Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(289,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.r (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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-0.180407 - 0.673288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.289 |
Dual form | 1728.2.r.f.1441.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.17731 | + | 3.77121i | −0.822944 | + | 1.42538i | 0.0805357 | + | 0.996752i | \(0.474337\pi\) |
−0.903480 | + | 0.428630i | \(0.858996\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.05328 | − | 2.91751i | −1.52362 | − | 0.879663i | −0.999609 | − | 0.0279511i | \(-0.991102\pi\) |
−0.524011 | − | 0.851712i | \(-0.675565\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.48133 | − | 2.00994i | 0.965546 | − | 0.557458i | 0.0676707 | − | 0.997708i | \(-0.478443\pi\) |
0.897876 | + | 0.440249i | \(0.145110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70739 | −0.414103 | −0.207051 | − | 0.978330i | \(-0.566387\pi\) | ||||
−0.207051 | + | 0.978330i | \(0.566387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.32123 | − | 5.75253i | −0.692523 | − | 1.19949i | −0.971008 | − | 0.239045i | \(-0.923166\pi\) |
0.278485 | − | 0.960441i | \(-0.410168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.06108 | − | 2.34467i | −0.754124 | − | 0.435394i | 0.0730578 | − | 0.997328i | \(-0.476724\pi\) |
−0.827182 | + | 0.561934i | \(0.810058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43071 | − | 4.21012i | −0.436569 | − | 0.756160i | 0.560853 | − | 0.827915i | \(-0.310473\pi\) |
−0.997422 | + | 0.0717553i | \(0.977140\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.54241i | 1.27490i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.75194i | − | 0.945613i | −0.881166 | − | 0.472807i | \(-0.843241\pi\) | ||
0.881166 | − | 0.472807i | \(-0.156759\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.646305 | − | 1.11943i | −0.100936 | − | 0.174826i | 0.811135 | − | 0.584860i | \(-0.198850\pi\) |
−0.912071 | + | 0.410033i | \(0.865517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.06782 | + | 1.77121i | 0.467838 | + | 0.270106i | 0.715334 | − | 0.698783i | \(-0.246274\pi\) |
−0.247496 | + | 0.968889i | \(0.579608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.30669 | − | 9.19145i | 0.774060 | − | 1.34071i | −0.161262 | − | 0.986912i | \(-0.551556\pi\) |
0.935322 | − | 0.353799i | \(-0.115110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.98133 | − | 10.3600i | −0.854475 | − | 1.47999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.506816i | 0.0696166i | 0.999394 | + | 0.0348083i | \(0.0110821\pi\) | ||||
−0.999394 | + | 0.0348083i | \(0.988918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.1066 | −1.36277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.62152 | − | 0.936184i | 0.211104 | − | 0.121881i | −0.390721 | − | 0.920509i | \(-0.627774\pi\) |
0.601824 | + | 0.798629i | \(0.294441\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.06108 | − | 0.612617i | −0.135858 | − | 0.0784376i | 0.430531 | − | 0.902576i | \(-0.358326\pi\) |
−0.566388 | + | 0.824138i | \(0.691660\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.48133 | − | 6.02983i | 0.431805 | − | 0.747909i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.36811 | − | 0.789879i | 0.167141 | − | 0.0964990i | −0.414096 | − | 0.910233i | \(-0.635902\pi\) |
0.581237 | + | 0.813734i | \(0.302569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.88549 | −1.17319 | −0.586596 | − | 0.809880i | \(-0.699532\pi\) | ||||
−0.586596 | + | 0.809880i | \(0.699532\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96265 | −0.931958 | −0.465979 | − | 0.884796i | \(-0.654298\pi\) | ||||
−0.465979 | + | 0.884796i | \(0.654298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.0051 | − | 12.7046i | 2.50771 | − | 1.44783i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.03339 | + | 1.78988i | −0.116265 | + | 0.201377i | −0.918285 | − | 0.395921i | \(-0.870426\pi\) |
0.802020 | + | 0.597298i | \(0.203759\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.33577 | + | 0.771205i | 0.146619 | + | 0.0846508i | 0.571515 | − | 0.820592i | \(-0.306356\pi\) |
−0.424896 | + | 0.905242i | \(0.639689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.56108 | + | 1.47864i | −0.277789 | + | 0.160381i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.96265 | −0.420040 | −0.210020 | − | 0.977697i | \(-0.567353\pi\) | ||||
−0.210020 | + | 0.977697i | \(0.567353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5051i | 1.83503i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.73205 | + | 3.00000i | 0.177705 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.06108 | + | 5.30195i | −0.310806 | + | 0.538332i | −0.978537 | − | 0.206071i | \(-0.933932\pi\) |
0.667731 | + | 0.744403i | \(0.267266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0051 | + | 5.77643i | 0.995541 | + | 0.574776i | 0.906926 | − | 0.421290i | \(-0.138423\pi\) |
0.0886151 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.110533 | − | 0.191448i | −0.0108911 | − | 0.0188639i | 0.860528 | − | 0.509402i | \(-0.170133\pi\) |
−0.871420 | + | 0.490538i | \(0.836800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.329957i | 0.0318982i | 0.999873 | + | 0.0159491i | \(0.00507697\pi\) | ||||
−0.999873 | + | 0.0159491i | \(0.994923\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.9253i | − | 1.71693i | −0.512873 | − | 0.858465i | \(-0.671419\pi\) | ||
0.512873 | − | 0.858465i | \(-0.328581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.04241 | − | 15.6619i | −0.850638 | − | 1.47335i | −0.880633 | − | 0.473799i | \(-0.842882\pi\) |
