Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1049,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.f (of order \(2\), degree \(1\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 22 x^{14} - 4 x^{13} - 80 x^{12} - 84 x^{11} + 1324 x^{10} - 3800 x^{9} + \cdots + 3204 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.9 | ||
Root | \(1.77273 + 1.86553i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1049 |
Dual form | 2100.2.f.i.1049.12 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0.437016 | − | 1.67601i | 0.252311 | − | 0.967646i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | − | 2.23607i | 0.534522 | − | 0.845154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61803 | − | 1.46489i | −0.872678 | − | 0.488296i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.83513i | 1.15633i | 0.815918 | + | 0.578167i | \(0.196232\pi\) | ||||
−0.815918 | + | 0.578167i | \(0.803768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.99070 | −1.66152 | −0.830761 | − | 0.556629i | \(-0.812095\pi\) | ||||
−0.830761 | + | 0.556629i | \(0.812095\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.07167i | 0.502453i | 0.967928 | + | 0.251226i | \(0.0808338\pi\) | ||||
−0.967928 | + | 0.251226i | \(0.919166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.11667i | 1.17385i | 0.809643 | + | 0.586923i | \(0.199661\pi\) | ||||
−0.809643 | + | 0.586923i | \(0.800339\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12964 | − | 3.34744i | −0.682944 | − | 0.730471i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.57561 | −1.78814 | −0.894069 | − | 0.447930i | \(-0.852161\pi\) | ||||
−0.894069 | + | 0.447930i | \(0.852161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.59929 | + | 3.74768i | −0.692684 | + | 0.721241i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.64583i | 1.04840i | 0.851594 | + | 0.524202i | \(0.175636\pi\) | ||||
−0.851594 | + | 0.524202i | \(0.824364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.95440i | 0.351020i | 0.984478 | + | 0.175510i | \(0.0561574\pi\) | ||||
−0.984478 | + | 0.175510i | \(0.943843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.42772 | + | 1.67601i | 1.11892 | + | 0.291756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.23607i | − | 0.367607i | −0.982963 | − | 0.183804i | \(-0.941159\pi\) | ||
0.982963 | − | 0.183804i | \(-0.0588411\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.61803 | + | 10.0405i | −0.419221 | + | 1.60777i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.49535 | −1.17058 | −0.585289 | − | 0.810825i | \(-0.699019\pi\) | ||||
−0.585289 | + | 0.810825i | \(0.699019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.47214i | − | 1.44449i | −0.691639 | − | 0.722244i | \(-0.743111\pi\) | ||
0.691639 | − | 0.722244i | \(-0.256889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.9190i | 1.88444i | 0.335000 | + | 0.942218i | \(0.391264\pi\) | ||||
−0.335000 | + | 0.942218i | \(0.608736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | − | 6.32456i | −0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.47214 | + | 0.905351i | 0.486196 | + | 0.126774i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6000 | 1.45603 | 0.728013 | − | 0.685563i | \(-0.240444\pi\) | ||||
0.728013 | + | 0.685563i | \(0.240444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.57561 | + | 2.23607i | 1.13587 | + | 0.296174i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.1277 | −1.57890 | −0.789449 | − | 0.613817i | \(-0.789633\pi\) | ||||
−0.789449 | + | 0.613817i | \(0.789633\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.37016i | − | 0.559542i | −0.960067 | − | 0.279771i | \(-0.909742\pi\) | ||
0.960067 | − | 0.279771i | \(-0.0902585\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.97805 | + | 3.78244i | −0.879152 | + | 0.476542i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.70820i | − | 0.819538i | −0.912189 | − | 0.409769i | \(-0.865609\pi\) | ||
0.912189 | − | 0.409769i | \(-0.134391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.74768 | + | 14.3728i | −0.451167 | + | 1.73028i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.02443i | − | 0.240255i | −0.992758 | − | 0.120128i | \(-0.961670\pi\) | ||
0.992758 | − | 0.120128i | \(-0.0383304\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41421 | 0.165521 | 0.0827606 | − | 0.996569i | \(-0.473626\pi\) | ||||
0.0827606 | + | 0.996569i | \(0.473626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.57561 | + | 5.42369i | 0.977281 | + | 0.618087i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.47214 | 0.840681 | 0.420340 | − | 0.907366i | \(-0.361911\pi\) | ||||
0.420340 | + | 0.907366i | \(0.361911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.70820 | + | 7.67026i | 0.523134 | + | 0.852251i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.49535i | − | 0.822722i | −0.911472 | − | 0.411361i | \(-0.865054\pi\) | ||
0.911472 | − | 0.411361i | \(-0.134946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.46248 | + | 2.46732i | 1.01448 | + | 0.264524i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.86297 | −0.303474 | −0.151737 | − | 0.988421i | \(-0.548487\pi\) | ||||
−0.151737 | + | 0.988421i | \(0.548487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.47214 | + | 13.3956i | −0.888121 | + | 1.40424i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.27559 | + | 0.854102i | 0.339663 | + | 0.0885662i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.206331 | 0.0209497 | 0.0104749 | − | 0.999945i | \(-0.496666\pi\) | ||||
0.0104749 | + | 0.999945i | \(0.496666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.61803 | − | 10.0405i | 0.564634 | − | 1.00911i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.86297 | −0.284876 | −0.142438 | − | 0.989804i | \(-0.545494\pi\) | ||||
−0.142438 | + | 0.989804i | \(0.545494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8539 | −1.16800 | −0.583999 | − | 0.811754i | \(-0.698513\pi\) | ||||
−0.583999 | + | 0.811754i | \(0.698513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.1512 | 1.65807 | 0.829035 | − | 0.559197i | \(-0.188890\pi\) | ||||
0.829035 | + | 0.559197i | \(0.188890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.47214 | 0.141005 | 0.0705025 | − | 0.997512i | \(-0.477540\pi\) | ||||
