Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(199,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.j (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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.396143 - 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.199 |
Dual form | 1350.2.j.f.1099.4 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.92048 | − | 1.68614i | 1.10384 | − | 0.637301i | 0.166612 | − | 0.986023i | \(-0.446717\pi\) |
0.937226 | + | 0.348721i | \(0.113384\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.18614 | − | 3.78651i | −0.659146 | − | 1.14167i | −0.980837 | − | 0.194830i | \(-0.937584\pi\) |
0.321691 | − | 0.946845i | \(-0.395749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.84096 | − | 3.37228i | −1.61999 | − | 0.935303i | −0.986920 | − | 0.161209i | \(-0.948461\pi\) |
−0.633071 | − | 0.774094i | \(-0.718206\pi\) | |||||||
\(14\) | 1.68614 | − | 2.92048i | 0.450640 | − | 0.780531i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.62772i | 0.394780i | 0.980325 | + | 0.197390i | \(0.0632465\pi\) | ||||
−0.980325 | + | 0.197390i | \(0.936754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.37228 | 0.544239 | 0.272119 | − | 0.962264i | \(-0.412275\pi\) | ||||
0.272119 | + | 0.962264i | \(0.412275\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.78651 | − | 2.18614i | −0.807286 | − | 0.466087i | ||||
\(23\) | −1.18843 | − | 0.686141i | −0.247805 | − | 0.143070i | 0.370954 | − | 0.928651i | \(-0.379031\pi\) |
−0.618759 | + | 0.785581i | \(0.712364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.74456 | −1.32272 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.37228i | − | 0.637301i | ||||||
\(29\) | −0.686141 | − | 1.18843i | −0.127413 | − | 0.220686i | 0.795261 | − | 0.606268i | \(-0.207334\pi\) |
−0.922674 | + | 0.385582i | \(0.874001\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.37228 | + | 4.10891i | −0.426074 | + | 0.737982i | −0.996520 | − | 0.0833529i | \(-0.973437\pi\) |
0.570446 | + | 0.821335i | \(0.306770\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.813859 | + | 1.40965i | 0.139576 | + | 0.241752i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 2.05446 | − | 1.18614i | 0.333277 | − | 0.192417i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.87375 | − | 2.81386i | 0.743240 | − | 0.429110i | −0.0800065 | − | 0.996794i | \(-0.525494\pi\) |
0.823246 | + | 0.567685i | \(0.192161\pi\) | |||||||
\(44\) | −4.37228 | −0.659146 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.37228 | −0.202332 | ||||||||
\(47\) | 6.38458 | − | 3.68614i | 0.931287 | − | 0.537679i | 0.0440687 | − | 0.999029i | \(-0.485968\pi\) |
0.887218 | + | 0.461350i | \(0.152635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.18614 | − | 3.78651i | 0.312306 | − | 0.540930i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.84096 | + | 3.37228i | −0.809996 | + | 0.467651i | ||||
\(53\) | − | 11.4891i | − | 1.57815i | −0.614295 | − | 0.789076i | \(-0.710560\pi\) | ||
0.614295 | − | 0.789076i | \(-0.289440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.68614 | − | 2.92048i | −0.225320 | − | 0.390266i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.18843 | − | 0.686141i | −0.156049 | − | 0.0900947i | ||||
\(59\) | −2.18614 | + | 3.78651i | −0.284611 | + | 0.492961i | −0.972515 | − | 0.232841i | \(-0.925198\pi\) |
0.687904 | + | 0.725802i | \(0.258531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.05842 | + | 7.02939i | 0.519628 | + | 0.900022i | 0.999740 | + | 0.0228144i | \(0.00726267\pi\) |
−0.480112 | + | 0.877207i | \(0.659404\pi\) | |||||||
\(62\) | 4.74456i | 0.602560i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.06218 | + | 3.50000i | 0.740613 | + | 0.427593i | 0.822292 | − | 0.569066i | \(-0.192695\pi\) |
−0.0816792 | + | 0.996659i | \(0.526028\pi\) | |||||||
\(68\) | 1.40965 | + | 0.813859i | 0.170945 | + | 0.0986949i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.11684i | − | 0.364799i | −0.983225 | − | 0.182399i | \(-0.941614\pi\) | ||
0.983225 | − | 0.182399i | \(-0.0583864\pi\) | |||||||
\(74\) | −2.00000 | − | 3.46410i | −0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.18614 | − | 2.05446i | 0.136060 | − | 0.235662i | ||||
\(77\) | −12.7692 | − | 7.37228i | −1.45518 | − | 0.840149i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | + | 1.73205i | 0.112509 | + | 0.194871i | 0.916781 | − | 0.399390i | \(-0.130778\pi\) |
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000i | 0.331295i | ||||||||
\(83\) | 6.38458 | − | 3.68614i | 0.700799 | − | 0.404607i | −0.106846 | − | 0.994276i | \(-0.534075\pi\) |
0.807645 | + | 0.589669i | \(0.200742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.81386 | − | 4.87375i | 0.303426 | − | 0.525550i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.78651 | + | 2.18614i | −0.403643 | + | 0.233043i | ||||
\(89\) | 16.1168 | 1.70838 | 0.854191 | − | 0.519959i | \(-0.174053\pi\) | ||||
0.854191 | + | 0.519959i | \(0.174053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.7446 | −2.38428 | ||||||||
\(92\) | −1.18843 | + | 0.686141i | −0.123902 | + | 0.0715351i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.68614 | − | 6.38458i | 0.380196 | − | 0.658519i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.25061 | + | 4.18614i | −0.736188 | + | 0.425038i | −0.820682 | − | 0.571386i | \(-0.806406\pi\) |
0.0844938 | + | 0.996424i | \(0.473073\pi\) | |||||||
\(98\) | − | 4.37228i | − | 0.441667i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.37228 | + | 2.37686i | 0.136547 | + | 0.236507i | 0.926187 | − | 0.377064i | \(-0.123066\pi\) |
−0.789640 | + | 0.613570i | \(0.789733\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8564 | − | 8.00000i | −1.36531 | − | 0.788263i | −0.374987 | − | 0.927030i | \(-0.622353\pi\) |
−0.990325 | + | 0.138767i | \(0.955686\pi\) | |||||||
\(104\) | −3.37228 | + | 5.84096i | −0.330679 | + | 0.572754i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.74456 | − | 9.94987i | −0.557961 | − | 0.966417i | ||||
\(107\) | − | 8.48913i | − | 0.820675i | −0.911934 | − | 0.410337i | \(-0.865411\pi\) | ||
0.911934 | − | 0.410337i | \(-0.134589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.3723 | −1.47240 | −0.736199 | − | 0.676765i | \(-0.763381\pi\) | ||||
−0.736199 | + | 0.676765i | \(0.763381\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.92048 | − | 1.68614i | −0.275960 | − | 0.159325i | ||||
\(113\) | −2.81929 | − | 1.62772i | −0.265217 | − | 0.153123i | 0.361495 | − | 0.932374i | \(-0.382266\pi\) |
−0.626712 | + | 0.779251i | \(0.715600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.37228 | −0.127413 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.37228i | 0.402501i | ||||||||
\(119\) | 2.74456 | + | 4.75372i | 0.251594 | + | 0.435773i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05842 | + | 7.02939i | −0.368947 | + | 0.639036i | ||||