0.0299946 | − | 0.999550i | \(-0.490451\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.96368 | − | 5.75253i | −0.929118 | − | 0.536426i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.71751 | − | 6.43892i | 0.340784 | − | 0.590254i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5237 | + | 19.9597i | 1.04761 | + | 1.81452i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.57568 | −0.406026 | −0.203013 | − | 0.979176i | \(-0.565073\pi\) | ||||
−0.203013 | + | 0.979176i | \(0.565073\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7281 | + | 6.77121i | −1.02469 | + | 0.591603i | −0.915458 | − | 0.402414i | \(-0.868171\pi\) |
−0.109228 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.54241 | − | 4.35461i | −0.654010 | − | 0.377593i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1887 | + | 19.3794i | −0.955917 | + | 1.65570i | −0.223660 | + | 0.974667i | \(0.571800\pi\) |
−0.732257 | + | 0.681029i | \(0.761533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.99602 | + | 5.77121i | −0.847851 | + | 0.489507i | −0.859925 | − | 0.510420i | \(-0.829490\pi\) |
0.0120739 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.4561 | −1.96150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.12217 | −0.674509 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.93892 | − | 1.11943i | 0.158842 | − | 0.0917076i | −0.418472 | − | 0.908230i | \(-0.637434\pi\) |
0.577314 | + | 0.816522i | \(0.304101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.51738 | − | 14.7525i | 0.693134 | − | 1.20054i | −0.277671 | − | 0.960676i | \(-0.589563\pi\) |
0.970806 | − | 0.239868i | \(-0.0771041\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.29214 | − | 4.21012i | −0.585719 | − | 0.338165i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0424108 | + | 0.0244859i | −0.00338475 | + | 0.00195419i | −0.501691 | − | 0.865047i | \(-0.667289\pi\) |
0.498307 | + | 0.867001i | \(0.333955\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.9253 | 2.27963 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.0848i | − | 1.49484i | −0.664353 | − | 0.747419i | \(-0.731293\pi\) | ||
0.664353 | − | 0.747419i | \(-0.268707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.99602 | + | 17.3136i | 0.773515 | + | 1.33977i | 0.935625 | + | 0.352995i | \(0.114837\pi\) |
−0.162110 | + | 0.986773i | \(0.551830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.57976 | − | 2.73622i | 0.121520 | − | 0.210478i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5000 | − | 6.06218i | −0.798300 | − | 0.460899i | 0.0445762 | − | 0.999006i | \(-0.485806\pi\) |
−0.842876 | + | 0.538107i | \(0.819140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.35461 | − | 7.54241i | −0.329178 | − | 0.570153i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.75194i | 0.427538i | 0.976884 | + | 0.213769i | \(0.0685740\pi\) | ||||
−0.976884 | + | 0.213769i | \(0.931426\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.98133 | − | 8.62791i | −0.366234 | − | 0.634337i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.62791 | + | 4.98133i | 0.630935 | + | 0.364271i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.110533 | + | 0.191448i | −0.00799786 | + | 0.0138527i | −0.869997 | − | 0.493058i | \(-0.835879\pi\) |
0.861999 | + | 0.506910i | \(0.169212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.02374 | − | 15.6296i | −0.649543 | − | 1.12504i | −0.983232 | − | 0.182358i | \(-0.941627\pi\) |
0.333689 | − | 0.942683i | \(-0.391706\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.82080i | − | 0.699703i | −0.936805 | − | 0.349852i | \(-0.886232\pi\) | ||
0.936805 | − | 0.349852i | \(-0.113768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.604760 | 0.0428703 | 0.0214352 | − | 0.999770i | \(-0.493176\pi\) | ||||
0.0214352 | + | 0.999770i | \(0.493176\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.6844 | − | 10.2101i | 1.24120 | − | 0.716610i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.93892 | − | 1.11943i | −0.135420 | − | 0.0781846i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.83502 | − | 10.1066i | 0.403617 | − | 0.699085i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.363941 | − | 0.210121i | 0.0250547 | − | 0.0144654i | −0.487420 | − | 0.873167i | \(-0.662062\pi\) |
0.512475 | + | 0.858702i | \(0.328729\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.13564 | 0.418447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.1696 | 1.43709 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.94398 | + | 3.43176i | −0.399835 | + | 0.230845i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3933 | + | 19.7339i | −0.762955 | + | 1.32148i | 0.178366 | + | 0.983964i | \(0.442919\pi\) |
−0.941321 | + | 0.337513i | \(0.890414\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.2494 | + | 5.91751i | 0.680279 | + | 0.392759i | 0.799960 | − | 0.600053i | \(-0.204854\pi\) |
−0.119681 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5848 | − | 7.84320i | 0.897710 | − | 0.518293i | 0.0212537 | − | 0.999774i | \(-0.493234\pi\) |
0.876457 | + | 0.481481i | \(0.159901\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.829557 | 0.0543461 | 0.0271731 | − | 0.999631i | \(-0.491349\pi\) | ||||
0.0271731 | + | 0.999631i | \(0.491349\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 18.3829i | − | 1.19917i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.60698 | + | 6.24747i | 0.233316 | + | 0.404115i | 0.958782 | − | 0.284143i | \(-0.0917090\pi\) |
−0.725466 | + | 0.688258i | \(0.758376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4627 | − | 18.1218i | 0.673959 | − | 1.16733i | −0.302813 | − | 0.953050i | \(-0.597926\pi\) |
0.976772 | − | 0.214281i | \(-0.0687408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.9440 | − | 10.3600i | −1.14640 | − | 0.661874i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.01989 | + | 6.96265i | 0.255779 | + | 0.443023i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.2553i | 1.27850i | 0.768999 | + | 0.639250i | \(0.220755\pi\) | ||||