0.0705025 | + | 0.997512i | \(0.477540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.74768 | − | 0.977198i | −0.355714 | − | 0.0927515i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.6245 | −1.18761 | −0.593805 | − | 0.804609i | \(-0.702375\pi\) | ||||
−0.593805 | + | 0.804609i | \(0.702375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.6839 | + | 8.77571i | 1.44997 | + | 0.811315i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.63238 | + | 2.92978i | 0.424650 | + | 0.268572i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.70820 | −0.337109 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.27559 | + | 12.5623i | −0.295350 | + | 1.13270i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.29180i | 0.292100i | 0.989277 | + | 0.146050i | \(0.0466560\pi\) | ||||
−0.989277 | + | 0.146050i | \(0.953344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.8754 | − | 4.13948i | −1.39775 | − | 0.364460i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.63238 | −0.404733 | −0.202367 | − | 0.979310i | \(-0.564863\pi\) | ||||
−0.202367 | + | 0.979310i | \(0.564863\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4412 | + | 7.23607i | 0.992080 | + | 0.627447i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.04885 | −0.345917 | −0.172958 | − | 0.984929i | \(-0.555333\pi\) | ||||
−0.172958 | + | 0.984929i | \(0.555333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.3956i | − | 1.13620i | −0.822959 | − | 0.568101i | \(-0.807678\pi\) | ||
0.822959 | − | 0.568101i | \(-0.192322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.6525 | + | 5.64583i | 1.82347 | + | 0.475465i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 22.9751i | − | 1.92128i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.9111 | + | 2.26410i | −0.982409 | + | 0.186740i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.57561i | 0.702541i | 0.936274 | + | 0.351271i | \(0.114250\pi\) | ||||
−0.936274 | + | 0.351271i | \(0.885750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.6525 | −1.76205 | −0.881027 | − | 0.473066i | \(-0.843147\pi\) | ||||
−0.881027 | + | 0.473066i | \(0.843147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.03476 | − | 5.42369i | 0.245346 | − | 0.438479i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.19859 | −0.574510 | −0.287255 | − | 0.957854i | \(-0.592743\pi\) | ||||
−0.287255 | + | 0.957854i | \(0.592743\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.63238 | − | 17.7658i | 0.367372 | − | 1.40892i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.1277 | + | 19.1756i | −0.955800 | + | 1.51125i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.94427i | − | 0.700569i | −0.936643 | − | 0.350285i | \(-0.886085\pi\) | ||
0.936643 | − | 0.350285i | \(-0.113915\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.56702i | 0.740318i | 0.928968 | + | 0.370159i | \(0.120697\pi\) | ||||
−0.928968 | + | 0.370159i | \(0.879303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.8885 | 1.76066 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.49535 | − | 13.3956i | 0.573184 | − | 1.02439i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4798i | 1.17690i | 0.808532 | + | 0.588452i | \(0.200263\pi\) | ||||
−0.808532 | + | 0.588452i | \(0.799737\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.30002 | + | 20.3262i | −0.398374 | + | 1.52781i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.55118i | − | 0.489658i | −0.969566 | − | 0.244829i | \(-0.921268\pi\) | ||
0.969566 | − | 0.244829i | \(-0.0787319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3044i | 1.28623i | 0.765771 | + | 0.643113i | \(0.222358\pi\) | ||||
−0.765771 | + | 0.643113i | \(0.777642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.32444 | − | 1.90983i | −0.541438 | − | 0.141179i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.94510 | −0.581003 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.28989 | + | 13.3483i | 0.239304 | + | 0.970945i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.74048i | 0.343009i | 0.985183 | + | 0.171504i | \(0.0548628\pi\) | ||||
−0.985183 | + | 0.171504i | \(0.945137\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0000i | 1.07972i | 0.841754 | + | 0.539862i | \(0.181524\pi\) | ||||
−0.841754 | + | 0.539862i | \(0.818476\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.02443 | 0.144234 | 0.0721172 | − | 0.997396i | \(-0.477024\pi\) | ||||
0.0721172 | + | 0.997396i | \(0.477024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.0193i | 1.20646i | 0.797566 | + | 0.603232i | \(0.206121\pi\) | ||||
−0.797566 | + | 0.603232i | \(0.793879\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.2430 | − | 2.93159i | −0.793022 | − | 0.206779i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6245 | + | 7.98441i | 0.886063 | + | 0.560396i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.4512 | + | 12.5623i | 1.56047 | + | 0.873141i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.6231 | −1.35736 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.70820 | −0.392969 | −0.196484 | − | 0.980507i | \(-0.562953\pi\) | ||||
−0.196484 | + | 0.980507i | \(0.562953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.39296 | − | 0.884707i | −0.232482 | − | 0.0606191i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.37016 | + | 2.76393i | 0.296666 | + | 0.187628i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.618034 | − | 2.37024i | 0.0417629 | − | 0.160166i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.4107i | − | 0.834836i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.40647 | 0.562939 | 0.281469 | − | 0.959570i | \(-0.409178\pi\) | ||||
0.281469 | + | 0.959570i | \(0.409178\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 22.1838i | − | 1.47239i | −0.676769 | − | 0.736196i | \(-0.736620\pi\) | ||
0.676769 | − | 0.736196i | \(-0.263380\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.90879i | 0.258300i | 0.991625 | + | 0.129150i | \(0.0412249\pi\) | ||||
−0.991625 | + | 0.129150i | \(0.958775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.8378 | − | 12.0026i | 0.844668 | − | 0.789712i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1268 | 0.990989 | 0.495494 | − | 0.868611i | \(-0.334987\pi\) | ||||
