − | 0.606494i | \(-0.792575\pi\) |
0.922783 | + | 0.385319i | \(0.125909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.07234 | − | 8.78555i | −0.390180 | − | 0.675812i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.55377 | − | 16.5476i | 0.726360 | − | 1.25809i | −0.232052 | − | 0.972703i | \(-0.574544\pi\) |
0.958412 | − | 0.285389i | \(-0.0921227\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.54944 | − | 0.238687i | −0.495091 | − | 0.0180431i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.03706 | + | 13.9206i | −0.600718 | + | 1.04047i | 0.391994 | + | 0.919968i | \(0.371785\pi\) |
−0.992712 | + | 0.120507i | \(0.961548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.05308 | 0.598581 | 0.299291 | − | 0.954162i | \(-0.403250\pi\) | ||||
0.299291 | + | 0.954162i | \(0.403250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.794182 | − | 1.37556i | −0.0583894 | − | 0.101133i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.28799 | + | 7.42702i | −0.313569 | + | 0.543118i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9814 | − | 20.7524i | 0.866946 | − | 1.50159i | 0.00184390 | − | 0.999998i | \(-0.499413\pi\) |
0.865102 | − | 0.501596i | \(-0.167254\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.88255 | − | 8.45682i | −0.351453 | − | 0.608735i | 0.635051 | − | 0.772470i | \(-0.280979\pi\) |
−0.986504 | + | 0.163735i | \(0.947646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2436 | 1.29980 | 0.649900 | − | 0.760020i | \(-0.274811\pi\) | ||||
0.649900 | + | 0.760020i | \(0.274811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.04944 | + | 15.6741i | −0.641498 | + | 1.11111i | 0.343601 | + | 0.939116i | \(0.388353\pi\) |
−0.985098 | + | 0.171991i | \(0.944980\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.2498 | − | 19.3479i | −0.719392 | − | 1.35796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.66690 | − | 8.08330i | 0.325950 | − | 0.564562i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.63781 | − | 9.76497i | −0.389975 | − | 0.675457i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.166208 | + | 0.287880i | −0.0114422 | + | 0.0198185i | −0.871690 | − | 0.490058i | \(-0.836976\pi\) |
0.860248 | + | 0.509877i | \(0.170309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.32327 | − | 2.29197i | −0.0902464 | − | 0.156311i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.35896 | − | 6.34053i | −0.228021 | − | 0.430423i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9876 | − | 22.4952i | −0.873642 | − | 1.51319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.16621 | − | 5.48403i | −0.212025 | − | 0.367238i | 0.740323 | − | 0.672251i | \(-0.234672\pi\) |
−0.952348 | + | 0.305013i | \(0.901339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.3090 | −1.54707 | −0.773537 | − | 0.633751i | \(-0.781515\pi\) | ||||
−0.773537 | + | 0.633751i | \(0.781515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.95420 | −0.327383 | −0.163691 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163691 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.13781 | + | 12.3630i | 0.467613 | + | 0.809930i | 0.999315 | − | 0.0370017i | \(-0.0117807\pi\) |
−0.531702 | + | 0.846932i | \(0.678447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.11745 | − | 3.66754i | 0.138127 | − | 0.239244i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.48762 | − | 4.30868i | 0.160911 | − | 0.278706i | −0.774285 | − | 0.632837i | \(-0.781890\pi\) |
0.935196 | + | 0.354132i | \(0.115224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.0891 | − | 0.809332i | −0.708454 | − | 0.0517063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.1520 | 2.17304 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.43268 | 0.153549 | 0.0767746 | − | 0.997048i | \(-0.475538\pi\) | ||||
0.0767746 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.477100 | −0.0299950 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.987620 | 0.0616061 | 0.0308030 | − | 0.999525i | \(-0.490194\pi\) | ||||
0.0308030 | + | 0.999525i | \(0.490194\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.23855 | + | 2.33795i | 0.0769597 | + | 0.145273i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.1854 | 1.05970 | 0.529848 | − | 0.848092i | \(-0.322249\pi\) | ||||
0.529848 | + | 0.848092i | \(0.322249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.88255 | − | 6.72477i | 0.238503 | − | 0.413099i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4523 | + | 19.8360i | −0.698262 | + | 1.20942i | 0.270807 | + | 0.962634i | \(0.412709\pi\) |