−0.768999 | + | 0.639250i | \(0.779245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.7588i | 2.43675i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.37237 | − | 5.84111i | −0.210363 | − | 0.364359i | 0.741465 | − | 0.670991i | \(-0.234131\pi\) |
−0.951828 | + | 0.306632i | \(0.900798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6917 | + | 12.5237i | 1.34786 | + | 0.778187i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2067 | − | 22.8747i | 0.814361 | − | 1.41051i | −0.0954250 | − | 0.995437i | \(-0.530421\pi\) |
0.909786 | − | 0.415078i | \(-0.136246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.438916 | + | 0.760225i | 0.0269624 | + | 0.0467002i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1704i | 1.41272i | 0.707851 | + | 0.706362i | \(0.249665\pi\) | ||||
−0.707851 | + | 0.706362i | \(0.750335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7626 | 1.07900 | 0.539502 | − | 0.841984i | \(-0.318613\pi\) | ||||
0.539502 | + | 0.841984i | \(0.318613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.1066 | − | 5.83502i | 0.609448 | − | 0.351865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.04241 | + | 5.22064i | 0.543306 | + | 0.313678i | 0.746418 | − | 0.665478i | \(-0.231772\pi\) |
−0.203112 | + | 0.979156i | \(0.565106\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4440 | + | 23.2857i | −0.802001 | + | 1.38911i | 0.116297 | + | 0.993215i | \(0.462898\pi\) |
−0.918297 | + | 0.395891i | \(0.870436\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1317 | − | 9.31362i | 0.958927 | − | 0.553637i | 0.0630847 | − | 0.998008i | \(-0.479906\pi\) |
0.895843 | + | 0.444371i | \(0.146573\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.62882 | 0.332259 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0848 | −0.828519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00506 | + | 0.580274i | −0.0587165 | + | 0.0339000i | −0.529071 | − | 0.848578i | \(-0.677459\pi\) |
0.470354 | + | 0.882478i | \(0.344126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.62152 | − | 2.80855i | 0.0944084 | − | 0.163520i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.1245 | − | 13.3510i | −1.33733 | − | 0.772106i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3592 | + | 7.71291i | −0.770009 | + | 0.444565i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.12217 | −0.121515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0848i | 1.08923i | 0.838687 | + | 0.544614i | \(0.183324\pi\) | ||||
−0.838687 | + | 0.544614i | \(0.816676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.56009 | + | 9.63036i | 0.315284 | + | 0.546088i | 0.979498 | − | 0.201455i | \(-0.0645669\pi\) |
−0.664214 | + | 0.747543i | \(0.731234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4627 | + | 23.3180i | −0.760954 | + | 1.31801i | 0.181405 | + | 0.983408i | \(0.441935\pi\) |
−0.942359 | + | 0.334603i | \(0.891398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4440 | − | 11.2260i | −1.09208 | − | 0.630514i | −0.157953 | − | 0.987447i | \(-0.550489\pi\) |
−0.934130 | + | 0.356932i | \(0.883823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.6812 | + | 23.6965i | 0.765999 | + | 1.32675i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.41478i | − | 0.190003i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.03978i | 0.445967i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.1086 | + | 40.0252i | 1.27402 | + | 2.20666i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5634 | − | 11.2949i | −1.07530 | − | 0.620826i | −0.145677 | − | 0.989332i | \(-0.546536\pi\) |
−0.929625 | + | 0.368506i | \(0.879869\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.36811 | − | 2.36964i | 0.0747478 | − | 0.129467i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.04241 | + | 12.1978i | 0.383625 | + | 0.664457i | 0.991577 | − | 0.129516i | \(-0.0413423\pi\) |
−0.607953 | + | 0.793973i | \(0.708009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3665i | 1.53613i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.6104 | 1.16685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.05745 | − | 3.49727i | 0.325181 | − | 0.187743i | −0.328519 | − | 0.944497i | \(-0.606549\pi\) |
0.653699 | + | 0.756754i | \(0.273216\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.16458 | + | 4.71382i | 0.437040 | + | 0.252325i | 0.702341 | − | 0.711840i | \(-0.252138\pi\) |
−0.265301 | + | 0.964166i | \(0.585471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.81128 | + | 6.60134i | −0.202854 | + | 0.351354i | −0.949447 | − | 0.313928i | \(-0.898355\pi\) |
0.746593 | + | 0.665281i | \(0.231688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8282 | + | 8.56108i | −0.787001 | + | 0.454375i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.8344 | −0.571820 | −0.285910 | − | 0.958257i | \(-0.592296\pi\) | ||||
−0.285910 | + | 0.958257i | \(0.592296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9440 | + | 6.89586i | −0.625176 | + | 0.360946i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4747 | − | 19.8747i | 0.598973 | − | 1.03745i | −0.394000 | − | 0.919110i | \(-0.628909\pi\) |
0.992973 | − | 0.118341i | \(-0.0377575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.91131 | − | 1.10349i | −0.0992302 | − | 0.0572906i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0984305 | − | 0.0568289i | 0.00509654 | − | 0.00294249i | −0.497450 | − | 0.867493i | \(-0.665730\pi\) |
0.502546 | + | 0.864550i | \(0.332397\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.8506 | −0.970856 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.2070i | − | 0.832497i | −0.909251 | − | 0.416249i | \(-0.863345\pi\) | ||