0.495494 | + | 0.868611i | \(0.334987\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.26544 | − | 12.5234i | 0.212113 | − | 0.813482i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.2703i | − | 1.18181i | −0.806742 | − | 0.590903i | \(-0.798771\pi\) | ||
0.806742 | − | 0.590903i | \(-0.201229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9343i | 0.833168i | 0.909097 | + | 0.416584i | \(0.136773\pi\) | ||||
−0.909097 | + | 0.416584i | \(0.863227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9130 | − | 4.53898i | 0.956670 | − | 0.291176i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 30.6525i | − | 1.95037i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.5623 | − | 3.27559i | −0.796104 | − | 0.207582i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6231 | 1.23860 | 0.619299 | − | 0.785155i | \(-0.287417\pi\) | ||||
0.619299 | + | 0.785155i | \(0.287417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 32.8885i | − | 2.06769i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.76941i | 0.110373i | 0.998476 | + | 0.0551865i | \(0.0175753\pi\) | ||||
−0.998476 | + | 0.0551865i | \(0.982425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00000 | − | 3.16228i | −0.310685 | − | 0.196494i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.27051 | − | 14.7810i | 0.511932 | − | 0.914919i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.1268 | −0.932758 | −0.466379 | − | 0.884585i | \(-0.654442\pi\) | ||||
−0.466379 | + | 0.884585i | \(0.654442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.25116 | + | 4.79837i | −0.0765700 | + | 0.293656i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.0249 | −1.58677 | −0.793383 | − | 0.608723i | \(-0.791682\pi\) | ||||
−0.793383 | + | 0.608723i | \(0.791682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1359i | 1.34466i | 0.740250 | + | 0.672331i | \(0.234707\pi\) | ||||
−0.740250 | + | 0.672331i | \(0.765293\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.7488 | + | 20.0535i | 1.13473 | + | 1.21369i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.7082i | − | 1.30432i | −0.758082 | − | 0.652160i | \(-0.773863\pi\) | ||
0.758082 | − | 0.652160i | \(-0.226137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.86297 | − | 5.11667i | 0.171402 | − | 0.306327i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.4352i | − | 0.861129i | −0.902560 | − | 0.430565i | \(-0.858314\pi\) | ||
0.902560 | − | 0.430565i | \(-0.141686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.7109 | −1.52835 | −0.764177 | − | 0.645007i | \(-0.776854\pi\) | ||||
−0.764177 | + | 0.645007i | \(0.776854\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6000 | + | 16.7601i | −0.625700 | + | 0.989319i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7082 | 0.747541 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0901699 | − | 0.345813i | 0.00528586 | − | 0.0202719i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.00630i | 0.409312i | 0.978834 | + | 0.204656i | \(0.0656076\pi\) | ||||
−0.978834 | + | 0.204656i | \(0.934392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.3728 | − | 13.8038i | −0.833996 | − | 0.800975i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 51.3739 | 2.97103 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1803 | − | 13.3956i | −1.22081 | − | 0.772111i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.25116 | + | 4.79837i | −0.0718775 | + | 0.275659i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.6051 | 0.890628 | 0.445314 | − | 0.895375i | \(-0.353092\pi\) | ||||
0.445314 | + | 0.895375i | \(0.353092\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.18034 | + | 19.8673i | −0.294699 | + | 1.13021i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6231 | 1.11272 | 0.556362 | − | 0.830940i | \(-0.312197\pi\) | ||||
0.556362 | + | 0.830940i | \(0.312197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.94510 | 0.449084 | 0.224542 | − | 0.974464i | \(-0.427911\pi\) | ||||
0.224542 | + | 0.974464i | \(0.427911\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.6780 | −1.21756 | −0.608778 | − | 0.793341i | \(-0.708340\pi\) | ||||
−0.608778 | + | 0.793341i | \(0.708340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.6525 | −1.21231 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.49535 | − | 28.7456i | 0.418350 | − | 1.60443i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.6000 | −0.589802 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.643347 | − | 2.46732i | 0.0355772 | − | 0.136443i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.8879 | + | 18.2703i | 1.59264 | + | 1.00727i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.81966 | 0.374842 | 0.187421 | − | 0.982280i | \(-0.439987\pi\) | ||||
0.187421 | + | 0.982280i | \(0.439987\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.27559 | + | 5.85410i | −0.179501 | + | 0.320803i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000i | 0.544735i | 0.962193 | + | 0.272367i | \(0.0878066\pi\) | ||||
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.51709 | + | 21.1587i | −0.299647 | + | 1.14919i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.49535 | −0.405896 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3848 | − | 2.23607i | −0.992685 | − | 0.120736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6780 | −1.16373 | −0.581867 | − | 0.813284i | \(-0.697678\pi\) | ||||
−0.581867 | + | 0.813284i | \(0.697678\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.9343i | − | 0.692355i | −0.938169 | − | 0.346177i | \(-0.887480\pi\) | ||
0.938169 | − | 0.346177i | \(-0.112520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.5623 | − | 22.4512i | 1.15091 | − | 1.19836i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.37392i | 0.126351i | 0.998002 | + | 0.0631754i | \(0.0201228\pi\) | ||||
−0.998002 | + | 0.0631754i | \(0.979877\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.93477 | − | 6.48357i | 0.367027 | − | 0.343147i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.02443i | − | 0.106845i | −0.998572 | − | 0.0534226i | \(-0.982987\pi\) | ||
0.998572 | − | 0.0534226i | \(-0.0170130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.18034 | −0.377913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.62054 | + | 6.21500i | −0.0850565 | + | 0.326203i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.9095 | −1.71786 | −0.858930 | − | 0.512093i | \(-0.828870\pi\) | ||||