−0.969069 | + | 0.246791i | \(0.920624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00364 | − | 12.1307i | −0.425441 | − | 0.736885i | 0.571021 | − | 0.820936i | \(-0.306548\pi\) |
−0.996462 | + | 0.0840504i | \(0.973214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.93454 | 0.237261 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2953 | 1.70010 | 0.850049 | − | 0.526703i | \(-0.176572\pi\) | ||||
0.850049 | + | 0.526703i | \(0.176572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.79782 | + | 15.2383i | 0.524834 | + | 0.909039i | 0.999582 | + | 0.0289175i | \(0.00920600\pi\) |
−0.474748 | + | 0.880122i | \(0.657461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.26145 | − | 16.0413i | −0.550536 | − | 0.953556i | −0.998236 | − | 0.0593725i | \(-0.981090\pi\) |
0.447700 | − | 0.894184i | \(-0.352243\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.25890 | + | 13.1724i | −0.487508 | + | 0.777541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.07598 | − | 10.5239i | −0.357411 | − | 0.619054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.04256 | − | 12.1981i | 0.411431 | − | 0.712619i | −0.583616 | − | 0.812030i | \(-0.698362\pi\) |
0.995046 | + | 0.0994108i | \(0.0316958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.14400 | + | 8.90966i | 0.299495 | + | 0.518741i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.722528 | − | 1.25146i | 0.0417849 | − | 0.0723736i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.06368 | + | 3.89550i | 0.118949 | + | 0.224533i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.55563 | + | 6.15854i | −0.203595 | + | 0.352637i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.85532 | 0.334180 | 0.167090 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167090 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.405446 | − | 0.702253i | −0.0229907 | − | 0.0398211i | 0.854301 | − | 0.519778i | \(-0.173985\pi\) |
−0.877292 | + | 0.479957i | \(0.840652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.28799 | + | 9.15907i | −0.298895 | + | 0.517701i | −0.975883 | − | 0.218292i | \(-0.929951\pi\) |
0.676988 | + | 0.735994i | \(0.263285\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.09820 | − | 10.5624i | 0.342509 | − | 0.593243i | −0.642389 | − | 0.766379i | \(-0.722057\pi\) |
0.984898 | + | 0.173136i | \(0.0553900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.57234 | + | 11.3836i | 0.367981 | + | 0.637361i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.3287 | 2.13267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.95853 | + | 10.3205i | −0.330520 | + | 0.572477i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.74721 | + | 5.97654i | −0.206590 | + | 0.329497i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.83310 | + | 13.5673i | −0.430546 | + | 0.745728i | −0.996920 | − | 0.0784202i | \(-0.975012\pi\) |
0.566374 | + | 0.824148i | \(0.308346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.98398 | + | 13.8287i | 0.436211 | + | 0.755540i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.21201 | + | 7.29541i | −0.229443 | + | 0.397406i | −0.957643 | − | 0.287958i | \(-0.907024\pi\) |
0.728200 | + | 0.685364i | \(0.240357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.15383 | + | 3.73054i | 0.116636 | + | 0.202020i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4098 | + | 2.01993i | 0.994035 | + | 0.109066i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.283662 | − | 0.491316i | −0.0152277 | − | 0.0263752i | 0.858311 | − | 0.513130i | \(-0.171514\pi\) |
−0.873539 | + | 0.486754i | \(0.838181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.00364189 | − | 0.00630794i | −0.000194946 | − | 0.000337656i | 0.865928 | − | 0.500169i | \(-0.166729\pi\) |
−0.866123 | + | 0.499831i | \(0.833395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.65383 | −0.354148 | −0.177074 | − | 0.984198i | \(-0.556663\pi\) | ||||
−0.177074 | + | 0.984198i | \(0.556663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.2051 | −1.07237 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.398568 | − | 0.690339i | −0.0210356 | − | 0.0364347i | 0.855316 | − | 0.518107i | \(-0.173363\pi\) |
−0.876352 | + | 0.481672i | \(0.840030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6971 | + | 27.1881i | −0.826162 | + | 1.43095i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7491 | + | 22.0820i | −0.667317 | + | 1.15583i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4327 | 0.805579 | 0.402790 | − | 0.915293i | \(-0.368041\pi\) | ||||