\(122\) | 7.02939 | + | 4.05842i | 0.636411 | + | 0.367432i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.37228 | + | 4.10891i | 0.213037 | + | 0.368991i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.11684i | − | 0.720253i | −0.932903 | − | 0.360127i | \(-0.882733\pi\) | ||
0.932903 | − | 0.360127i | \(-0.117267\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.37228 | + | 2.37686i | −0.119897 | + | 0.207667i | −0.919727 | − | 0.392560i | \(-0.871590\pi\) |
0.799830 | + | 0.600227i | \(0.204923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | − | 4.00000i | 0.600751 | − | 0.346844i | ||||
\(134\) | 7.00000 | 0.604708 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.62772 | 0.139576 | ||||||||
\(137\) | 16.5557 | − | 9.55842i | 1.41445 | − | 0.816631i | 0.418643 | − | 0.908151i | \(-0.362506\pi\) |
0.995803 | + | 0.0915197i | \(0.0291724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.441578 | − | 0.764836i | 0.0374542 | − | 0.0648725i | −0.846691 | − | 0.532085i | \(-0.821409\pi\) |
0.884145 | + | 0.467213i | \(0.154742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.19615 | − | 3.00000i | 0.436051 | − | 0.251754i | ||||
\(143\) | 29.4891i | 2.46600i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.55842 | − | 2.69927i | −0.128976 | − | 0.223393i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | −0.941578 | + | 1.63086i | −0.0771371 | + | 0.133605i | −0.902014 | − | 0.431708i | \(-0.857911\pi\) |
0.824877 | + | 0.565313i | \(0.191245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | − | 2.37228i | − | 0.192417i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.7446 | −1.18815 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.84096 | + | 3.37228i | 0.466160 | + | 0.269137i | 0.714631 | − | 0.699502i | \(-0.246595\pi\) |
−0.248471 | + | 0.968639i | \(0.579928\pi\) | |||||||
\(158\) | 1.73205 | + | 1.00000i | 0.137795 | + | 0.0795557i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.62772 | −0.364715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4891i | 1.68316i | 0.540134 | + | 0.841579i | \(0.318374\pi\) | ||||
−0.540134 | + | 0.841579i | \(0.681626\pi\) | |||||||
\(164\) | 1.50000 | + | 2.59808i | 0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.68614 | − | 6.38458i | 0.286100 | − | 0.495540i | ||||
\(167\) | 11.5807 | + | 6.68614i | 0.896144 | + | 0.517389i | 0.875947 | − | 0.482407i | \(-0.160237\pi\) |
0.0201970 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.2446 | + | 28.1364i | 1.24958 | + | 2.16434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5.62772i | − | 0.429110i | ||||||
\(173\) | 17.9653 | − | 10.3723i | 1.36588 | − | 0.788590i | 0.375479 | − | 0.926831i | \(-0.377478\pi\) |
0.990399 | + | 0.138241i | \(0.0441448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.18614 | + | 3.78651i | −0.164787 | + | 0.285419i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.9576 | − | 8.05842i | 1.04617 | − | 0.604004i | ||||
\(179\) | −14.7446 | −1.10206 | −0.551030 | − | 0.834485i | \(-0.685765\pi\) | ||||
−0.551030 | + | 0.834485i | \(0.685765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8614 | 1.55062 | 0.775308 | − | 0.631583i | \(-0.217595\pi\) | ||||
0.775308 | + | 0.631583i | \(0.217595\pi\) | |||||||
\(182\) | −19.6974 | + | 11.3723i | −1.46007 | + | 0.842970i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.686141 | + | 1.18843i | −0.0505830 | + | 0.0876123i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.16337 | − | 3.55842i | 0.450710 | − | 0.260218i | ||||
\(188\) | − | 7.37228i | − | 0.537679i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.74456 | + | 15.1460i | 0.632734 | + | 1.09593i | 0.986990 | + | 0.160780i | \(0.0514008\pi\) |
−0.354256 | + | 0.935148i | \(0.615266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2877 | + | 10.5584i | 1.31638 | + | 0.760012i | 0.983144 | − | 0.182832i | \(-0.0585264\pi\) |
0.333235 | + | 0.942844i | \(0.391860\pi\) | |||||||
\(194\) | −4.18614 | + | 7.25061i | −0.300547 | + | 0.520563i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.18614 | − | 3.78651i | −0.156153 | − | 0.270465i | ||||
\(197\) | 5.48913i | 0.391084i | 0.980695 | + | 0.195542i | \(0.0626466\pi\) | ||||
−0.980695 | + | 0.195542i | \(0.937353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.4891 | −0.956219 | −0.478109 | − | 0.878300i | \(-0.658678\pi\) | ||||
−0.478109 | + | 0.878300i | \(0.658678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.37686 | + | 1.37228i | 0.167235 | + | 0.0965534i | ||||
\(203\) | −4.00772 | − | 2.31386i | −0.281287 | − | 0.162401i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.0000 | −1.11477 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.74456i | 0.467651i | ||||||||
\(209\) | −5.18614 | − | 8.98266i | −0.358733 | − | 0.621344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.37228 | − | 16.2333i | 0.645214 | − | 1.11754i | −0.339037 | − | 0.940773i | \(-0.610101\pi\) |
0.984252 | − | 0.176771i | \(-0.0565653\pi\) | |||||||
\(212\) | −9.94987 | − | 5.74456i | −0.683360 | − | 0.394538i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.24456 | − | 7.35180i | −0.290152 | − | 0.502559i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000i | 1.08615i | ||||||||
\(218\) | −13.3128 | + | 7.68614i | −0.901656 | + | 0.520571i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.48913 | − | 9.50744i | 0.369239 | − | 0.639540i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.73977 | + | 3.31386i | −0.384364 | + | 0.221912i | −0.679715 | − | 0.733476i | \(-0.737897\pi\) |
0.295351 | + | 0.955389i | \(0.404563\pi\) | |||||||
\(224\) | −3.37228 | −0.225320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.25544 | −0.216548 | ||||||||
\(227\) | −16.5557 | + | 9.55842i | −1.09884 | + | 0.634415i | −0.935916 | − | 0.352224i | \(-0.885426\pi\) |
−0.162923 | + | 0.986639i | \(0.552092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.31386 | − | 10.9359i | 0.417232 | − | 0.722666i | −0.578428 | − | 0.815733i | \(-0.696334\pi\) |
0.995660 | + | 0.0930670i | \(0.0296671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.18843 | + | 0.686141i | −0.0780243 | + | 0.0450473i | ||||
\(233\) | 7.11684i | 0.466240i | 0.972448 | + | 0.233120i | \(0.0748935\pi\) | ||||
−0.972448 | + | 0.233120i | \(0.925107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.18614 | + | 3.78651i | 0.142306 | + | 0.246481i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.75372 | + | 2.74456i | 0.308138 | + | 0.177904i | ||||
\(239\) | 1.62772 | − | 2.81929i | 0.105288 | − | 0.182365i | −0.808568 | − | 0.588403i | \(-0.799757\pi\) |
0.913856 | + | 0.406038i | \(0.133090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.24456 | + | 10.8159i | 0.402248 | + | 0.696713i | 0.993997 | − | 0.109409i | \(-0.0348958\pi\) |
−0.591749 | + | 0.806122i | \(0.701562\pi\) | |||||||