−0.858930 | + | 0.512093i | \(0.828870\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.6231 | + | 10.9799i | 1.02154 | + | 0.571589i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.9907 | − | 23.7024i | 0.778279 | − | 1.23057i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.6525i | − | 0.810454i | −0.914216 | − | 0.405227i | \(-0.867192\pi\) | ||
0.914216 | − | 0.405227i | \(-0.132808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 33.8225i | − | 1.74195i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1803 | −0.882495 | −0.441247 | − | 0.897386i | \(-0.645464\pi\) | ||||
−0.441247 | + | 0.897386i | \(0.645464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.51709 | + | 1.43857i | 0.282649 | + | 0.0737001i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 2.86297i | − | 0.146291i | −0.997321 | − | 0.0731455i | \(-0.976696\pi\) | ||
0.997321 | − | 0.0731455i | \(-0.0233037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.8756 | + | 24.7984i | −0.705338 | + | 1.26057i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.45653i | 0.378061i | 0.981971 | + | 0.189031i | \(0.0605345\pi\) | ||||
−0.981971 | + | 0.189031i | \(0.939465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.7658i | − | 0.898454i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.02443 | + | 7.76393i | −0.102119 | + | 0.391639i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.2117 | −1.01439 | −0.507197 | − | 0.861830i | \(-0.669318\pi\) | ||||
−0.507197 | + | 0.861830i | \(0.669318\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.1277 | − | 16.0134i | 0.857459 | − | 0.801671i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.9863i | 1.04801i | 0.851716 | + | 0.524004i | \(0.175562\pi\) | ||||
−0.851716 | + | 0.524004i | \(0.824438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.7082i | − | 0.583227i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.57561 | 0.425077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.62365i | 0.179178i | 0.995979 | + | 0.0895889i | \(0.0285553\pi\) | ||||
−0.995979 | + | 0.0895889i | \(0.971445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.76941 | + | 6.78593i | −0.0872787 | + | 0.334725i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.1512 | + | 27.1184i | −0.843956 | + | 1.33441i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.4512 | − | 5.85410i | −1.09944 | − | 0.286677i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2213 | 0.645903 | 0.322951 | − | 0.946416i | \(-0.395325\pi\) | ||||
0.322951 | + | 0.946416i | \(0.395325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8885 | −0.823097 | −0.411549 | − | 0.911388i | \(-0.635012\pi\) | ||||
−0.411549 | + | 0.911388i | \(0.635012\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.9250 | − | 33.8225i | 0.920163 | − | 1.64451i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.77198 | − | 6.18034i | −0.472899 | − | 0.299088i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.5066 | − | 10.0405i | −1.85912 | − | 0.484760i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.23815i | 0.107808i | 0.998546 | + | 0.0539040i | \(0.0171665\pi\) | ||||
−0.998546 | + | 0.0539040i | \(0.982834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.255039 | −0.0122564 | −0.00612820 | − | 0.999981i | \(-0.501951\pi\) | ||||
−0.00612820 | + | 0.999981i | \(0.501951\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 43.8786i | − | 2.09900i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 32.3693i | − | 1.54490i | −0.635074 | − | 0.772451i | \(-0.719031\pi\) | ||
0.635074 | − | 0.772451i | \(-0.280969\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.41067 | + | 20.9526i | −0.0671746 | + | 0.997741i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.6000 | −0.503623 | −0.251811 | − | 0.967776i | \(-0.581026\pi\) | ||||
−0.251811 | + | 0.967776i | \(0.581026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.3728 | + | 3.74768i | 0.679811 | + | 0.177259i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33.3971i | − | 1.57611i | −0.615608 | − | 0.788053i | \(-0.711089\pi\) | ||
0.615608 | − | 0.788053i | \(-0.288911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 28.7456i | − | 1.35358i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.46248 | + | 36.2898i | −0.444586 | + | 1.70504i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.36068i | 0.344318i | 0.985069 | + | 0.172159i | \(0.0550743\pi\) | ||||
−0.985069 | + | 0.172159i | \(0.944926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.76393 | − | 7.45653i | −0.362389 | − | 0.348041i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.86297 | 0.133342 | 0.0666709 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666709 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.6525i | − | 0.959802i | −0.877323 | − | 0.479901i | \(-0.840673\pi\) | ||
0.877323 | − | 0.479901i | \(-0.159327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.4300i | − | 0.575191i | −0.957752 | − | 0.287596i | \(-0.907144\pi\) | ||
0.957752 | − | 0.287596i | \(-0.0928559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | − | 9.48683i | −0.692636 | − | 0.438061i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.14590 | + | 12.0649i | −0.144955 | + | 0.555922i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.3269 | 1.67031 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.7512 | − | 15.5279i | −1.27064 | − | 0.710972i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.6573 | −1.40077 | −0.700383 | − | 0.713767i | \(-0.746988\pi\) | ||||
−0.700383 | + | 0.713767i | \(0.746988\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3956i | 0.610788i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.8386 | + | 28.7063i | 1.22120 | + | 1.30618i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.76393i | 0.351817i | 0.984406 | + | 0.175909i | \(0.0562863\pi\) | ||||
−0.984406 | + | 0.175909i | \(0.943714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.9907 | − | 3.90879i | −0.677903 | − | 0.176762i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.71605i | − | 0.122574i | −0.998120 | − | 0.0612869i | \(-0.980480\pi\) | ||