0.402790 | + | 0.915293i | \(0.368041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.87085 | + | 10.9585i | −0.356717 | + | 0.568939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2422 | 0.530321 | 0.265160 | − | 0.964204i | \(-0.414575\pi\) | ||||
0.265160 | + | 0.964204i | \(0.414575\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.8131 | −2.05048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0087 | −1.28461 | −0.642304 | − | 0.766450i | \(-0.722021\pi\) | ||||
−0.642304 | + | 0.766450i | \(0.722021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.26695 | −0.320226 | −0.160113 | − | 0.987099i | \(-0.551186\pi\) | ||||
−0.160113 | + | 0.987099i | \(0.551186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.67054 | + | 0.243101i | 0.339962 | + | 0.0123896i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.6342 | 1.09690 | 0.548448 | − | 0.836185i | \(-0.315219\pi\) | ||||
0.548448 | + | 0.836185i | \(0.315219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.810892 | − | 1.40451i | 0.0410086 | − | 0.0710290i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.66071 | + | 11.5367i | −0.335137 | + | 0.580473i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05308 | + | 3.55605i | 0.103041 | + | 0.178473i | 0.912936 | − | 0.408102i | \(-0.133809\pi\) |
−0.809895 | + | 0.586575i | \(0.800476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.7417 | −0.836041 | −0.418021 | − | 0.908438i | \(-0.637276\pi\) | ||||
−0.418021 | + | 0.908438i | \(0.637276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0472 | −0.649926 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.794182 | − | 1.37556i | −0.0393661 | − | 0.0681842i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.38255 | + | 7.59079i | 0.216703 | + | 0.375341i | 0.953798 | − | 0.300449i | \(-0.0971364\pi\) |
−0.737095 | + | 0.675789i | \(0.763803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.02221 | − | 15.1431i | −0.394747 | − | 0.745144i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.87890 | − | 3.25436i | −0.0922318 | − | 0.159750i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.210149 | + | 0.363988i | −0.0102664 | + | 0.0177820i | −0.871113 | − | 0.491083i | \(-0.836601\pi\) |
0.860847 | + | 0.508865i | \(0.169935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.28799 | + | 5.69497i | 0.160247 | + | 0.277556i | 0.934957 | − | 0.354761i | \(-0.115438\pi\) |
−0.774710 | + | 0.632316i | \(0.782104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.68725 | + | 11.5827i | −0.324379 | + | 0.561841i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.29232 | − | 10.0358i | 0.304507 | − | 0.485667i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0439 | − | 19.1287i | 0.531968 | − | 0.921395i | −0.467336 | − | 0.884080i | \(-0.654786\pi\) |
0.999304 | − | 0.0373155i | \(-0.0118806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.43268 | −0.453306 | −0.226653 | − | 0.973976i | \(-0.572778\pi\) | ||||
−0.226653 | + | 0.973976i | \(0.572778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.06615 | + | 1.84663i | 0.0510010 | + | 0.0883363i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.6032 | + | 27.0256i | −0.744701 | + | 1.28986i | 0.205634 | + | 0.978629i | \(0.434074\pi\) |
−0.950334 | + | 0.311231i | \(0.899259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.52723 | + | 11.3055i | −0.310118 | + | 0.537140i | −0.978388 | − | 0.206779i | \(-0.933702\pi\) |
0.668270 | + | 0.743919i | \(0.267035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.54944 | + | 4.41576i | 0.120855 | + | 0.209327i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.91706 | 0.468015 | 0.234008 | − | 0.972235i | \(-0.424816\pi\) | ||||
0.234008 | + | 0.972235i | \(0.424816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.66690 | − | 8.08330i | 0.219756 | − | 0.380628i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7396 | + | 17.1290i | −0.503482 | + | 0.803019i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2615 | − | 21.2375i | 0.573566 | − | 0.993446i | −0.422629 | − | 0.906303i | \(-0.638893\pi\) |
0.996196 | − | 0.0871436i | \(-0.0277739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.75526 | − | 3.04020i | −0.0817506 | − | 0.141596i | 0.822251 | − | 0.569125i | \(-0.192718\pi\) |
−0.904002 | + | 0.427528i | \(0.859384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.69413 | + | 15.0587i | −0.404050 | + | 0.699836i | −0.994210 | − | 0.107451i | \(-0.965731\pi\) |
0.590160 | + | 0.807286i | \(0.299065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.69894 | + | 11.6029i | 0.309990 | + | 0.536918i | 0.978360 | − | 0.206911i | \(-0.0663410\pi\) |