\(242\) | 8.11684i | 0.521770i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.11684 | 0.519628 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8564 | − | 8.00000i | −0.881662 | − | 0.509028i | ||||
\(248\) | 4.10891 | + | 2.37228i | 0.260916 | + | 0.150640i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6060 | 1.55312 | 0.776558 | − | 0.630046i | \(-0.216964\pi\) | ||||
0.776558 | + | 0.630046i | \(0.216964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | −4.05842 | − | 7.02939i | −0.254648 | − | 0.441063i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.78651 | + | 2.18614i | 0.236196 | + | 0.136368i | 0.613427 | − | 0.789751i | \(-0.289790\pi\) |
−0.377231 | + | 0.926119i | \(0.623124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.74456 | − | 11.6819i | −0.419087 | − | 0.725880i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.74456i | 0.169560i | ||||||||
\(263\) | −15.1460 | + | 8.74456i | −0.933944 | + | 0.539213i | −0.888057 | − | 0.459734i | \(-0.847945\pi\) |
−0.0458872 | + | 0.998947i | \(0.514611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.00000 | − | 6.92820i | 0.245256 | − | 0.424795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.06218 | − | 3.50000i | 0.370306 | − | 0.213797i | ||||
\(269\) | −1.37228 | −0.0836695 | −0.0418347 | − | 0.999125i | \(-0.513320\pi\) | ||||
−0.0418347 | + | 0.999125i | \(0.513320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 1.40965 | − | 0.813859i | 0.0854723 | − | 0.0493475i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.55842 | − | 16.5557i | 0.577445 | − | 1.00016i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5012 | − | 8.37228i | 0.871294 | − | 0.503042i | 0.00351574 | − | 0.999994i | \(-0.498881\pi\) |
0.867778 | + | 0.496952i | \(0.165548\pi\) | |||||||
\(278\) | − | 0.883156i | − | 0.0529682i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.686141 | − | 1.18843i | −0.0409317 | − | 0.0708958i | 0.844834 | − | 0.535029i | \(-0.179699\pi\) |
−0.885765 | + | 0.464133i | \(0.846366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.71810 | − | 1.56930i | −0.161574 | − | 0.0932850i | 0.417033 | − | 0.908892i | \(-0.363070\pi\) |
−0.578607 | + | 0.815607i | \(0.696403\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.7446 | + | 25.5383i | 0.871864 | + | 1.51011i | ||||
\(287\) | 10.1168i | 0.597178i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3505 | 0.844149 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.69927 | − | 1.55842i | −0.157963 | − | 0.0911997i | ||||
\(293\) | −22.7190 | − | 13.1168i | −1.32726 | − | 0.766294i | −0.342385 | − | 0.939560i | \(-0.611235\pi\) |
−0.984875 | + | 0.173265i | \(0.944568\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.88316i | 0.109088i | ||||||||
\(299\) | 4.62772 | + | 8.01544i | 0.267628 | + | 0.463545i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.48913 | − | 16.4356i | 0.546944 | − | 0.947335i | ||||
\(302\) | 8.66025 | + | 5.00000i | 0.498342 | + | 0.287718i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.18614 | − | 2.05446i | −0.0680298 | − | 0.117831i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.23369i | 0.0704103i | 0.999380 | + | 0.0352051i | \(0.0112085\pi\) | ||||
−0.999380 | + | 0.0352051i | \(0.988792\pi\) | |||||||
\(308\) | −12.7692 | + | 7.37228i | −0.727591 | + | 0.420075i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3723 | + | 17.9653i | −0.588158 | + | 1.01872i | 0.406315 | + | 0.913733i | \(0.366813\pi\) |
−0.994474 | + | 0.104987i | \(0.966520\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.14170 | + | 1.81386i | −0.177579 | + | 0.102525i | −0.586155 | − | 0.810199i | \(-0.699359\pi\) |
0.408576 | + | 0.912724i | \(0.366026\pi\) | |||||||
\(314\) | 6.74456 | 0.380618 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −2.37686 | + | 1.37228i | −0.133498 | + | 0.0770750i | −0.565262 | − | 0.824912i | \(-0.691225\pi\) |
0.431764 | + | 0.901987i | \(0.357891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.00772 | + | 2.31386i | −0.223342 | + | 0.128946i | ||||
\(323\) | 3.86141i | 0.214854i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.7446 | + | 18.6101i | 0.595086 | + | 1.03072i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.59808 | + | 1.50000i | 0.143455 | + | 0.0828236i | ||||
\(329\) | 12.4307 | − | 21.5306i | 0.685327 | − | 1.18702i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.11684 | − | 14.0588i | −0.446142 | − | 0.772741i | 0.551989 | − | 0.833851i | \(-0.313869\pi\) |
−0.998131 | + | 0.0611107i | \(0.980536\pi\) | |||||||
\(332\) | − | 7.37228i | − | 0.404607i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.3723 | 0.731699 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05446 | + | 1.18614i | 0.111913 | + | 0.0646132i | 0.554912 | − | 0.831909i | \(-0.312752\pi\) |
−0.442999 | + | 0.896522i | \(0.646085\pi\) | |||||||
\(338\) | 28.1364 | + | 16.2446i | 1.53042 | + | 0.883588i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7446 | 1.12338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.86141i | 0.478471i | ||||||||
\(344\) | −2.81386 | − | 4.87375i | −0.151713 | − | 0.262775i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.3723 | − | 17.9653i | 0.557617 | − | 0.965821i | ||||
\(347\) | −4.22894 | − | 2.44158i | −0.227021 | − | 0.131071i | 0.382176 | − | 0.924090i | \(-0.375175\pi\) |
−0.609197 | + | 0.793019i | \(0.708508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.05842 | + | 15.6896i | 0.484886 | + | 0.839848i | 0.999849 | − | 0.0173648i | \(-0.00552768\pi\) |
−0.514963 | + | 0.857212i | \(0.672194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.37228i | 0.233043i | ||||||||
\(353\) | −18.4901 | + | 10.6753i | −0.984129 | + | 0.568187i | −0.903514 | − | 0.428558i | \(-0.859022\pi\) |
−0.0806147 | + | 0.996745i | \(0.525688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.05842 | − | 13.9576i | 0.427096 | − | 0.739751i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.7692 | + | 7.37228i | −0.674871 | + | 0.389637i | ||||
\(359\) | −17.4891 | −0.923041 | −0.461520 | − | 0.887130i | \(-0.652696\pi\) | ||||
−0.461520 | + | 0.887130i | \(0.652696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3723 | −0.703804 | ||||||||
\(362\) | 18.0665 | − | 10.4307i | 0.949555 | − | 0.548226i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.3723 | + | 19.6974i | −0.596070 | + | 1.03242i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8564 | + | 8.00000i | −0.723299 | + | 0.417597i | −0.815966 | − | 0.578101i | \(-0.803794\pi\) |
0.0926670 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(368\) | 1.37228i | 0.0715351i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.3723 | − | 33.5538i | −1.00576 | − | 1.74203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.4140 | − | 7.74456i | −0.694549 | − | 0.400998i | 0.110765 | − | 0.993847i | \(-0.464670\pi\) |
−0.805314 | + | 0.592848i | \(0.798003\pi\) | |||||||