0.998120 | − | 0.0612869i | \(-0.0195204\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6963 | −0.526773 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.52675 | − | 2.86297i | −0.203053 | − | 0.128422i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3475 | 0.507985 | 0.253992 | − | 0.967206i | \(-0.418256\pi\) | ||||
0.253992 | + | 0.967206i | \(0.418256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.0344 | + | 4.18094i | 0.716366 | + | 0.186791i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 4.14333i | − | 0.184742i | −0.995725 | − | 0.0923710i | \(-0.970555\pi\) | ||
0.995725 | − | 0.0923710i | \(-0.0294446\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0027 | − | 38.3615i | 0.444234 | − | 1.70369i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.3925 | 0.948206 | 0.474103 | − | 0.880469i | \(-0.342772\pi\) | ||||
0.474103 | + | 0.880469i | \(0.342772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | − | 3.16228i | 0.0884748 | − | 0.139891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.1756 | − | 18.4164i | −0.846625 | − | 0.813104i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −49.5462 | −2.17904 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.9443 | + | 6.76490i | 1.13883 | + | 0.296946i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2462 | 1.71941 | 0.859703 | − | 0.510794i | \(-0.170648\pi\) | ||||
0.859703 | + | 0.510794i | \(0.170648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.48528 | −0.371035 | −0.185518 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185518 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.04885 | −0.176371 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.5410 | 2.19744 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.7508 | + | 17.7658i | 1.37787 | + | 0.770969i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.9025 | 1.94494 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.9799 | − | 2.86297i | −0.473816 | − | 0.123546i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.2555 | − | 11.5054i | 1.04476 | − | 0.495572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.6525 | −0.500979 | −0.250490 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250490 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.0024 | + | 7.56231i | 1.24461 | + | 0.324530i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7082i | 0.714391i | 0.934030 | + | 0.357196i | \(0.116267\pi\) | ||||
−0.934030 | + | 0.357196i | \(0.883733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.40180 | + | 11.4412i | −0.273222 | + | 0.488300i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.8879 | −1.23066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.5672 | − | 16.7082i | 0.449363 | − | 0.710505i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.1756 | −0.812498 | −0.406249 | − | 0.913762i | \(-0.633163\pi\) | ||||
−0.406249 | + | 0.913762i | \(0.633163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.7448i | 2.40005i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.47214 | + | 13.3161i | −0.146594 | + | 0.562206i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 33.5202i | − | 1.41271i | −0.707858 | − | 0.706355i | \(-0.750338\pi\) | ||
0.707858 | − | 0.706355i | \(-0.249662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.8096 | + | 0.319515i | 0.999910 | + | 0.0134184i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21.6780i | − | 0.908788i | −0.890801 | − | 0.454394i | \(-0.849856\pi\) | ||
0.890801 | − | 0.454394i | \(-0.150144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.94510 | + | 2.07167i | 0.331911 | + | 0.0865450i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.9805 | 1.66441 | 0.832206 | − | 0.554467i | \(-0.187078\pi\) | ||||
0.832206 | + | 0.554467i | \(0.187078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.1402 | + | 6.55524i | 1.04479 | + | 0.272426i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7601 | − | 10.6000i | −0.695327 | − | 0.439763i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.6525i | 1.68365i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 17.8537i | − | 0.736900i | −0.929648 | − | 0.368450i | \(-0.879889\pi\) | ||
0.929648 | − | 0.368450i | \(-0.120111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | −0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.884707 | − | 3.39296i | 0.0363920 | − | 0.139568i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.3676i | 1.82196i | 0.412451 | + | 0.910980i | \(0.364673\pi\) | ||||
−0.412451 | + | 0.910980i | \(0.635327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.5245 | + | 7.43769i | 1.16743 | + | 0.304405i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.7435i | 0.561546i | 0.959774 | + | 0.280773i | \(0.0905907\pi\) | ||||
−0.959774 | + | 0.280773i | \(0.909409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.7912i | 1.09284i | 0.837512 | + | 0.546419i | \(0.184009\pi\) | ||||
−0.837512 | + | 0.546419i | \(0.815991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.82677 | + | 17.5623i | −0.400177 | + | 0.715192i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.9349 | 1.70209 | 0.851043 | − | 0.525096i | \(-0.175970\pi\) | ||||
0.851043 | + | 0.525096i | \(0.175970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.8991 | − | 17.6694i | 0.765828 | − | 0.716002i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 77.3942i | − | 3.13103i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.23607i | − | 0.0903139i | −0.998980 | − | 0.0451570i | \(-0.985621\pi\) | ||
0.998980 | − | 0.0451570i | \(-0.0143788\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.57561 | −0.345241 | −0.172620 | − | 0.984988i | \(-0.555223\pi\) | ||||
−0.172620 | + | 0.984988i | \(0.555223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 39.2641i | − | 1.57816i | −0.614291 | − | 0.789079i | \(-0.710558\pi\) | ||
0.614291 | − | 0.789079i | \(-0.289442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.8661 | − | 32.1386i | 1.23861 | − | 1.28968i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.04885 | + | 6.40180i | −0.162214 | + | 0.256483i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.57561 | + | 32.8885i | −0.342477 | + | 1.31344i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.63238 | 0.184705 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.5279 | −0.657964 | −0.328982 | − | 0.944336i | \(-0.606706\pi\) | ||||