−0.668370 | + | 0.743829i | \(0.733008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4512 | − | 23.5036i | −0.574945 | − | 1.08529i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.32327 | − | 2.29197i | −0.0608441 | − | 0.105385i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.79232 | − | 15.2287i | −0.403419 | − | 0.698743i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8058 | 0.950641 | 0.475321 | − | 0.879813i | \(-0.342332\pi\) | ||||
0.475321 | + | 0.879813i | \(0.342332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.81089 | 0.219358 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.13093 | − | 1.95882i | −0.0513528 | − | 0.0889456i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2472 | + | 28.1410i | −0.736231 | + | 1.27519i | 0.217950 | + | 0.975960i | \(0.430063\pi\) |
−0.954181 | + | 0.299230i | \(0.903270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.66071 | + | 16.7328i | −0.435982 | + | 0.755142i | −0.997375 | − | 0.0724067i | \(-0.976932\pi\) |
0.561394 | + | 0.827549i | \(0.310265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.6822 | −2.01238 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.6334 | + | 1.22573i | 1.50866 | + | 0.0549816i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1506 | 0.499169 | 0.249585 | − | 0.968353i | \(-0.419706\pi\) | ||||
0.249585 | + | 0.968353i | \(0.419706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7651 | −1.81763 | −0.908813 | − | 0.417204i | \(-0.863010\pi\) | ||||
−0.908813 | + | 0.417204i | \(0.863010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1135 | 0.850537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.44506 | −0.0640510 | −0.0320255 | − | 0.999487i | \(-0.510196\pi\) | ||||
−0.0320255 | + | 0.999487i | \(0.510196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.5617 | − | 35.9844i | 0.998073 | − | 1.59186i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.68725 | −0.426871 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.11745 | − | 3.66754i | 0.0931255 | − | 0.161298i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.64214 | + | 16.7007i | −0.422430 | + | 0.731670i | −0.996177 | − | 0.0873630i | \(-0.972156\pi\) |
0.573747 | + | 0.819033i | \(0.305489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.3454 | + | 31.7752i | 0.802189 | + | 1.38943i | 0.918173 | + | 0.396180i | \(0.129665\pi\) |
−0.115984 | + | 0.993251i | \(0.537002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.6428 | −0.637851 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9098 | −0.996077 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.1353 | + | 24.4830i | 0.612266 | + | 1.06048i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.45125 | + | 4.24568i | 0.105977 | + | 0.183557i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0891 | − | 0.809332i | −0.477639 | − | 0.0348604i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.62543 | − | 2.81532i | −0.0698825 | − | 0.121040i | 0.828967 | − | 0.559298i | \(-0.188929\pi\) |
−0.898849 | + | 0.438258i | \(0.855596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.81708 | + | 3.14728i | −0.0778352 | + | 0.134815i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.95853 | + | 5.12432i | 0.126498 | + | 0.219100i | 0.922317 | − | 0.386433i | \(-0.126293\pi\) |
−0.795820 | + | 0.605534i | \(0.792960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.3738 | − | 50.8769i | 1.25137 | − | 2.16743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7873 | − | 18.7999i | 0.501247 | − | 0.799454i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8040 | + | 22.1772i | −0.542523 | + | 0.939678i | 0.456235 | + | 0.889859i | \(0.349198\pi\) |
−0.998758 | + | 0.0498188i | \(0.984136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.01594 | 0.339038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3189 | + | 40.3895i | 0.982773 | + | 1.70221i | 0.651443 | + | 0.758698i | \(0.274164\pi\) |
0.331330 | + | 0.943515i | \(0.392503\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.4585 | + | 26.7750i | −0.650345 | + | 1.12643i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5989 | − | 27.0181i | 0.653939 | − | 1.13266i | −0.328219 | − | 0.944602i | \(-0.606449\pi\) |
0.982159 | − | 0.188054i | \(-0.0602182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.83812 | − | 13.5760i | −0.328015 | − | 0.568139i | 0.654103 | − | 0.756406i | \(-0.273046\pi\) |
−0.982118 | + | 0.188267i | \(0.939713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.744051 | −0.0310291 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.99567 | − | 12.1169i | 0.291234 | − | 0.504431i | −0.682868 | − | 0.730542i | \(-0.739268\pi\) |