\(374\) | 3.55842 | − | 6.16337i | 0.184002 | − | 0.318700i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.68614 | − | 6.38458i | −0.190098 | − | 0.329260i | ||||
\(377\) | 9.25544i | 0.476679i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8614 | −0.917479 | −0.458739 | − | 0.888571i | \(-0.651699\pi\) | ||||
−0.458739 | + | 0.888571i | \(0.651699\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.1460 | + | 8.74456i | 0.774938 | + | 0.447411i | ||||
\(383\) | 19.8997 | + | 11.4891i | 1.01683 | + | 0.587067i | 0.913184 | − | 0.407547i | \(-0.133616\pi\) |
0.103646 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.1168 | 1.07482 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.37228i | 0.425038i | ||||||||
\(389\) | 2.31386 | + | 4.00772i | 0.117317 | + | 0.203200i | 0.918704 | − | 0.394947i | \(-0.129237\pi\) |
−0.801386 | + | 0.598147i | \(0.795904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.11684 | − | 1.93443i | 0.0564812 | − | 0.0978284i | ||||
\(392\) | −3.78651 | − | 2.18614i | −0.191247 | − | 0.110417i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.74456 | + | 4.75372i | 0.138269 | + | 0.239489i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7446i | 1.14152i | 0.821118 | + | 0.570758i | \(0.193351\pi\) | ||||
−0.821118 | + | 0.570758i | \(0.806649\pi\) | |||||||
\(398\) | −11.6819 | + | 6.74456i | −0.585562 | + | 0.338074i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.558422 | + | 0.967215i | −0.0278863 | + | 0.0483004i | −0.879632 | − | 0.475655i | \(-0.842211\pi\) |
0.851745 | + | 0.523956i | \(0.175544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.7128 | − | 16.0000i | 1.38047 | − | 0.797017i | ||||
\(404\) | 2.74456 | 0.136547 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.62772 | −0.229670 | ||||||||
\(407\) | −15.1460 | + | 8.74456i | −0.750761 | + | 0.433452i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.93070 | − | 15.4684i | 0.441595 | − | 0.764865i | −0.556213 | − | 0.831040i | \(-0.687746\pi\) |
0.997808 | + | 0.0661749i | \(0.0210795\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.8564 | + | 8.00000i | −0.682656 | + | 0.394132i | ||||
\(413\) | 14.7446i | 0.725532i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.37228 | + | 5.84096i | 0.165340 | + | 0.286377i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.98266 | − | 5.18614i | −0.439356 | − | 0.253662i | ||||
\(419\) | −12.8614 | + | 22.2766i | −0.628321 | + | 1.08828i | 0.359568 | + | 0.933119i | \(0.382924\pi\) |
−0.987889 | + | 0.155165i | \(0.950409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.2337 | − | 26.3855i | −0.742445 | − | 1.28595i | −0.951379 | − | 0.308022i | \(-0.900333\pi\) |
0.208935 | − | 0.977930i | \(-0.433000\pi\) | |||||||
\(422\) | − | 18.7446i | − | 0.912471i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.4891 | −0.557961 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.7051 | + | 13.6861i | 1.14717 | + | 0.662319i | ||||
\(428\) | −7.35180 | − | 4.24456i | −0.355363 | − | 0.205169i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.23369 | −0.396603 | −0.198301 | − | 0.980141i | \(-0.563542\pi\) | ||||
−0.198301 | + | 0.980141i | \(0.563542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.37228i | − | 0.306232i | −0.988208 | − | 0.153116i | \(-0.951069\pi\) | ||
0.988208 | − | 0.153116i | \(-0.0489309\pi\) | |||||||
\(434\) | 8.00000 | + | 13.8564i | 0.384012 | + | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.68614 | + | 13.3128i | −0.368099 | + | 0.637567i | ||||
\(437\) | −2.81929 | − | 1.62772i | −0.134865 | − | 0.0778643i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.11684 | − | 15.7908i | −0.435123 | − | 0.753656i | 0.562182 | − | 0.827013i | \(-0.309962\pi\) |
−0.997306 | + | 0.0733577i | \(0.976629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 10.9783i | − | 0.522182i | ||||||
\(443\) | −3.04051 | + | 1.75544i | −0.144459 | + | 0.0834033i | −0.570487 | − | 0.821306i | \(-0.693246\pi\) |
0.426029 | + | 0.904710i | \(0.359912\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.31386 | + | 5.73977i | −0.156916 | + | 0.271786i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.92048 | + | 1.68614i | −0.137980 | + | 0.0796627i | ||||
\(449\) | 9.86141 | 0.465389 | 0.232694 | − | 0.972550i | \(-0.425246\pi\) | ||||
0.232694 | + | 0.972550i | \(0.425246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.1168 | 0.617648 | ||||||||
\(452\) | −2.81929 | + | 1.62772i | −0.132608 | + | 0.0765614i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.55842 | + | 16.5557i | −0.448599 | + | 0.776996i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1571 | − | 6.44158i | 0.521909 | − | 0.301324i | −0.215806 | − | 0.976436i | \(-0.569238\pi\) |
0.737715 | + | 0.675112i | \(0.235905\pi\) | |||||||
\(458\) | − | 12.6277i | − | 0.590055i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.941578 | + | 1.63086i | 0.0438537 | + | 0.0759568i | 0.887119 | − | 0.461541i | \(-0.152703\pi\) |
−0.843265 | + | 0.537497i | \(0.819370\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3205 | + | 10.0000i | 0.804952 | + | 0.464739i | 0.845200 | − | 0.534450i | \(-0.179481\pi\) |
−0.0402476 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(464\) | −0.686141 | + | 1.18843i | −0.0318533 | + | 0.0551715i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.55842 | + | 6.16337i | 0.164841 | + | 0.285512i | ||||
\(467\) | − | 43.1168i | − | 1.99521i | −0.0691713 | − | 0.997605i | \(-0.522036\pi\) | ||
0.0691713 | − | 0.997605i | \(-0.477964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.6060 | 1.09002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.78651 | + | 2.18614i | 0.174288 | + | 0.100625i | ||||
\(473\) | −21.3094 | − | 12.3030i | −0.979807 | − | 0.565692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.48913 | 0.251594 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 3.25544i | − | 0.148900i | ||||||
\(479\) | 0.255437 | + | 0.442430i | 0.0116712 | + | 0.0202152i | 0.871802 | − | 0.489858i | \(-0.162952\pi\) |
−0.860131 | + | 0.510074i | \(0.829618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4891 | + | 23.3639i | −0.615051 | + | 1.06530i | ||||
\(482\) | 10.8159 | + | 6.24456i | 0.492651 | + | 0.284432i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.05842 | + | 7.02939i | 0.184474 | + | 0.319518i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.7446i | − | 0.577511i | −0.957403 | − | 0.288756i | \(-0.906758\pi\) | ||
0.957403 | − | 0.288756i | \(-0.0932415\pi\) | |||||||
\(488\) | 7.02939 | − | 4.05842i | 0.318206 | − | 0.183716i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3030 | + | 31.7017i | −0.826002 | + | 1.43068i | 0.0751489 | + | 0.997172i | \(0.476057\pi\) |
−0.901151 | + | 0.433505i | \(0.857277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.93443 | − | 1.11684i | 0.0871224 | − | 0.0503001i | ||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.74456 | 0.213037 | ||||||||