0.909251 | − | 0.416249i | \(-0.136655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.03874 | + | 12.1914i | 0.359663 | + | 0.622954i | 0.987904 | − | 0.155064i | \(-0.0495585\pi\) |
−0.628242 | + | 0.778018i | \(0.716225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.0051 | − | 38.1139i | 1.12148 | − | 1.94246i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.0051 | − | 14.4367i | −1.26781 | − | 0.731969i | −0.293234 | − | 0.956041i | \(-0.594732\pi\) |
−0.974573 | + | 0.224072i | \(0.928065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.67063 | + | 9.82181i | 0.286776 | + | 0.496710i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.57976i | 0.180117i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.85934i | − | 0.143506i | −0.997422 | − | 0.0717531i | \(-0.977141\pi\) | ||
0.997422 | − | 0.0717531i | \(-0.0228594\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.7739 | + | 18.6610i | 0.538025 | + | 0.931886i | 0.999010 | + | 0.0444786i | \(0.0141626\pi\) |
−0.460986 | + | 0.887408i | \(0.652504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.9242 | − | 9.77121i | −0.843056 | − | 0.486738i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.7813 | + | 29.0661i | −0.831821 | + | 1.44076i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4627 | + | 18.1218i | 0.517345 | + | 0.896068i | 0.999797 | + | 0.0201454i | \(0.00641290\pi\) |
−0.482452 | + | 0.875922i | \(0.660254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.15344i | 0.401204i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.67153 | 0.131140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9678 | − | 6.33229i | 0.535814 | − | 0.309353i | −0.207567 | − | 0.978221i | \(-0.566554\pi\) |
0.743381 | + | 0.668868i | \(0.233221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1086 | + | 13.3417i | 1.12624 | + | 0.650236i | 0.942987 | − | 0.332829i | \(-0.108003\pi\) |
0.183255 | + | 0.983065i | \(0.441337\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.70739 | − | 2.95729i | 0.0828205 | − | 0.143449i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.62061 | − | 2.66771i | 0.223607 | − | 0.129100i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.6772 | 1.14049 | 0.570246 | − | 0.821474i | \(-0.306848\pi\) | ||||
0.570246 | + | 0.821474i | \(0.306848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.96265 | 0.382661 | 0.191330 | − | 0.981526i | \(-0.438720\pi\) | ||||
0.191330 | + | 0.981526i | \(0.438720\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.5051 | − | 6.64245i | 0.550362 | − | 0.317752i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.33903 | + | 9.24747i | −0.254818 | + | 0.441358i | −0.964846 | − | 0.262816i | \(-0.915349\pi\) |
0.710028 | + | 0.704173i | \(0.248682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.1566 | + | 6.44125i | 0.530065 | + | 0.306033i | 0.741043 | − | 0.671458i | \(-0.234332\pi\) |
−0.210978 | + | 0.977491i | \(0.567665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.94398 | + | 3.43176i | −0.281772 | + | 0.162681i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.547875 | 0.0258558 | 0.0129279 | − | 0.999916i | \(-0.495885\pi\) | ||||
0.0129279 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.54241i | 0.355158i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.1598 | + | 26.2576i | 0.710704 | + | 1.23098i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.90157 | + | 17.1500i | −0.463176 | + | 0.802244i | −0.999117 | − | 0.0420111i | \(-0.986624\pi\) |
0.535941 | + | 0.844255i | \(0.319957\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1833 | + | 7.03400i | 0.567431 | + | 0.327606i | 0.756122 | − | 0.654430i | \(-0.227091\pi\) |
−0.188692 | + | 0.982036i | \(0.560425\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.22954 | − | 10.7899i | −0.289511 | − | 0.501448i | 0.684182 | − | 0.729311i | \(-0.260159\pi\) |
−0.973693 | + | 0.227863i | \(0.926826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 29.3401i | − | 1.35770i | −0.734278 | − | 0.678849i | \(-0.762479\pi\) | ||
0.734278 | − | 0.678849i | \(-0.237521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.87923i | 0.317653i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3350 | − | 17.9008i | −0.475205 | − | 0.823079i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.46410 | − | 2.00000i | −0.158944 | − | 0.0917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.96368 | + | 17.2576i | −0.455252 | + | 0.788520i | −0.998703 | − | 0.0509214i | \(-0.983784\pi\) |
0.543451 | + | 0.839441i | \(0.317118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.5611 | − | 20.0244i | −0.527140 | − | 0.913033i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6039i | 0.481499i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.46828 | −0.338420 | −0.169210 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169210 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.2186 | − | 17.4467i | 1.36375 | − | 0.787359i | 0.373626 | − | 0.927580i | \(-0.378114\pi\) |
0.990120 | + | 0.140220i | \(0.0447811\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.93385 | + | 4.00326i | 0.312285 | + | 0.180298i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.5237 | − | 37.2802i | 0.965472 | − | 1.67225i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.4480 | − | 18.7339i | 1.45257 | − | 0.838643i | 0.453945 | − | 0.891030i | \(-0.350016\pi\) |
0.998627 | + | 0.0523870i | \(0.0166830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.8991 | −0.485968 | −0.242984 | − | 0.970030i | \(-0.578126\pi\) | ||||
−0.242984 | + | 0.970030i | \(0.578126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0101 | 0.890439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.06108 | + | 2.34467i | −0.180004 | + | 0.103926i | −0.587295 | − | 0.809373i | \(-0.699807\pi\) |