0.974102 | + | 0.226110i | \(0.0726010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.93021 | + | 5.53120i | 0.121565 | + | 0.229473i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.88255 | − | 6.72477i | 0.160799 | − | 0.278511i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.44801 | + | 2.50803i | 0.0597658 | + | 0.103517i | 0.894360 | − | 0.447348i | \(-0.147631\pi\) |
−0.834594 | + | 0.550865i | \(0.814298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.62612 | − | 16.6729i | 0.396637 | − | 0.686996i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.04394 | + | 3.54021i | 0.0839346 | + | 0.145379i | 0.904937 | − | 0.425546i | \(-0.139918\pi\) |
−0.821002 | + | 0.570925i | \(0.806585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0531 | + | 19.2238i | −0.494128 | + | 0.788100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.88255 | + | 17.1171i | 0.403790 | + | 0.699385i | 0.994180 | − | 0.107734i | \(-0.0343593\pi\) |
−0.590390 | + | 0.807118i | \(0.701026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4320 | − | 23.2649i | −0.547902 | − | 0.948994i | −0.998418 | − | 0.0562261i | \(-0.982093\pi\) |
0.450516 | − | 0.892768i | \(-0.351240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4647 | 0.547419 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.2422 | 0.618661 | 0.309331 | − | 0.950955i | \(-0.399895\pi\) | ||||
0.309331 | + | 0.950955i | \(0.399895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.41342 | + | 11.1084i | 0.259459 | + | 0.449396i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.36033 | + | 2.35617i | −0.0549434 | + | 0.0951648i | −0.892189 | − | 0.451662i | \(-0.850831\pi\) |
0.837246 | + | 0.546827i | \(0.184165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.21812 | − | 15.9663i | 0.371108 | − | 0.642777i | −0.618629 | − | 0.785684i | \(-0.712311\pi\) |
0.989736 | + | 0.142906i | \(0.0456448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.107546 | −0.00432262 | −0.00216131 | − | 0.999998i | \(-0.500688\pi\) | ||||
−0.00216131 | + | 0.999998i | \(0.500688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.97593 | − | 7.50516i | −0.159292 | − | 0.300688i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.47848 | −0.259139 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.39926 | 0.215282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7266 | −1.42225 | −0.711126 | − | 0.703064i | \(-0.751815\pi\) | ||||
−0.711126 | + | 0.703064i | \(0.751815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.3475 | −0.847152 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9164 | − | 27.8615i | 0.749494 | − | 1.10391i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3128 | −0.683813 | −0.341906 | − | 0.939734i | \(-0.611073\pi\) | ||||
−0.341906 | + | 0.939734i | \(0.611073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.4821 | + | 25.0838i | −0.571119 | + | 0.989207i | 0.425332 | + | 0.905037i | \(0.360157\pi\) |
−0.996451 | + | 0.0841700i | \(0.973176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.27816 | − | 2.21384i | 0.0502497 | − | 0.0870350i | −0.839807 | − | 0.542886i | \(-0.817332\pi\) |
0.890056 | + | 0.455851i | \(0.150665\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.14400 | + | 8.90966i | 0.201920 | + | 0.349735i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.9766 | −1.17308 | −0.586538 | − | 0.809922i | \(-0.699509\pi\) | ||||
−0.586538 | + | 0.809922i | \(0.699509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.04580 | 0.197156 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.63162 | − | 13.2183i | −0.297286 | − | 0.514914i | 0.678228 | − | 0.734851i | \(-0.262748\pi\) |
−0.975514 | + | 0.219937i | \(0.929415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6261 | + | 23.6011i | 0.529994 | + | 0.917977i | 0.999388 | + | 0.0349881i | \(0.0111393\pi\) |
−0.469393 | + | 0.882989i | \(0.655527\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.9654 | − | 26.3618i | −0.541555 | − | 1.02227i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.24288 | − | 2.15273i | −0.0481245 | − | 0.0833541i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.55563 | + | 6.15854i | −0.137264 | + | 0.237748i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2280 | + | 40.2320i | 0.895372 | + | 1.55083i | 0.833344 | + | 0.552755i | \(0.186423\pi\) |
0.0620280 | + | 0.998074i | \(0.480243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.54944 | − | 4.41576i | 0.0979830 | − | 0.169712i | −0.812867 | − | 0.582450i | \(-0.802094\pi\) |