\(497\) | 17.5229 | − | 10.1168i | 0.786009 | − | 0.453802i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.55842 | − | 13.0916i | 0.338361 | − | 0.586059i | −0.645763 | − | 0.763538i | \(-0.723461\pi\) |
0.984125 | + | 0.177479i | \(0.0567940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.3094 | − | 12.3030i | 0.951085 | − | 0.549109i | ||||
\(503\) | − | 6.86141i | − | 0.305935i | −0.988231 | − | 0.152967i | \(-0.951117\pi\) | ||
0.988231 | − | 0.152967i | \(-0.0488830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.02939 | − | 4.05842i | −0.311879 | − | 0.180063i | ||||
\(509\) | 21.1753 | − | 36.6766i | 0.938577 | − | 1.62566i | 0.170450 | − | 0.985366i | \(-0.445478\pi\) |
0.768127 | − | 0.640297i | \(-0.221189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.25544 | − | 9.10268i | −0.232487 | − | 0.402679i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.37228 | 0.192853 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.9152 | − | 16.1168i | −1.22771 | − | 0.708818i | ||||
\(518\) | −11.6819 | − | 6.74456i | −0.513274 | − | 0.296339i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.76631 | 0.296438 | 0.148219 | − | 0.988955i | \(-0.452646\pi\) | ||||
0.148219 | + | 0.988955i | \(0.452646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6.11684i | − | 0.267471i | −0.991017 | − | 0.133735i | \(-0.957303\pi\) | ||
0.991017 | − | 0.133735i | \(-0.0426972\pi\) | |||||||
\(524\) | 1.37228 | + | 2.37686i | 0.0599484 | + | 0.103834i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.74456 | + | 15.1460i | −0.381281 | + | 0.660398i | ||||
\(527\) | −6.68815 | − | 3.86141i | −0.291340 | − | 0.168206i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5584 | − | 18.2877i | −0.459062 | − | 0.795118i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 8.00000i | − | 0.346844i | ||||||
\(533\) | 17.5229 | − | 10.1168i | 0.759001 | − | 0.438209i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.50000 | − | 6.06218i | 0.151177 | − | 0.261846i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.18843 | + | 0.686141i | −0.0512369 | + | 0.0295816i | ||||
\(539\) | −19.1168 | −0.823421 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3723 | 1.17683 | 0.588413 | − | 0.808560i | \(-0.299753\pi\) | ||||
0.588413 | + | 0.808560i | \(0.299753\pi\) | |||||||
\(542\) | 6.92820 | − | 4.00000i | 0.297592 | − | 0.171815i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.813859 | − | 1.40965i | 0.0348939 | − | 0.0604381i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.5195 | + | 14.7337i | −1.09113 | + | 0.629967i | −0.933878 | − | 0.357591i | \(-0.883598\pi\) |
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(548\) | − | 19.1168i | − | 0.816631i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62772 | − | 2.81929i | −0.0693431 | − | 0.120106i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.84096 | + | 3.37228i | 0.248383 | + | 0.143404i | ||||
\(554\) | 8.37228 | − | 14.5012i | 0.355704 | − | 0.616098i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.441578 | − | 0.764836i | −0.0187271 | − | 0.0324363i | ||||
\(557\) | 44.2337i | 1.87424i | 0.349005 | + | 0.937121i | \(0.386520\pi\) | ||||
−0.349005 | + | 0.937121i | \(0.613480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.9565 | −1.60539 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.18843 | − | 0.686141i | −0.0501309 | − | 0.0289431i | ||||
\(563\) | 35.2670 | + | 20.3614i | 1.48633 | + | 0.858131i | 0.999879 | − | 0.0155787i | \(-0.00495904\pi\) |
0.486448 | + | 0.873710i | \(0.338292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.13859 | −0.131925 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 15.3030 | + | 26.5055i | 0.641534 | + | 1.11117i | 0.985090 | + | 0.172038i | \(0.0550352\pi\) |
−0.343556 | + | 0.939132i | \(0.611631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.30298 | + | 7.45299i | −0.180074 | + | 0.311898i | −0.941906 | − | 0.335878i | \(-0.890967\pi\) |
0.761831 | + | 0.647775i | \(0.224300\pi\) | |||||||
\(572\) | 25.5383 | + | 14.7446i | 1.06781 | + | 0.616501i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.05842 | + | 8.76144i | 0.211134 | + | 0.365696i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 41.1168i | − | 1.71172i | −0.517210 | − | 0.855858i | \(-0.673030\pi\) | ||
0.517210 | − | 0.855858i | \(-0.326970\pi\) | |||||||
\(578\) | 12.4279 | − | 7.17527i | 0.516934 | − | 0.298452i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.4307 | − | 21.5306i | 0.515712 | − | 0.893240i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.5036 | + | 25.1168i | −1.80174 | + | 1.04023i | ||||
\(584\) | −3.11684 | −0.128976 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.2337 | −1.08370 | ||||||||
\(587\) | −23.3827 | + | 13.5000i | −0.965107 | + | 0.557205i | −0.897741 | − | 0.440524i | \(-0.854793\pi\) |
−0.0673658 | + | 0.997728i | \(0.521459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.62772 | + | 9.74749i | −0.231886 | + | 0.401639i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.46410 | + | 2.00000i | −0.142374 | + | 0.0821995i | ||||
\(593\) | − | 19.7228i | − | 0.809919i | −0.914335 | − | 0.404959i | \(-0.867286\pi\) | ||
0.914335 | − | 0.404959i | \(-0.132714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.941578 | + | 1.63086i | 0.0385685 | + | 0.0668027i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.01544 | + | 4.62772i | 0.327776 | + | 0.189241i | ||||
\(599\) | 1.88316 | − | 3.26172i | 0.0769437 | − | 0.133270i | −0.824986 | − | 0.565153i | \(-0.808817\pi\) |
0.901930 | + | 0.431883i | \(0.142151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.930703 | + | 1.61203i | 0.0379642 | + | 0.0657559i | 0.884383 | − | 0.466762i | \(-0.154579\pi\) |
−0.846419 | + | 0.532517i | \(0.821246\pi\) | |||||||
\(602\) | − | 18.9783i | − | 0.773496i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6896 | − | 9.05842i | −0.636823 | − | 0.367670i | 0.146567 | − | 0.989201i | \(-0.453178\pi\) |
−0.783390 | + | 0.621531i | \(0.786511\pi\) | |||||||
\(608\) | −2.05446 | − | 1.18614i | −0.0833192 | − | 0.0481044i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.7228 | −2.01157 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.2337i | − | 1.38269i | −0.722527 | − | 0.691343i | \(-0.757019\pi\) | ||
0.722527 | − | 0.691343i | \(-0.242981\pi\) | |||||||
\(614\) | 0.616844 | + | 1.06841i | 0.0248938 | + | 0.0431173i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.37228 | + | 12.7692i | −0.297038 | + | 0.514484i | ||||
\(617\) | −4.22894 | − | 2.44158i | −0.170251 | − | 0.0982942i | 0.412453 | − | 0.910979i | \(-0.364672\pi\) |
−0.582704 | + | 0.812684i | \(0.698005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4416 | − | 18.0853i | −0.419682 | − | 0.726911i | 0.576225 | − | 0.817291i | \(-0.304525\pi\) |