0.407290 | + | 0.913299i | \(0.366474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.3371 | − | 30.0288i | 0.766950 | − | 1.32840i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.331598 | − | 0.191448i | −0.0146119 | − | 0.00843621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −53.6323 | + | 30.9646i | −2.35875 | + | 1.36182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.4249 | 1.15770 | 0.578848 | − | 0.815435i | \(-0.303502\pi\) | ||||
0.578848 | + | 0.815435i | \(0.303502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13.8880i | − | 0.607278i | −0.952787 | − | 0.303639i | \(-0.901798\pi\) | ||
0.952787 | − | 0.303639i | \(-0.0982017\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.15018 | + | 7.18832i | 0.180785 | + | 0.313128i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5611 | + | 18.2923i | −0.459178 | + | 0.795319i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.50000 | − | 2.59808i | −0.194917 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.285751 | + | 0.494936i | 0.0123541 | + | 0.0213979i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 69.8023i | 3.00660i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.0161i | − | 1.07553i | −0.843096 | − | 0.537763i | \(-0.819269\pi\) | ||
0.843096 | − | 0.537763i | \(-0.180731\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.5237 | − | 26.8879i | −0.664964 | − | 1.15175i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4236 | + | 7.17277i | 0.531195 | + | 0.306686i | 0.741503 | − | 0.670950i | \(-0.234113\pi\) |
−0.210308 | + | 0.977635i | \(0.567447\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.68934 | − | 8.12217i | 0.199772 | − | 0.346016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | − | 7.79423i | −0.191359 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 32.9912i | − | 1.39788i | −0.715179 | − | 0.698941i | \(-0.753655\pi\) | ||
0.715179 | − | 0.698941i | \(-0.246345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2401 | 0.602292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6459 | + | 12.4973i | −0.912266 | + | 0.526697i | −0.881160 | − | 0.472819i | \(-0.843236\pi\) |
−0.0311065 | + | 0.999516i | \(0.509903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.1272 | − | 15.6619i | −1.14125 | − | 0.658902i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.79261 | + | 4.83694i | −0.117072 | + | 0.202775i | −0.918606 | − | 0.395174i | \(-0.870684\pi\) |
0.801534 | + | 0.597949i | \(0.204018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.83221 | − | 2.78988i | 0.202222 | − | 0.116753i | −0.395470 | − | 0.918479i | \(-0.629418\pi\) |
0.597691 | + | 0.801726i | \(0.296085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.2849 | 0.554019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.04748 | −0.376651 | −0.188326 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188326 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.81675 | + | 3.35830i | −0.241319 | + | 0.139326i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.47864 | − | 2.56108i | 0.0612391 | − | 0.106069i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.24617 | + | 3.60623i | 0.257807 | + | 0.148845i | 0.623334 | − | 0.781956i | \(-0.285778\pi\) |
−0.365527 | + | 0.930801i | \(0.619111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.42024 | − | 4.86143i | 0.346950 | − | 0.200312i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0475 | 1.02858 | 0.514288 | − | 0.857617i | \(-0.328056\pi\) | ||||
0.514288 | + | 0.857617i | \(0.328056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 12.8778i | − | 0.527940i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1026 | − | 34.8187i | −0.821369 | − | 1.42265i | −0.904663 | − | 0.426128i | \(-0.859877\pi\) |
0.0832941 | − | 0.996525i | \(-0.473456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.48133 | − | 9.49394i | 0.223588 | − | 0.387266i | −0.732307 | − | 0.680975i | \(-0.761556\pi\) |
0.955895 | + | 0.293709i | \(0.0948897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.5712 | + | 19.9597i | 1.40552 | + | 0.811477i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2370 | − | 24.6592i | −0.577861 | − | 1.00088i | −0.995724 | − | 0.0923747i | \(-0.970554\pi\) |
0.417863 | − | 0.908510i | \(-0.362779\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 42.6646i | − | 1.72602i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.3632i | − | 0.580125i | −0.957008 | − | 0.290063i | \(-0.906324\pi\) | ||
0.957008 | − | 0.290063i | \(-0.0936761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.316348 | − | 0.547931i | −0.0127357 | − | 0.0220589i | 0.859587 | − | 0.510989i | \(-0.170721\pi\) |
−0.872323 | + | 0.488930i | \(0.837387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9516 | − | 16.7152i | −1.16366 | − | 0.671840i | −0.211482 | − | 0.977382i | \(-0.567829\pi\) |
−0.952179 | + | 0.305542i | \(0.901162\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.62791 | − | 14.9440i | 0.345670 | − | 0.598718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.82080i | 0.391581i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.59765 | −0.302458 | −0.151229 | − | 0.988499i | \(-0.548323\pi\) | ||||
−0.151229 | + | 0.988499i | \(0.548323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.86352 | + | 3.96265i | −0.272370 | + | 0.157253i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.6459 | − | 24.0443i | −1.65007 | − | 0.952669i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.8774 | + | 20.5723i | −0.469130 | + | 0.812558i | −0.999377 | − | 0.0352856i | \(-0.988766\pi\) |
0.530247 | + | 0.847843i | \(0.322099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4236 | + | 7.17277i | −0.489939 | + | 0.282867i | −0.724549 | − | 0.689223i | \(-0.757952\pi\) |