−0.328982 | + | 0.944336i | \(0.606706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.49458 | + | 9.56702i | −0.0991505 | + | 0.380255i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.9721 | + | 37.8885i | 0.712081 | + | 1.50120i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.96556 | + | 5.30002i | −0.117316 | + | 0.209665i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.0779i | 0.437552i | 0.975775 | + | 0.218776i | \(0.0702064\pi\) | ||||
−0.975775 | + | 0.218776i | \(0.929794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.08036 | −0.0426054 | −0.0213027 | − | 0.999773i | \(-0.506781\pi\) | ||||
−0.0213027 | + | 0.999773i | \(0.506781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 18.5295i | − | 0.728471i | −0.931307 | − | 0.364236i | \(-0.881330\pi\) | ||
0.931307 | − | 0.364236i | \(-0.118670\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 46.5114i | − | 1.82573i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.54221 | − | 6.11656i | 0.256410 | − | 0.239727i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.55118 | −0.256367 | −0.128184 | − | 0.991750i | \(-0.540915\pi\) | ||||
−0.128184 | + | 0.991750i | \(0.540915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.70246 | − | 2.07167i | −0.144447 | − | 0.0808234i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.4704i | 1.53755i | 0.639521 | + | 0.768773i | \(0.279133\pi\) | ||||
−0.639521 | + | 0.768773i | \(0.720867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.02546i | 0.351050i | 0.984475 | + | 0.175525i | \(0.0561623\pi\) | ||||
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.8005 | − | 5.42369i | −0.807826 | − | 0.210639i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 48.4164i | − | 1.87469i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.67376 | − | 14.0893i | 0.142036 | − | 0.544726i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.7601 | 0.647017 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.3050i | 1.20672i | 0.797470 | + | 0.603359i | \(0.206171\pi\) | ||||
−0.797470 | + | 0.603359i | \(0.793829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.2243i | 1.54595i | 0.634439 | + | 0.772973i | \(0.281231\pi\) | ||||
−0.634439 | + | 0.772973i | \(0.718769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.291796 | − | 0.461370i | 0.0111981 | − | 0.0177058i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.1803 | − | 9.69468i | −1.42475 | − | 0.371501i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.07328 | −0.232388 | −0.116194 | − | 0.993227i | \(-0.537069\pi\) | ||||
−0.116194 | + | 0.993227i | \(0.537069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.55118 | + | 1.70820i | 0.249943 | + | 0.0651720i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −63.5017 | −2.41922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.4211i | − | 0.852938i | −0.904502 | − | 0.426469i | \(-0.859757\pi\) | ||
0.904502 | − | 0.426469i | \(-0.140243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.5061 | − | 26.7617i | −0.551042 | − | 1.01659i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 15.5279i | − | 0.588160i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.61065 | − | 25.3527i | 0.250038 | − | 0.958926i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5619i | 1.11654i | 0.829660 | + | 0.558270i | \(0.188535\pi\) | ||||
−0.829660 | + | 0.558270i | \(0.811465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4412 | 0.431514 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.04885 | + | 6.40180i | −0.152273 | + | 0.240764i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.3050 | 1.47613 | 0.738064 | − | 0.674730i | \(-0.235740\pi\) | ||||
0.738064 | + | 0.674730i | \(0.235740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.5623 | − | 10.9458i | −0.733644 | − | 0.410501i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.7601i | − | 0.627672i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.6212 | − | 7.98441i | −1.14357 | − | 0.298183i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.0249 | 0.970565 | 0.485282 | − | 0.874358i | \(-0.338717\pi\) | ||||
0.485282 | + | 0.874358i | \(0.338717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.7639 | + | 26.5061i | −0.624321 | + | 0.987139i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.6780 | + | 5.65248i | 0.806212 | + | 0.210218i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.3531 | −0.643592 | −0.321796 | − | 0.946809i | \(-0.604286\pi\) | ||||
−0.321796 | + | 0.946809i | \(0.604286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.09017 | − | 26.9780i | −0.0403767 | − | 0.999185i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.6231 | 0.725786 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.7758 | 1.50609 | 0.753044 | − | 0.657971i | \(-0.228585\pi\) | ||||
0.753044 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7268 | 0.947660 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5967 | −0.463379 | −0.231689 | − | 0.972790i | \(-0.574425\pi\) | ||||
−0.231689 | + | 0.972790i | \(0.574425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −51.3739 | − | 13.3956i | −1.88727 | − | 0.492101i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.55118 | −0.240339 | −0.120170 | − | 0.992753i | \(-0.538344\pi\) | ||||
−0.120170 | + | 0.992753i | \(0.538344\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.9799 | + | 19.6231i | −0.401732 | + | 0.717971i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.2555 | − | 38.3513i | 0.886276 | − | 1.40133i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.1246 | 1.42768 | 0.713839 | − | 0.700310i | \(-0.246955\pi\) | ||||
0.713839 | + | 0.700310i | \(0.246955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.57561 | − | 32.8885i | 0.312512 | − | 1.19853i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7639i | 0.645641i | 0.946460 | + | 0.322821i | \(0.104631\pi\) | ||||
−0.946460 | + | 0.322821i | \(0.895369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −55.1216 | − | 14.3728i | −2.00079 | − | 0.521700i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2555 | 0.879260 | 0.439630 | − | 0.898179i | \(-0.355110\pi\) | ||||