−0.995907 | + | 0.0903798i | \(0.971192\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.7446i | 0.831781i | ||||||||
\(623\) | 47.0689 | − | 27.1753i | 1.88578 | − | 1.08875i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.81386 | + | 3.14170i | −0.0724964 | + | 0.125567i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.84096 | − | 3.37228i | 0.233080 | − | 0.134569i | ||||
\(629\) | 6.51087 | 0.259606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7228 | −0.944390 | −0.472195 | − | 0.881494i | \(-0.656538\pi\) | ||||
−0.472195 | + | 0.881494i | \(0.656538\pi\) | |||||||
\(632\) | 1.73205 | − | 1.00000i | 0.0688973 | − | 0.0397779i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.37228 | + | 2.37686i | −0.0545003 | + | 0.0943972i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.5383 | + | 14.7446i | −1.01187 | + | 0.584201i | ||||
\(638\) | 6.00000i | 0.237542i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | − | 33.7750i | −0.770204 | − | 1.33403i | −0.937451 | − | 0.348117i | \(-0.886821\pi\) |
0.167247 | − | 0.985915i | \(-0.446512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.52628 | + | 5.50000i | 0.375680 | + | 0.216899i | 0.675937 | − | 0.736959i | \(-0.263739\pi\) |
−0.300257 | + | 0.953858i | \(0.597072\pi\) | |||||||
\(644\) | −2.31386 | + | 4.00772i | −0.0911788 | + | 0.157926i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.93070 | + | 3.34408i | 0.0759625 | + | 0.131571i | ||||
\(647\) | 39.0951i | 1.53699i | 0.639858 | + | 0.768493i | \(0.278993\pi\) | ||||
−0.639858 | + | 0.768493i | \(0.721007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.1168 | 0.750402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.6101 | + | 10.7446i | 0.728829 | + | 0.420790i | ||||
\(653\) | −17.0805 | − | 9.86141i | −0.668410 | − | 0.385907i | 0.127064 | − | 0.991895i | \(-0.459445\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 24.8614i | − | 0.969199i | ||||||
\(659\) | −8.74456 | − | 15.1460i | −0.340640 | − | 0.590005i | 0.643912 | − | 0.765100i | \(-0.277310\pi\) |
−0.984552 | + | 0.175094i | \(0.943977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.11684 | − | 10.5947i | 0.237918 | − | 0.412085i | −0.722199 | − | 0.691685i | \(-0.756868\pi\) |
0.960117 | + | 0.279600i | \(0.0902018\pi\) | |||||||
\(662\) | −14.0588 | − | 8.11684i | −0.546410 | − | 0.315470i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.68614 | − | 6.38458i | −0.143050 | − | 0.247770i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88316i | 0.0729161i | ||||||||
\(668\) | 11.5807 | − | 6.68614i | 0.448072 | − | 0.258695i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7446 | − | 30.7345i | 0.685021 | − | 1.18649i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.66025 | − | 5.00000i | 0.333828 | − | 0.192736i | −0.323711 | − | 0.946156i | \(-0.604931\pi\) |
0.657539 | + | 0.753420i | \(0.271597\pi\) | |||||||
\(674\) | 2.37228 | 0.0913769 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32.4891 | 1.24958 | ||||||||
\(677\) | −11.8843 | + | 6.86141i | −0.456751 | + | 0.263705i | −0.710677 | − | 0.703518i | \(-0.751611\pi\) |
0.253926 | + | 0.967224i | \(0.418278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1168 | + | 24.4511i | −0.541755 | + | 0.938347i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.9653 | − | 10.3723i | 0.687928 | − | 0.397175i | ||||
\(683\) | − | 30.0951i | − | 1.15156i | −0.817606 | − | 0.575778i | \(-0.804699\pi\) | ||
0.817606 | − | 0.575778i | \(-0.195301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.43070 | + | 7.67420i | 0.169165 | + | 0.293002i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.87375 | − | 2.81386i | −0.185810 | − | 0.107277i | ||||
\(689\) | −38.7446 | + | 67.1076i | −1.47605 | + | 2.55659i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1168 | + | 31.3793i | 0.689197 | + | 1.19372i | 0.972098 | + | 0.234575i | \(0.0753700\pi\) |
−0.282901 | + | 0.959149i | \(0.591297\pi\) | |||||||
\(692\) | − | 20.7446i | − | 0.788590i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.88316 | −0.185362 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.22894 | − | 2.44158i | −0.160182 | − | 0.0924814i | ||||
\(698\) | 15.6896 | + | 9.05842i | 0.593862 | + | 0.342866i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.8614 | −1.61885 | −0.809426 | − | 0.587221i | \(-0.800222\pi\) | ||||
−0.809426 | + | 0.587221i | \(0.800222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.48913i | − | 0.357889i | ||||||
\(704\) | 2.18614 | + | 3.78651i | 0.0823933 | + | 0.142709i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6753 | + | 18.4901i | −0.401769 | + | 0.695884i | ||||
\(707\) | 8.01544 | + | 4.62772i | 0.301452 | + | 0.174043i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.43070 | + | 2.47805i | 0.0537312 | + | 0.0930652i | 0.891640 | − | 0.452745i | \(-0.149555\pi\) |
−0.837909 | + | 0.545810i | \(0.816222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 16.1168i | − | 0.604004i | ||||||
\(713\) | 5.63858 | − | 3.25544i | 0.211167 | − | 0.121917i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.37228 | + | 12.7692i | −0.275515 | + | 0.477206i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.1460 | + | 8.74456i | −0.565245 | + | 0.326344i | ||||
\(719\) | −3.76631 | −0.140460 | −0.0702299 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702299 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.9565 | −2.00945 | ||||||||
\(722\) | −11.5807 | + | 6.68614i | −0.430990 | + | 0.248832i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.4307 | − | 18.0665i | 0.387654 | − | 0.671436i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.6896 | − | 9.05842i | 0.581897 | − | 0.335958i | −0.179990 | − | 0.983668i | \(-0.557607\pi\) |
0.761887 | + | 0.647710i | \(0.224273\pi\) | |||||||
\(728\) | 22.7446i | 0.842970i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.58017 | + | 7.93309i | 0.169404 | + | 0.293416i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.202380 | − | 0.116844i | −0.00747506 | − | 0.00431573i | 0.496258 | − | 0.868175i | \(-0.334707\pi\) |
−0.503733 | + | 0.863859i | \(0.668040\pi\) | |||||||
\(734\) | −8.00000 | + | 13.8564i | −0.295285 | + | 0.511449i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.686141 | + | 1.18843i | 0.0252915 | + | 0.0438061i | ||||
\(737\) | − | 30.6060i | − | 1.12739i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.1168 | 1.51251 | 0.756254 | − | 0.654278i | \(-0.227028\pi\) | ||||
0.756254 | + | 0.654278i | \(0.227028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.5538 | − | 19.3723i | −1.23180 | − | 0.711179i | ||||
\(743\) | −6.82701 | − | 3.94158i | −0.250459 | − | 0.144602i | 0.369516 | − | 0.929225i | \(-0.379524\pi\) |
−0.619974 | + | 0.784622i | \(0.712857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.4891 | −0.567097 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 7.11684i | − | 0.260218i | ||||||