0.234610 | + | 0.972090i | \(0.424619\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.5781 | −1.12352 | −0.561761 | − | 0.827299i | \(-0.689876\pi\) | ||||
−0.561761 | + | 0.827299i | \(0.689876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9253 | −0.428856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7443 | + | 8.51265i | −0.576990 | + | 0.333126i | −0.759936 | − | 0.649997i | \(-0.774770\pi\) |
0.182946 | + | 0.983123i | \(0.441437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7281 | + | 20.3136i | −0.458254 | + | 0.793719i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8209 | + | 6.24747i | 0.421524 | + | 0.243367i | 0.695729 | − | 0.718304i | \(-0.255081\pi\) |
−0.274205 | + | 0.961671i | \(0.588415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.1272 | − | 17.3940i | 1.17181 | − | 0.676547i | 0.217707 | − | 0.976014i | \(-0.430142\pi\) |
0.954107 | + | 0.299467i | \(0.0968090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.0848 | −0.584964 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1487i | 1.20608i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.57463 | + | 6.19145i | 0.137997 | + | 0.239018i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0237 | + | 22.5578i | −0.502028 | + | 0.869538i | 0.497969 | + | 0.867195i | \(0.334079\pi\) |
−0.999997 | + | 0.00234354i | \(0.999254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8829 | + | 16.6755i | 1.11006 | + | 0.640893i | 0.938845 | − | 0.344340i | \(-0.111897\pi\) |
0.171215 | + | 0.985234i | \(0.445231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3298 | − | 23.0880i | −0.511552 | − | 0.886034i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26.4249i | − | 1.01112i | −0.862791 | − | 0.505560i | \(-0.831286\pi\) | ||
0.862791 | − | 0.505560i | \(-0.168714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.7588i | 1.48090i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.01867 | + | 1.76439i | 0.0388084 | + | 0.0672181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6521 | − | 10.1914i | −0.671518 | − | 0.387701i | 0.125134 | − | 0.992140i | \(-0.460064\pi\) |
−0.796651 | + | 0.604439i | \(0.793397\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.99602 | + | 17.3136i | −0.379171 | + | 0.656743i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.10349 | + | 1.91131i | 0.0417978 | + | 0.0723960i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 49.8696i | − | 1.88355i | −0.336247 | − | 0.941774i | \(-0.609158\pi\) | ||
0.336247 | − | 0.941774i | \(-0.390842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.5039 | 0.433877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.5682 | + | 25.1541i | −1.63855 | + | 0.946017i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.57469 | + | 4.95060i | 0.322029 | + | 0.185924i | 0.652297 | − | 0.757964i | \(-0.273806\pi\) |
−0.330267 | + | 0.943887i | \(0.607139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.1459 | + | 27.9655i | −0.604669 | + | 1.04732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.1842 | + | 20.3136i | −1.31582 | + | 0.759686i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5562 | −0.953084 | −0.476542 | − | 0.879152i | \(-0.658110\pi\) | ||||
−0.476542 | + | 0.879152i | \(0.658110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.962653 | 0.0358511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.12217 | − | 4.68934i | 0.301650 | − | 0.174158i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0702 | + | 34.7627i | −0.744364 | + | 1.28928i | 0.206128 | + | 0.978525i | \(0.433914\pi\) |
−0.950491 | + | 0.310751i | \(0.899420\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.23796 | − | 3.02414i | −0.193733 | − | 0.111852i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.9965 | − | 23.6694i | 1.51424 | − | 0.874247i | 0.514380 | − | 0.857562i | \(-0.328022\pi\) |
0.999861 | − | 0.0166852i | \(-0.00531131\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.21792 | −0.339546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9627i | 1.39648i | 0.715864 | + | 0.698239i | \(0.246033\pi\) | ||||
−0.715864 | + | 0.698239i | \(0.753967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.25980 | − | 12.5743i | −0.266336 | − | 0.461308i | 0.701577 | − | 0.712594i | \(-0.252480\pi\) |
−0.967913 | + | 0.251286i | \(0.919146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.93892 | − | 3.35830i | 0.0710364 | − | 0.123039i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.24434 | − | 0.718418i | −0.0454671 | − | 0.0262504i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.3216 | + | 31.7339i | 0.668563 | + | 1.15798i | 0.978306 | + | 0.207165i | \(0.0664236\pi\) |
−0.309743 | + | 0.950820i | \(0.600243\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 29.5051i | − | 1.07380i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.02727i | − | 0.0736822i | −0.999321 | − | 0.0368411i | \(-0.988270\pi\) | ||
0.999321 | − | 0.0368411i | \(-0.0117295\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.60349 | − | 14.9017i | −0.311876 | − | 0.540186i | 0.666892 | − | 0.745154i | \(-0.267624\pi\) |
−0.978769 | + | 0.204968i | \(0.934291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 67.5999 | + | 39.0288i | 2.44728 | + | 1.41294i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.76336 | − | 6.51832i | 0.135887 | − | 0.235363i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4253 | − | 23.2533i | −0.484129 | − | 0.838536i | 0.515705 | − | 0.856766i | \(-0.327530\pi\) |
−0.999834 | + | 0.0182304i | \(0.994197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.41305i | 0.158726i | 0.996846 | + | 0.0793632i | \(0.0252887\pi\) | ||||