0.439630 | + | 0.898179i | \(0.355110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.08191 | − | 3.29180i | 0.0753704 | − | 0.119171i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 72.6537 | 2.62337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.8369i | 0.895640i | 0.894124 | + | 0.447820i | \(0.147799\pi\) | ||||
−0.894124 | + | 0.447820i | \(0.852201\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.96556 | + | 0.773262i | 0.106802 | + | 0.0278483i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30.1682i | − | 1.08508i | −0.840031 | − | 0.542538i | \(-0.817464\pi\) | ||
0.840031 | − | 0.542538i | \(-0.182536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.48510 | + | 6.99810i | −0.268526 | + | 0.251055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 38.3513i | − | 1.37408i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.76393 | 0.277815 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.1587 | − | 20.3210i | −0.756152 | − | 0.726213i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2967 | −0.866083 | −0.433041 | − | 0.901374i | \(-0.642560\pi\) | ||||
−0.433041 | + | 0.901374i | \(0.642560\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.61065 | + | 25.3527i | −0.235345 | + | 0.902579i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.8537 | + | 28.2291i | −0.634804 | + | 1.00371i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1803i | 0.929691i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.79761i | 0.276205i | 0.990418 | + | 0.138103i | \(0.0441004\pi\) | ||||
−0.990418 | + | 0.138103i | \(0.955900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.7639 | −0.946840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.49535 | + | 4.19393i | 0.264835 | + | 0.148185i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.42369i | 0.191398i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.3733 | + | 43.6180i | −0.400359 | + | 1.53543i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.1970i | 0.428824i | 0.976743 | + | 0.214412i | \(0.0687835\pi\) | ||||
−0.976743 | + | 0.214412i | \(0.931216\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.0246i | − | 1.30011i | −0.759887 | − | 0.650055i | \(-0.774746\pi\) | ||
0.759887 | − | 0.650055i | \(-0.225254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.1001 | + | 9.67376i | 1.30116 | + | 0.339274i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.4658 | 1.69560 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.8034 | − | 22.6595i | 1.46073 | − | 0.791786i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.6596i | 1.31433i | 0.753746 | + | 0.657165i | \(0.228245\pi\) | ||||
−0.753746 | + | 0.657165i | \(0.771755\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27.3607i | − | 0.953733i | −0.878976 | − | 0.476867i | \(-0.841772\pi\) | ||
0.878976 | − | 0.476867i | \(-0.158228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.7268 | −0.894609 | −0.447305 | − | 0.894382i | \(-0.647616\pi\) | ||||
−0.447305 | + | 0.894382i | \(0.647616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.5061i | 0.920595i | 0.887765 | + | 0.460298i | \(0.152257\pi\) | ||||
−0.887765 | + | 0.460298i | \(0.847743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.3832 | − | 9.48683i | −1.26212 | − | 0.329095i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.1024 | − | 6.21500i | 0.453970 | − | 0.215337i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.32444 | − | 7.03444i | −0.253170 | − | 0.243146i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.1092 | −1.45377 | −0.726885 | − | 0.686759i | \(-0.759033\pi\) | ||||
−0.726885 | + | 0.686759i | \(0.759033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.87539 | −0.0991513 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.1935 | − | 6.30840i | −0.833269 | − | 0.217273i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.24419 | + | 8.29180i | −0.180193 | + | 0.284909i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.2361 | + | 43.0918i | −0.385621 | + | 1.47891i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.1756i | 0.657332i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.1081 | −1.37327 | −0.686637 | − | 0.727001i | \(-0.740914\pi\) | ||||
−0.686637 | + | 0.727001i | \(0.740914\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.76941i | − | 0.0604420i | −0.999543 | − | 0.0302210i | \(-0.990379\pi\) | ||
0.999543 | − | 0.0302210i | \(-0.00962111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.3352i | 1.58094i | 0.612503 | + | 0.790468i | \(0.290163\pi\) | ||||
−0.612503 | + | 0.790468i | \(0.709837\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.4578 | + | 25.0902i | 0.799439 | + | 0.855073i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.6733 | 0.567566 | 0.283783 | − | 0.958889i | \(-0.408410\pi\) | ||||
0.283783 | + | 0.958889i | \(0.408410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.55369 | − | 21.2991i | 0.188613 | − | 0.723356i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.6566i | 0.972108i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.1869i | 1.36168i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.540182 | − | 0.302252i | −0.0182824 | − | 0.0102297i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 24.4721i | − | 0.826365i | −0.910648 | − | 0.413183i | \(-0.864417\pi\) | ||
0.910648 | − | 0.413183i | \(-0.135583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.7426 | + | 3.06187i | 0.396070 | + | 0.103274i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.7508 | −1.06971 | −0.534856 | − | 0.844943i | \(-0.679634\pi\) | ||||
−0.534856 | + | 0.844943i | \(0.679634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.8885i | 1.44331i | 0.692251 | + | 0.721657i | \(0.256619\pi\) | ||||
−0.692251 | + | 0.721657i | \(0.743381\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.2120i | 0.947266i | 0.880722 | + | 0.473633i | \(0.157058\pi\) | ||||
−0.880722 | + | 0.473633i | \(0.842942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.36068 | + | 4.65530i | 0.246869 | + | 0.156134i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.4164 | + | 18.0566i | −0.985487 | + | 0.604918i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −66.1025 | −2.21204 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.4512 | − | 86.1033i | 0.749625 | − | 2.87491i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.0342 | −0.368011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.9597i | 0.731584i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.7074 | + | 29.6444i | −1.05516 | + | 0.986504i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.3050i | 1.37151i | 0.727833 | + | 0.685754i | \(0.240527\pi\) | ||||