0.910850 | + | 0.412738i | \(0.135428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76371 | + | 3.32927i | 0.0676852 | + | 0.127766i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.77197 | + | 13.4614i | −0.297386 | + | 0.515088i | −0.975537 | − | 0.219835i | \(-0.929448\pi\) |
0.678151 | + | 0.734923i | \(0.262782\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.7738 | −1.29043 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.7596 | + | 20.3682i | 0.448005 | + | 0.775967i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.6483 | − | 20.1755i | 0.443123 | − | 0.767512i | −0.554796 | − | 0.831986i | \(-0.687204\pi\) |
0.997919 | + | 0.0644744i | \(0.0205371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3665 | − | 17.9553i | 0.393225 | − | 0.681085i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.8640 | + | 27.4772i | 0.600891 | + | 1.04077i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.6464 | 1.72404 | 0.862020 | − | 0.506874i | \(-0.169199\pi\) | ||||
0.862020 | + | 0.506874i | \(0.169199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.54944 | + | 6.14781i | −0.133870 | + | 0.231869i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.8163 | − | 1.15951i | −1.19658 | − | 0.0436079i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.00069 | + | 15.5897i | −0.338028 | + | 0.585482i | −0.984062 | − | 0.177827i | \(-0.943093\pi\) |
0.646034 | + | 0.763309i | \(0.276427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.407305 | − | 0.705474i | −0.0152537 | − | 0.0264202i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.06870 | − | 10.5113i | 0.226957 | − | 0.393100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4389 | + | 31.9371i | 0.687654 | + | 1.19105i | 0.972595 | + | 0.232506i | \(0.0746926\pi\) |
−0.284941 | + | 0.958545i | \(0.591974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.1254 | + | 0.587674i | 0.600542 | + | 0.0218861i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.2498 | + | 17.7531i | 0.380666 | + | 0.659334i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2429 | − | 26.4014i | −0.565327 | − | 0.979175i | −0.997019 | − | 0.0771543i | \(-0.975417\pi\) |
0.431692 | − | 0.902021i | \(-0.357917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.99628 | 0.332739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.15059 | 0.227177 | 0.113589 | − | 0.993528i | \(-0.463765\pi\) | ||||
0.113589 | + | 0.993528i | \(0.463765\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.98398 | + | 13.8287i | 0.294094 | + | 0.509385i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3912 | − | 35.3186i | 0.750103 | − | 1.29922i | −0.197670 | − | 0.980269i | \(-0.563337\pi\) |
0.947772 | − | 0.318947i | \(-0.103329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.25271 | − | 12.5621i | 0.266076 | − | 0.460858i | −0.701769 | − | 0.712405i | \(-0.747606\pi\) |
0.967845 | + | 0.251547i | \(0.0809394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.27342 | 0.303115 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.82279 | − | 7.21608i | −0.139682 | − | 0.263670i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.18911 | −0.152863 | −0.0764314 | − | 0.997075i | \(-0.524353\pi\) | ||||
−0.0764314 | + | 0.997075i | \(0.524353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.830556 | −0.0302270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.38688 | 0.0867525 | 0.0433763 | − | 0.999059i | \(-0.486189\pi\) | ||||
0.0433763 | + | 0.999059i | \(0.486189\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.63416 | −0.131738 | −0.0658692 | − | 0.997828i | \(-0.520982\pi\) | ||||
−0.0658692 | + | 0.997828i | \(0.520982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.21565 | − | 5.12874i | 0.116414 | − | 0.185673i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.1606 | −1.12515 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.9672 | + | 34.5842i | −0.720035 | + | 1.24714i | 0.240950 | + | 0.970538i | \(0.422541\pi\) |
−0.960985 | + | 0.276600i | \(0.910792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0698 | + | 31.2978i | −0.649925 | + | 1.12570i | 0.333215 | + | 0.942851i | \(0.391867\pi\) |
−0.983140 | + | 0.182853i | \(0.941467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.35896 | + | 5.81788i | 0.120657 | + | 0.208985i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.7156 | −1.49462 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2051 | −0.722994 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.03961 | + | 12.1930i | 0.251254 | + | 0.435186i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.3189 | − | 38.6574i | −0.795582 | − | 1.37799i | −0.922469 | − | 0.386071i | \(-0.873832\pi\) |