−0.996846 | + | 0.0793632i | \(0.974711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.72286 | 0.349255 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.23887 | − | 1.29261i | 0.0802157 | − | 0.0463126i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.9541 | + | 28.8410i | 1.78750 | + | 1.03201i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0424108 | + | 0.0734576i | −0.00151371 | + | 0.00262182i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7765 | + | 17.1914i | −1.06142 | + | 0.612809i | −0.925824 | − | 0.377956i | \(-0.876627\pi\) |
−0.135593 | + | 0.990765i | \(0.543294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 78.7524 | 2.80011 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.92531 | −0.174903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8269 | − | 11.4471i | 0.702304 | − | 0.405475i | −0.105901 | − | 0.994377i | \(-0.533773\pi\) |
0.808205 | + | 0.588901i | \(0.200439\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.06058 | + | 15.6934i | −0.320540 | + | 0.555192i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.2375 | + | 23.2311i | 1.41995 | + | 0.819809i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.3880 | − | 25.0501i | 1.52922 | − | 0.882898i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.7922 | −1.22323 | −0.611614 | − | 0.791156i | \(-0.709480\pi\) | ||||
−0.611614 | + | 0.791156i | \(0.709480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.6810i | − | 0.410174i | −0.978744 | − | 0.205087i | \(-0.934252\pi\) | ||
0.978744 | − | 0.205087i | \(-0.0657478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.5279 | − | 28.6272i | −0.578948 | − | 1.00277i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.54241 | + | 6.13564i | −0.123933 | + | 0.214659i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9389 | + | 8.04764i | 0.486472 | + | 0.280864i | 0.723109 | − | 0.690733i | \(-0.242712\pi\) |
−0.236638 | + | 0.971598i | \(0.576046\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.40163 | − | 11.0880i | −0.223147 | − | 0.386502i | 0.732615 | − | 0.680643i | \(-0.238300\pi\) |
−0.955762 | + | 0.294142i | \(0.904966\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9253i | 0.901511i | 0.892647 | + | 0.450756i | \(0.148845\pi\) | ||||
−0.892647 | + | 0.450756i | \(0.851155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 49.0708i | − | 1.70430i | −0.523299 | − | 0.852149i | \(-0.675299\pi\) | ||
0.523299 | − | 0.852149i | \(-0.324701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.2125 | + | 17.6885i | 0.353841 | + | 0.612870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.9881 | + | 17.3136i | 1.03778 | + | 0.599162i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1275 | − | 26.2016i | 0.522259 | − | 0.904579i | −0.477406 | − | 0.878683i | \(-0.658423\pi\) |
0.999665 | − | 0.0258959i | \(-0.00824385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50506 | − | 6.07095i | −0.120864 | − | 0.209343i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 5.47244i | − | 0.188258i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −100.363 | −3.44851 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.0882 | + | 19.1035i | −1.13425 | + | 0.654859i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.9389 | − | 14.9758i | −0.888132 | − | 0.512763i | −0.0148007 | − | 0.999890i | \(-0.504711\pi\) |
−0.873331 | + | 0.487127i | \(0.838045\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.9016 | − | 20.6141i | 0.406550 | − | 0.704165i | −0.587951 | − | 0.808897i | \(-0.700065\pi\) |
0.994501 | + | 0.104732i | \(0.0333984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5000 | − | 16.4545i | 0.972406 | − | 0.561419i | 0.0724371 | − | 0.997373i | \(-0.476922\pi\) |
0.899969 | + | 0.435954i | \(0.143589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.3906 | −1.23875 | −0.619375 | − | 0.785095i | \(-0.712614\pi\) | ||||
−0.619375 | + | 0.785095i | \(0.712614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.4440 | − | 6.02983i | 0.354288 | − | 0.204548i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.17523 | − | 5.49965i | 0.107588 | − | 0.186349i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −45.7234 | − | 26.3984i | −1.54573 | − | 0.892430i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.3529 | + | 24.4525i | −1.43016 | + | 0.825701i | −0.997132 | − | 0.0756818i | \(-0.975887\pi\) |
−0.433024 | + | 0.901383i | \(0.642553\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.9627 | −1.34638 | −0.673188 | − | 0.739471i | \(-0.735076\pi\) | ||||
−0.673188 | + | 0.739471i | \(0.735076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.5949 | − | 39.1354i | −0.758661 | − | 1.31404i | −0.943534 | − | 0.331277i | \(-0.892521\pi\) |
0.184873 | − | 0.982762i | \(-0.440813\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.96265 | − | 17.2558i | 0.334137 | − | 0.578742i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.3829 | + | 10.6134i | 0.615160 | + | 0.355163i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.19615 | − | 9.00000i | −0.173688 | − | 0.300837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7969i | 0.760318i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.865333i | − | 0.0288284i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.98133 | + | 8.62791i | 0.165585 | + | 0.286801i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.9726 | − | 20.1914i | −1.16125 | − | 0.670446i | −0.209644 | − | 0.977778i | \(-0.567231\pi\) |
−0.951602 | + | 0.307332i | \(0.900564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.26071 | − | 7.37976i | 0.141164 | − | 0.244503i | −0.786771 | − | 0.617244i | \(-0.788249\pi\) |
0.927935 | + | 0.372742i | \(0.121582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | − | 7.79423i | −0.148928 | − | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 58.9720i | − | 1.94743i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.00834 | 0.0662490 | 0.0331245 | − | 0.999451i | \(-0.489454\pi\) | ||||