−0.727833 | + | 0.685754i | \(0.759473\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.49535 | + | 4.19393i | 0.248605 | + | 0.139104i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.8245i | 1.12066i | 0.828271 | + | 0.560328i | \(0.189325\pi\) | ||||
−0.828271 | + | 0.560328i | \(0.810675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.7456 | 0.951342 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.55118 | + | 10.3583i | −0.216339 | + | 0.342062i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.3050 | −0.933694 | −0.466847 | − | 0.884338i | \(-0.654610\pi\) | ||||
−0.466847 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.81966 | − | 26.1543i | 0.224715 | − | 0.861812i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.1277i | 0.399189i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.0339 | + | 17.3646i | 1.01929 | + | 0.570329i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.86297 | −0.0939310 | −0.0469655 | − | 0.998897i | \(-0.514955\pi\) | ||||
−0.0469655 | + | 0.998897i | \(0.514955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.3607 | − | 15.3500i | 1.06058 | − | 0.503077i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.57561 | − | 32.8885i | 0.280753 | − | 1.07672i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1660 | 0.724133 | 0.362067 | − | 0.932152i | \(-0.382071\pi\) | ||||
0.362067 | + | 0.932152i | \(0.382071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.47214 | − | 13.3161i | 0.113309 | − | 0.434554i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2213 | −0.431002 | −0.215501 | − | 0.976504i | \(-0.569138\pi\) | ||||
−0.215501 | + | 0.976504i | \(0.569138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.2772 | 2.09315 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.5025 | −1.80359 | −0.901794 | − | 0.432166i | \(-0.857750\pi\) | ||||
−0.901794 | + | 0.432166i | \(0.857750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.47214 | −0.275017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.47362 | + | 36.3325i | −0.307203 | + | 1.17816i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.3804 | −1.47001 | −0.735007 | − | 0.678060i | \(-0.762821\pi\) | ||||
−0.735007 | + | 0.678060i | \(0.762821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.46248 | + | 36.2898i | −0.305879 | + | 1.17308i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.72594 | + | 9.05351i | −0.184900 | + | 0.292353i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.1803 | 0.876785 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.9025 | − | 25.1246i | −1.44696 | − | 0.809629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 14.0689i | − | 0.452425i | −0.974078 | − | 0.226212i | \(-0.927366\pi\) | ||
0.974078 | − | 0.226212i | \(-0.0726343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.63238 | + | 17.7658i | −0.148814 | + | 0.570719i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.1619 | −0.743301 | −0.371651 | − | 0.928373i | \(-0.621208\pi\) | ||||
−0.371651 | + | 0.928373i | \(0.621208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.9535 | − | 18.9443i | −0.960266 | − | 0.607325i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.7268 | 0.823074 | 0.411537 | − | 0.911393i | \(-0.364992\pi\) | ||||
0.411537 | + | 0.911393i | \(0.364992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 10.9799i | − | 0.350918i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.85410 | − | 2.15651i | −0.123052 | − | 0.0688522i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.9035i | − | 0.666717i | −0.942800 | − | 0.333358i | \(-0.891818\pi\) | ||
0.942800 | − | 0.333358i | \(-0.108182\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 43.2457 | − | 40.4320i | 1.37653 | − | 1.28696i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 81.2293i | 2.58294i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.7214 | 1.83358 | 0.916790 | − | 0.399370i | \(-0.130771\pi\) | ||||
0.916790 | + | 0.399370i | \(0.130771\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.98030 | − | 11.4298i | 0.0945770 | − | 0.362715i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.35466 | 0.201254 | 0.100627 | − | 0.994924i | \(-0.467915\pi\) | ||||
0.100627 | + | 0.994924i | \(0.467915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.38006 | + | 8.04827i | 0.265133 | + | 0.254636i |
(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 | 2100.2.f.i.1049.9 | 16 | ||
3.2 | odd | 2 | inner | 2100.2.f.i.1049.11 | 16 | ||
5.2 | odd | 4 | 2100.2.d.k.1301.1 | ✓ | 8 | ||
5.3 | odd | 4 | 2100.2.d.l.1301.8 | yes | 8 | ||
5.4 | even | 2 | inner | 2100.2.f.i.1049.8 | 16 | ||
7.6 | odd | 2 | inner | 2100.2.f.i.1049.7 | 16 | ||
15.2 | even | 4 | 2100.2.d.k.1301.7 | yes | 8 | ||
15.8 | even | 4 | 2100.2.d.l.1301.2 | yes | 8 | ||
15.14 | odd | 2 | inner | 2100.2.f.i.1049.6 | 16 | ||
21.20 | even | 2 | inner | 2100.2.f.i.1049.5 | 16 | ||
35.13 | even | 4 | 2100.2.d.l.1301.1 | yes | 8 | ||
35.27 | even | 4 | 2100.2.d.k.1301.8 | yes | 8 | ||
35.34 | odd | 2 | inner | 2100.2.f.i.1049.10 | 16 | ||
105.62 | odd | 4 | 2100.2.d.k.1301.2 | yes | 8 | ||
105.83 | odd | 4 | 2100.2.d.l.1301.7 | yes | 8 | ||
105.104 | even | 2 | inner | 2100.2.f.i.1049.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.d.k.1301.1 | ✓ | 8 | 5.2 | odd | 4 | ||
2100.2.d.k.1301.2 | yes | 8 | 105.62 | odd | 4 | ||
2100.2.d.k.1301.7 | yes | 8 | 15.2 | even | 4 | ||
2100.2.d.k.1301.8 | yes | 8 | 35.27 | even | 4 | ||
2100.2.d.l.1301.1 | yes | 8 | 35.13 | even | 4 | ||
2100.2.d.l.1301.2 | yes | 8 | 15.8 | even | 4 | ||
2100.2.d.l.1301.7 | yes | 8 | 105.83 | odd | 4 | ||
2100.2.d.l.1301.8 | yes | 8 | 5.3 | odd | 4 | ||
2100.2.f.i.1049.5 | 16 | 21.20 | even | 2 | inner | ||
2100.2.f.i.1049.6 | 16 | 15.14 | odd | 2 | inner | ||
2100.2.f.i.1049.7 | 16 | 7.6 | odd | 2 | inner | ||
2100.2.f.i.1049.8 | 16 | 5.4 | even | 2 | inner | ||
2100.2.f.i.1049.9 | 16 | 1.1 | even | 1 | trivial | ||
2100.2.f.i.1049.10 | 16 | 35.34 | odd | 2 | inner | ||
2100.2.f.i.1049.11 | 16 | 3.2 | odd | 2 | inner | ||
2100.2.f.i.1049.12 | 16 | 105.104 | even | 2 | inner |