0.126888 | − | 0.991917i | \(-0.459501\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.3566 | − | 43.6319i | 0.972689 | − | 1.55137i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7694 | − | 18.6532i | −0.382433 | − | 0.662394i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.2836 | + | 45.5245i | −0.931012 | + | 1.61256i | −0.149418 | + | 0.988774i | \(0.547740\pi\) |
−0.781595 | + | 0.623786i | \(0.785593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.19777 | + | 12.4669i | 0.254639 | + | 0.441047i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.7491 | + | 22.0820i | −0.449905 | + | 0.779258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.26145 | − | 0.0459722i | −0.0444603 | − | 0.00162031i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.40290 | + | 12.8222i | −0.260272 | + | 0.450804i | −0.966314 | − | 0.257365i | \(-0.917146\pi\) |
0.706042 | + | 0.708170i | \(0.250479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0704 | −0.950571 | −0.475285 | − | 0.879832i | \(-0.657655\pi\) | ||||
−0.475285 | + | 0.879832i | \(0.657655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.4425 | + | 30.2113i | 0.610984 | + | 1.05826i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.91411 | + | 10.2435i | −0.206908 | + | 0.358376i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.9091 | − | 37.9477i | 0.764632 | − | 1.32438i | −0.175808 | − | 0.984424i | \(-0.556254\pi\) |
0.940441 | − | 0.339958i | \(-0.110413\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6712 | + | 27.1434i | 0.546265 | + | 0.946158i | 0.998526 | + | 0.0542727i | \(0.0172840\pi\) |
−0.452262 | + | 0.891885i | \(0.649383\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7665 | −0.513480 | −0.256740 | − | 0.966480i | \(-0.582648\pi\) | ||||
−0.256740 | + | 0.966480i | \(0.582648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0036 | + | 25.9871i | −0.521098 | + | 0.902568i | 0.478601 | + | 0.878033i | \(0.341144\pi\) |
−0.999699 | + | 0.0245357i | \(0.992189\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.2298 | − | 31.2689i | 0.735569 | − | 1.08340i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.62110 | + | 4.53987i | −0.0907068 | + | 0.157109i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.0167 | + | 31.2059i | 0.622006 | + | 1.07735i | 0.989112 | + | 0.147167i | \(0.0470154\pi\) |
−0.367106 | + | 0.930179i | \(0.619651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7429 | + | 34.1957i | −0.680789 | + | 1.17916i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.05673 | + | 13.9547i | 0.277160 | + | 0.480055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.4134 | − | 0.816833i | −0.770134 | − | 0.0280667i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.150186 | + | 0.260130i | 0.00514831 | + | 0.00891713i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2658 | − | 21.2450i | −0.419972 | − | 0.727413i | 0.575964 | − | 0.817475i | \(-0.304627\pi\) |
−0.995936 | + | 0.0900617i | \(0.971294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.0480 | −0.992260 | −0.496130 | − | 0.868248i | \(-0.665246\pi\) | ||||
−0.496130 | + | 0.868248i | \(0.665246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.2953 | −0.863064 | −0.431532 | − | 0.902098i | \(-0.642027\pi\) | ||||
−0.431532 | + | 0.902098i | \(0.642027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.34981 | − | 2.33795i | −0.0459482 | − | 0.0795846i | 0.842137 | − | 0.539264i | \(-0.181298\pi\) |
−0.888085 | + | 0.459680i | \(0.847964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1749 | + | 26.2836i | −0.515961 | + | 0.893671i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.66071 | + | 11.5367i | −0.225949 | + | 0.391355i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.3643 | −1.63876 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.4010 | + | 1.14438i | 1.06155 | + | 0.0386870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0916 | −0.374537 | −0.187268 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187268 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3942 | 1.36091 | 0.680457 | − | 0.732788i | \(-0.261781\pi\) | ||||
0.680457 | + | 0.732788i | \(0.261781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2581 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.5672 | 1.36211 | 0.681056 | − | 0.732231i | \(-0.261521\pi\) | ||||