0.0331245 | + | 0.999451i | \(0.489454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.4146 | + | 19.8693i | −1.13277 | + | 0.654006i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.96265 | + | 5.75194i | 0.327570 | + | 0.189123i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.9864 | − | 25.9572i | 0.491688 | − | 0.851628i | −0.508267 | − | 0.861200i | \(-0.669714\pi\) |
0.999954 | + | 0.00957195i | \(0.00304689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.7199 | − | 11.9627i | 0.679068 | − | 0.392060i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.2558 | 0.564326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.0475 | −1.47164 | −0.735818 | − | 0.677179i | \(-0.763202\pi\) | ||||
−0.735818 | + | 0.677179i | \(0.763202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.3880 | + | 26.7821i | −1.51220 | + | 0.873072i | −0.512306 | + | 0.858803i | \(0.671209\pi\) |
−0.999898 | + | 0.0142686i | \(0.995458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.29305 | + | 7.43578i | −0.139801 | + | 0.242142i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.6417 | + | 11.9175i | 0.670766 | + | 0.387267i | 0.796367 | − | 0.604814i | \(-0.206752\pi\) |
−0.125601 | + | 0.992081i | \(0.540086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.7206 | + | 16.0045i | −0.899849 | + | 0.519528i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.4732 | 1.05191 | 0.525955 | − | 0.850513i | \(-0.323708\pi\) | ||||
0.525955 | + | 0.850513i | \(0.323708\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.382896i | 0.0123902i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.7225 | − | 84.3899i | −1.57333 | − | 2.72509i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.68325 | − | 6.37958i | 0.118815 | − | 0.205793i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.0712 | − | 15.6296i | −0.871453 | − | 0.503134i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.83221 | + | 8.36964i | 0.155393 | + | 0.269149i | 0.933202 | − | 0.359352i | \(-0.117002\pi\) |
−0.777809 | + | 0.628501i | \(0.783669\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 49.8133i | − | 1.59858i | −0.600943 | − | 0.799292i | \(-0.705208\pi\) | ||
0.600943 | − | 0.799292i | \(-0.294792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 50.2627i | − | 1.61135i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.59029 | − | 6.21856i | −0.114863 | − | 0.198949i | 0.802862 | − | 0.596165i | \(-0.203310\pi\) |
−0.917725 | + | 0.397216i | \(0.869976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0244 | + | 11.5611i | 0.639982 | + | 0.369494i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.38174 | − | 4.12530i | 0.0759658 | − | 0.131577i | −0.825540 | − | 0.564344i | \(-0.809129\pi\) |
0.901506 | + | 0.432767i | \(0.142463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.50506 | − | 14.7312i | −0.270994 | − | 0.469375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 23.5303i | − | 0.748220i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.5781 | −0.907815 | −0.453907 | − | 0.891049i | \(-0.649970\pi\) | ||||
−0.453907 | + | 0.891049i | \(0.649970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.907140 | − | 0.523738i | 0.0287583 | − | 0.0166036i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.2494 | − | 18.6192i | −1.02135 | − | 0.589676i | −0.106854 | − | 0.994275i | \(-0.534078\pi\) |
−0.914494 | + | 0.404599i | \(0.867411\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.r.f.289.1 | 12 | ||
3.2 | odd | 2 | 576.2.r.e.97.4 | yes | 12 | ||
4.3 | odd | 2 | inner | 1728.2.r.f.289.6 | 12 | ||
8.3 | odd | 2 | 1728.2.r.e.289.6 | 12 | |||
8.5 | even | 2 | 1728.2.r.e.289.1 | 12 | |||
9.2 | odd | 6 | 5184.2.d.q.2593.6 | 12 | |||
9.4 | even | 3 | 1728.2.r.e.1441.1 | 12 | |||
9.5 | odd | 6 | 576.2.r.f.481.3 | yes | 12 | ||
9.7 | even | 3 | 5184.2.d.r.2593.12 | 12 | |||
12.11 | even | 2 | 576.2.r.e.97.3 | ✓ | 12 | ||
24.5 | odd | 2 | 576.2.r.f.97.3 | yes | 12 | ||
24.11 | even | 2 | 576.2.r.f.97.4 | yes | 12 | ||
36.7 | odd | 6 | 5184.2.d.r.2593.7 | 12 | |||
36.11 | even | 6 | 5184.2.d.q.2593.1 | 12 | |||
36.23 | even | 6 | 576.2.r.f.481.4 | yes | 12 | ||
36.31 | odd | 6 | 1728.2.r.e.1441.6 | 12 | |||
72.5 | odd | 6 | 576.2.r.e.481.4 | yes | 12 | ||
72.11 | even | 6 | 5184.2.d.q.2593.7 | 12 | |||
72.13 | even | 6 | inner | 1728.2.r.f.1441.1 | 12 | ||
72.29 | odd | 6 | 5184.2.d.q.2593.12 | 12 | |||
72.43 | odd | 6 | 5184.2.d.r.2593.1 | 12 | |||
72.59 | even | 6 | 576.2.r.e.481.3 | yes | 12 | ||
72.61 | even | 6 | 5184.2.d.r.2593.6 | 12 | |||
72.67 | odd | 6 | inner | 1728.2.r.f.1441.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.3 | ✓ | 12 | 12.11 | even | 2 | ||
576.2.r.e.97.4 | yes | 12 | 3.2 | odd | 2 | ||
576.2.r.e.481.3 | yes | 12 | 72.59 | even | 6 | ||
576.2.r.e.481.4 | yes | 12 | 72.5 | odd | 6 | ||
576.2.r.f.97.3 | yes | 12 | 24.5 | odd | 2 | ||
576.2.r.f.97.4 | yes | 12 | 24.11 | even | 2 | ||
576.2.r.f.481.3 | yes | 12 | 9.5 | odd | 6 | ||
576.2.r.f.481.4 | yes | 12 | 36.23 | even | 6 | ||
1728.2.r.e.289.1 | 12 | 8.5 | even | 2 | |||
1728.2.r.e.289.6 | 12 | 8.3 | odd | 2 | |||
1728.2.r.e.1441.1 | 12 | 9.4 | even | 3 | |||
1728.2.r.e.1441.6 | 12 | 36.31 | odd | 6 | |||
1728.2.r.f.289.1 | 12 | 1.1 | even | 1 | trivial | ||
1728.2.r.f.289.6 | 12 | 4.3 | odd | 2 | inner | ||
1728.2.r.f.1441.1 | 12 | 72.13 | even | 6 | inner | ||
1728.2.r.f.1441.6 | 12 | 72.67 | odd | 6 | inner | ||
5184.2.d.q.2593.1 | 12 | 36.11 | even | 6 | |||
5184.2.d.q.2593.6 | 12 | 9.2 | odd | 6 | |||
5184.2.d.q.2593.7 | 12 | 72.11 | even | 6 | |||
5184.2.d.q.2593.12 | 12 | 72.29 | odd | 6 | |||
5184.2.d.r.2593.1 | 12 | 72.43 | odd | 6 | |||
5184.2.d.r.2593.6 | 12 | 72.61 | even | 6 | |||
5184.2.d.r.2593.7 | 12 | 36.7 | odd | 6 | |||
5184.2.d.r.2593.12 | 12 | 9.7 | even | 3 |