\(749\) | −14.3139 | − | 24.7923i | −0.523017 | − | 0.905892i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.11684 | + | 14.0588i | −0.296188 | + | 0.513012i | −0.975261 | − | 0.221059i | \(-0.929049\pi\) |
0.679073 | + | 0.734071i | \(0.262382\pi\) | |||||||
\(752\) | −6.38458 | − | 3.68614i | −0.232822 | − | 0.134420i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.62772 | + | 8.01544i | 0.168532 | + | 0.291905i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.0000i | − | 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | −15.4684 | + | 8.93070i | −0.561839 | + | 0.324378i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.5475 | + | 44.2496i | −0.926098 | + | 1.60405i | −0.136312 | + | 0.990666i | \(0.543525\pi\) |
−0.789786 | + | 0.613383i | \(0.789808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.8945 | + | 25.9198i | −1.62529 | + | 0.938361i | ||||
\(764\) | 17.4891 | 0.632734 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.9783 | 0.830238 | ||||||||
\(767\) | 25.5383 | − | 14.7446i | 0.922136 | − | 0.532395i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.4307 | + | 40.5832i | −0.844933 | + | 1.46347i | 0.0407468 | + | 0.999170i | \(0.487026\pi\) |
−0.885680 | + | 0.464297i | \(0.846307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.2877 | − | 10.5584i | 0.658190 | − | 0.380006i | ||||
\(773\) | 3.25544i | 0.117090i | 0.998285 | + | 0.0585450i | \(0.0186461\pi\) | ||||
−0.998285 | + | 0.0585450i | \(0.981354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.18614 | + | 7.25061i | 0.150274 | + | 0.260282i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.00772 | + | 2.31386i | 0.143684 | + | 0.0829559i | ||||
\(779\) | −3.55842 | + | 6.16337i | −0.127494 | + | 0.220826i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1168 | − | 22.7190i | −0.469358 | − | 0.812951i | ||||
\(782\) | − | 2.23369i | − | 0.0798765i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.37228 | −0.156153 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.2487 | + | 14.0000i | 0.864373 | + | 0.499046i | 0.865474 | − | 0.500953i | \(-0.167017\pi\) |
−0.00110111 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(788\) | 4.75372 | + | 2.74456i | 0.169344 | + | 0.0977710i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9783 | −0.390342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 54.7446i | − | 1.94404i | ||||||
\(794\) | 11.3723 | + | 19.6974i | 0.403587 | + | 0.699033i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.74456 | + | 11.6819i | −0.239055 | + | 0.414055i | ||||
\(797\) | 12.7692 | + | 7.37228i | 0.452307 | + | 0.261140i | 0.708804 | − | 0.705405i | \(-0.249235\pi\) |
−0.256497 | + | 0.966545i | \(0.582568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | + | 10.3923i | 0.212265 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.11684i | 0.0394371i | ||||||||
\(803\) | −11.8020 | + | 6.81386i | −0.416482 | + | 0.240456i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.0000 | − | 27.7128i | 0.563576 | − | 0.976142i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.37686 | − | 1.37228i | 0.0836177 | − | 0.0482767i | ||||
\(809\) | 39.3505 | 1.38349 | 0.691746 | − | 0.722141i | \(-0.256842\pi\) | ||||
0.691746 | + | 0.722141i | \(0.256842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.62772 | 0.127386 | 0.0636932 | − | 0.997970i | \(-0.479712\pi\) | ||||
0.0636932 | + | 0.997970i | \(0.479712\pi\) | |||||||
\(812\) | −4.00772 | + | 2.31386i | −0.140643 | + | 0.0812005i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.74456 | + | 15.1460i | −0.306497 | + | 0.530868i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5619 | − | 6.67527i | 0.404500 | − | 0.233538i | ||||
\(818\) | − | 17.8614i | − | 0.624509i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.9198 | − | 20.6457i | −0.416005 | − | 0.720542i | 0.579528 | − | 0.814952i | \(-0.303237\pi\) |
−0.995533 | + | 0.0944104i | \(0.969903\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7330 | − | 12.5475i | −0.757564 | − | 0.437380i | 0.0708562 | − | 0.997487i | \(-0.477427\pi\) |
−0.828421 | + | 0.560107i | \(0.810760\pi\) | |||||||
\(824\) | −8.00000 | + | 13.8564i | −0.278693 | + | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.37228 | + | 12.7692i | 0.256514 | + | 0.444296i | ||||
\(827\) | − | 36.8614i | − | 1.28180i | −0.767626 | − | 0.640898i | \(-0.778562\pi\) | ||
0.767626 | − | 0.640898i | \(-0.221438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.1168 | 1.74063 | 0.870315 | − | 0.492496i | \(-0.163915\pi\) | ||||
0.870315 | + | 0.492496i | \(0.163915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.84096 | + | 3.37228i | 0.202499 | + | 0.116913i | ||||
\(833\) | 6.16337 | + | 3.55842i | 0.213548 | + | 0.123292i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.3723 | −0.358733 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.7228i | 0.888580i | ||||||||
\(839\) | −4.88316 | − | 8.45787i | −0.168585 | − | 0.291998i | 0.769337 | − | 0.638843i | \(-0.220587\pi\) |
−0.937923 | + | 0.346844i | \(0.887253\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5584 | − | 23.4839i | 0.467532 | − | 0.809789i | ||||
\(842\) | −26.3855 | − | 15.2337i | −0.909305 | − | 0.524988i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.37228 | − | 16.2333i | −0.322607 | − | 0.558772i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.3723i | 0.940523i | ||||||||
\(848\) | −9.94987 | + | 5.74456i | −0.341680 | + | 0.197269i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.74456 | + | 4.75372i | −0.0940824 | + | 0.162955i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.3793 | − | 18.1168i | 1.07441 | − | 0.620309i | 0.145024 | − | 0.989428i | \(-0.453674\pi\) |
0.929382 | + | 0.369119i | \(0.120341\pi\) | |||||||
\(854\) | 27.3723 | 0.936660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.48913 | −0.290152 | ||||||||
\(857\) | −0.442430 | + | 0.255437i | −0.0151131 | + | 0.00872557i | −0.507538 | − | 0.861630i | \(-0.669444\pi\) |
0.492424 | + | 0.870355i | \(0.336111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.55842 | + | 14.8236i | −0.292010 | + | 0.505775i | −0.974285 | − | 0.225320i | \(-0.927657\pi\) |
0.682275 | + | 0.731095i | \(0.260991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.13058 | + | 4.11684i | −0.242869 | + | 0.140220i | ||||
\(863\) | − | 2.39403i | − | 0.0814938i | −0.999170 | − | 0.0407469i | \(-0.987026\pi\) | ||
0.999170 | − | 0.0407469i | \(-0.0129737\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.18614 | − | 5.51856i | −0.108269 | − | 0.187528i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.8564 | + | 8.00000i | 0.470317 | + | 0.271538i | ||||
\(869\) | 4.37228 | − | 7.57301i | 0.148319 | − | 0.256897i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.6060 | − | 40.8867i | −0.799858 | − | 1.38539i | ||||