0.681056 | + | 0.732231i | \(0.261521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.5352 | + | 1.29504i | 1.19181 | + | 0.0434343i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.9271 | −0.633371 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7658 | − | 22.1110i | 0.426713 | − | 0.739089i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.2218 | + | 19.4367i | −0.374267 | + | 0.648249i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1978 | + | 22.8592i | 0.439681 | + | 0.761551i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.7912 | −0.425195 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.1135 | −0.999901 | −0.499950 | − | 0.866054i | \(-0.666648\pi\) | ||||
−0.499950 | + | 0.866054i | \(0.666648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6113 | + | 25.3075i | 0.484093 | + | 0.838473i | 0.999833 | − | 0.0182717i | \(-0.00581638\pi\) |
−0.515740 | + | 0.856745i | \(0.672483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.87890 | − | 3.25436i | −0.0621826 | − | 0.107704i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.39926 | − | 0.306102i | −0.277368 | − | 0.0101084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.52359 | + | 9.56714i | 0.182206 | + | 0.315591i | 0.942632 | − | 0.333835i | \(-0.108343\pi\) |
−0.760425 | + | 0.649426i | \(0.775009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.5989 | − | 52.9988i | 1.00717 | − | 1.74448i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.23855 | − | 2.14523i | −0.0407233 | − | 0.0705348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.1669 | + | 36.6621i | −0.694463 | + | 1.20285i | 0.275898 | + | 0.961187i | \(0.411025\pi\) |
−0.970361 | + | 0.241659i | \(0.922309\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.6476 | + | 44.7291i | 0.709473 | + | 1.46594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.81089 | − | 11.7968i | 0.222740 | − | 0.385797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7651 | −0.384349 | −0.192174 | − | 0.981361i | \(-0.561554\pi\) | ||||
−0.192174 | + | 0.981361i | \(0.561554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.28799 | + | 12.6232i | 0.237582 | + | 0.411504i | 0.960020 | − | 0.279932i | \(-0.0903119\pi\) |
−0.722438 | + | 0.691436i | \(0.756979\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.882546 | + | 1.52861i | −0.0287397 | + | 0.0497785i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.12178 | + | 5.40709i | −0.101444 | + | 0.175707i | −0.912280 | − | 0.409567i | \(-0.865680\pi\) |
0.810836 | + | 0.585274i | \(0.199013\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.6148 | − | 66.8828i | −1.25349 | − | 2.17111i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.0173 | −0.907570 | −0.453785 | − | 0.891111i | \(-0.649927\pi\) | ||||
−0.453785 | + | 0.891111i | \(0.649927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.0309 | + | 32.9624i | −0.615825 | + | 1.06664i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 56.2199 | + | 2.04887i | 1.81544 | + | 0.0661616i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.8225 | − | 20.4772i | 0.381371 | − | 0.660554i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.75526 | + | 13.4325i | 0.249651 | + | 0.432408i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.7837 | + | 27.3381i | −0.507568 | + | 0.879134i | 0.492393 | + | 0.870373i | \(0.336122\pi\) |
−0.999962 | + | 0.00876132i | \(0.997211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.82141 | + | 4.88683i | 0.0905434 | + | 0.156826i | 0.907740 | − | 0.419533i | \(-0.137806\pi\) |
−0.817196 | + | 0.576359i | \(0.804473\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3454 | + | 29.2596i | −0.588127 | + | 0.938021i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.24652 | + | 5.62314i | 0.103865 | + | 0.179900i | 0.913274 | − | 0.407346i | \(-0.133546\pi\) |
−0.809409 | + | 0.587246i | \(0.800212\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.54944 | + | 4.41576i | 0.0814805 | + | 0.141128i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.3063 | −0.966620 | −0.483310 | − | 0.875449i | \(-0.660566\pi\) | ||||
−0.483310 | + | 0.875449i | \(0.660566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.9774 | −0.923298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.250241 | + | 0.433430i | 0.00795720 | + | 0.0137823i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1669 | + | 19.3416i | −0.354728 | + | 0.614407i | −0.987071 | − | 0.160281i | \(-0.948760\pi\) |
0.632343 | + | 0.774688i | \(0.282093\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3738 | − | 24.8962i | 0.455680 | − | 0.789262i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.76509 | −0.277593 | −0.138797 | − | 0.990321i | \(-0.544323\pi\) | ||||
−0.138797 | + | 0.990321i | \(0.544323\pi\) | |||||||
\(998\) | 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 \(a_p\))