\(872\) | 15.3723i | 0.520571i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.25544 | −0.110117 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.1392 | − | 17.9783i | −1.05150 | − | 0.607082i | −0.128429 | − | 0.991719i | \(-0.540994\pi\) |
−0.923068 | + | 0.384636i | \(0.874327\pi\) | |||||||
\(878\) | −15.7908 | − | 9.11684i | −0.532915 | − | 0.307679i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.3505 | 0.820390 | 0.410195 | − | 0.911998i | \(-0.365461\pi\) | ||||
0.410195 | + | 0.911998i | \(0.365461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.7228i | 1.50504i | 0.658568 | + | 0.752521i | \(0.271163\pi\) | ||||
−0.658568 | + | 0.752521i | \(0.728837\pi\) | |||||||
\(884\) | −5.48913 | − | 9.50744i | −0.184619 | − | 0.319770i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.75544 | + | 3.04051i | −0.0589751 | + | 0.102148i | ||||
\(887\) | 17.0805 | + | 9.86141i | 0.573506 | + | 0.331114i | 0.758548 | − | 0.651617i | \(-0.225909\pi\) |
−0.185043 | + | 0.982730i | \(0.559242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.6861 | − | 23.7051i | −0.459018 | − | 0.795043i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.62772i | 0.221912i | ||||||||
\(893\) | 15.1460 | − | 8.74456i | 0.506842 | − | 0.292626i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.68614 | + | 2.92048i | −0.0563300 | + | 0.0975664i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.54023 | − | 4.93070i | 0.284991 | − | 0.164540i | ||||
\(899\) | 6.51087 | 0.217150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.7011 | 0.623023 | ||||||||
\(902\) | 11.3595 | − | 6.55842i | 0.378231 | − | 0.218372i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.62772 | + | 2.81929i | −0.0541371 | + | 0.0937682i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.06218 | + | 3.50000i | −0.201291 | + | 0.116216i | −0.597258 | − | 0.802049i | \(-0.703743\pi\) |
0.395966 | + | 0.918265i | \(0.370410\pi\) | |||||||
\(908\) | 19.1168i | 0.634415i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0000 | − | 36.3731i | −0.695761 | − | 1.20509i | −0.969923 | − | 0.243410i | \(-0.921734\pi\) |
0.274162 | − | 0.961683i | \(-0.411599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.9152 | − | 16.1168i | −0.923858 | − | 0.533390i | ||||
\(914\) | 6.44158 | − | 11.1571i | 0.213068 | − | 0.369045i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.31386 | − | 10.9359i | −0.208616 | − | 0.361333i | ||||
\(917\) | 9.25544i | 0.305641i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4674 | 0.873078 | 0.436539 | − | 0.899685i | \(-0.356204\pi\) | ||||
0.436539 | + | 0.899685i | \(0.356204\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.63086 | + | 0.941578i | 0.0537095 | + | 0.0310092i | ||||
\(923\) | −35.0458 | − | 20.2337i | −1.15355 | − | 0.666000i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.37228i | 0.0450473i | ||||||||
\(929\) | −25.9783 | − | 44.9956i | −0.852319 | − | 1.47626i | −0.879110 | − | 0.476618i | \(-0.841862\pi\) |
0.0267916 | − | 0.999641i | \(-0.491471\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.18614 | − | 8.98266i | 0.169969 | − | 0.294395i | ||||
\(932\) | 6.16337 | + | 3.55842i | 0.201888 | + | 0.116560i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.5584 | − | 37.3403i | −0.705413 | − | 1.22181i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.7228i | 1.29769i | 0.760922 | + | 0.648844i | \(0.224747\pi\) | ||||
−0.760922 | + | 0.648844i | \(0.775253\pi\) | |||||||
\(938\) | 20.4434 | − | 11.8030i | 0.667500 | − | 0.385381i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.6861 | − | 37.5615i | 0.706948 | − | 1.22447i | −0.259036 | − | 0.965868i | \(-0.583405\pi\) |
0.965984 | − | 0.258602i | \(-0.0832619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.56529 | − | 2.05842i | 0.116102 | − | 0.0670314i | ||||
\(944\) | 4.37228 | 0.142306 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.6060 | −0.800009 | ||||||||
\(947\) | 30.0708 | − | 17.3614i | 0.977171 | − | 0.564170i | 0.0757561 | − | 0.997126i | \(-0.475863\pi\) |
0.901415 | + | 0.432956i | \(0.142530\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.5109 | + | 18.2054i | −0.341197 | + | 0.590971i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.75372 | − | 2.74456i | 0.154069 | − | 0.0889518i | ||||
\(953\) | 2.13859i | 0.0692758i | 0.999400 | + | 0.0346379i | \(0.0110278\pi\) | ||||
−0.999400 | + | 0.0346379i | \(0.988972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.62772 | − | 2.81929i | −0.0526442 | − | 0.0911824i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.442430 | + | 0.255437i | 0.0142943 | + | 0.00825281i | ||||
\(959\) | 32.2337 | − | 55.8304i | 1.04088 | − | 1.80286i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.24456 | + | 7.35180i | 0.136921 | + | 0.237155i | ||||
\(962\) | 26.9783i | 0.869814i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.4891 | 0.402248 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.2781 | − | 18.0584i | −1.00584 | − | 0.580720i | −0.0958662 | − | 0.995394i | \(-0.530562\pi\) |
−0.909970 | + | 0.414675i | \(0.863895\pi\) | |||||||
\(968\) | 7.02939 | + | 4.05842i | 0.225933 | + | 0.130443i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9783 | 0.737407 | 0.368704 | − | 0.929547i | \(-0.379802\pi\) | ||||
0.368704 | + | 0.929547i | \(0.379802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.97825i | − | 0.0954783i | ||||||
\(974\) | −6.37228 | − | 11.0371i | −0.204181 | − | 0.353652i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.05842 | − | 7.02939i | 0.129907 | − | 0.225005i | ||||
\(977\) | −19.8174 | − | 11.4416i | −0.634015 | − | 0.366049i | 0.148291 | − | 0.988944i | \(-0.452623\pi\) |
−0.782305 | + | 0.622895i | \(0.785956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.2337 | − | 61.0265i | −1.12607 | − | 1.95042i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.6060i | 1.16814i | ||||||||
\(983\) | −11.1383 | + | 6.43070i | −0.355257 | + | 0.205108i | −0.666998 | − | 0.745059i | \(-0.732421\pi\) |
0.311741 | + | 0.950167i | \(0.399088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.11684 | − | 1.93443i | 0.0355676 | − | 0.0616048i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.8564 | + | 8.00000i | −0.440831 | + | 0.254514i | ||||
\(989\) | −7.72281 | −0.245571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2337 | 0.515680 | 0.257840 | − | 0.966188i | \(-0.416989\pi\) | ||||
0.257840 | + | 0.966188i | \(0.416989\pi\) | |||||||
\(992\) | 4.10891 | − | 2.37228i | 0.130458 | − | 0.0753200i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.1168 | − | 17.5229i | 0.320887 | − | 0.555792i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.1244 | − | 7.00000i | 0.383982 | − | 0.221692i | −0.295567 | − | 0.955322i | \(-0.595509\pi\) |
0.679549 | + | 0.733630i | \(0.262175\pi\) | |||||||
\(998\) | − | 15.1168i | − | 0.478515i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))