Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(34,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.p (of order \(4\), degree \(2\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.4 | ||
Root | \(0.236276 + 0.236276i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.265 |
Dual form | 273.2.p.e.34.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.695639 | − | 0.695639i | 0.491891 | − | 0.491891i | −0.417011 | − | 0.908902i | \(-0.636922\pi\) |
0.908902 | + | 0.417011i | \(0.136922\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.03217i | 0.516087i | ||||||||
\(5\) | −1.23628 | − | 1.23628i | −0.552880 | − | 0.552880i | 0.374391 | − | 0.927271i | \(-0.377852\pi\) |
−0.927271 | + | 0.374391i | \(0.877852\pi\) | |||||||
\(6\) | 0.695639 | + | 0.695639i | 0.283993 | + | 0.283993i | ||||
\(7\) | 2.35624 | + | 1.20338i | 0.890576 | + | 0.454834i | ||||
\(8\) | 2.10930 | + | 2.10930i | 0.745749 | + | 0.745749i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.72000 | −0.543913 | ||||||||
\(11\) | 0.436434 | + | 0.436434i | 0.131590 | + | 0.131590i | 0.769834 | − | 0.638244i | \(-0.220339\pi\) |
−0.638244 | + | 0.769834i | \(0.720339\pi\) | |||||||
\(12\) | −1.03217 | −0.297963 | ||||||||
\(13\) | 2.38061 | + | 2.70790i | 0.660262 | + | 0.751036i | ||||
\(14\) | 2.47621 | − | 0.801978i | 0.661795 | − | 0.214338i | ||||
\(15\) | 1.23628 | − | 1.23628i | 0.319205 | − | 0.319205i | ||||
\(16\) | 0.870270 | 0.217567 | ||||||||
\(17\) | −2.40676 | −0.583724 | −0.291862 | − | 0.956460i | \(-0.594275\pi\) | ||||
−0.291862 | + | 0.956460i | \(0.594275\pi\) | |||||||
\(18\) | −0.695639 | + | 0.695639i | −0.163964 | + | 0.163964i | ||||
\(19\) | 3.04121 | + | 3.04121i | 0.697702 | + | 0.697702i | 0.963914 | − | 0.266212i | \(-0.0857723\pi\) |
−0.266212 | + | 0.963914i | \(0.585772\pi\) | |||||||
\(20\) | 1.27605 | − | 1.27605i | 0.285334 | − | 0.285334i | ||||
\(21\) | −1.20338 | + | 2.35624i | −0.262599 | + | 0.514174i | ||||
\(22\) | 0.607201 | 0.129456 | ||||||||
\(23\) | − | 5.07339i | − | 1.05787i | −0.848661 | − | 0.528937i | \(-0.822591\pi\) | ||
0.848661 | − | 0.528937i | \(-0.177409\pi\) | |||||||
\(24\) | −2.10930 | + | 2.10930i | −0.430558 | + | 0.430558i | ||||
\(25\) | − | 1.94324i | − | 0.388648i | ||||||
\(26\) | 3.53976 | + | 0.227675i | 0.694204 | + | 0.0446508i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.24209 | + | 2.43205i | −0.234734 | + | 0.459615i | ||||
\(29\) | 0.166822 | 0.0309781 | 0.0154890 | − | 0.999880i | \(-0.495069\pi\) | ||||
0.0154890 | + | 0.999880i | \(0.495069\pi\) | |||||||
\(30\) | − | 1.72000i | − | 0.314028i | ||||||
\(31\) | −2.47255 | − | 2.47255i | −0.444084 | − | 0.444084i | 0.449298 | − | 0.893382i | \(-0.351674\pi\) |
−0.893382 | + | 0.449298i | \(0.851674\pi\) | |||||||
\(32\) | −3.61320 | + | 3.61320i | −0.638730 | + | 0.638730i | ||||
\(33\) | −0.436434 | + | 0.436434i | −0.0759735 | + | 0.0759735i | ||||
\(34\) | −1.67423 | + | 1.67423i | −0.287128 | + | 0.287128i | ||||
\(35\) | −1.42526 | − | 4.40068i | −0.240913 | − | 0.743850i | ||||
\(36\) | − | 1.03217i | − | 0.172029i | ||||||
\(37\) | −5.59931 | − | 5.59931i | −0.920521 | − | 0.920521i | 0.0765450 | − | 0.997066i | \(-0.475611\pi\) |
−0.997066 | + | 0.0765450i | \(0.975611\pi\) | |||||||
\(38\) | 4.23117 | 0.686386 | ||||||||
\(39\) | −2.70790 | + | 2.38061i | −0.433611 | + | 0.381202i | ||||
\(40\) | − | 5.21535i | − | 0.824619i | ||||||
\(41\) | −4.82807 | − | 4.82807i | −0.754018 | − | 0.754018i | 0.221209 | − | 0.975227i | \(-0.429000\pi\) |
−0.975227 | + | 0.221209i | \(0.929000\pi\) | |||||||
\(42\) | 0.801978 | + | 2.47621i | 0.123748 | + | 0.382087i | ||||
\(43\) | − | 6.37008i | − | 0.971428i | −0.874118 | − | 0.485714i | \(-0.838560\pi\) | ||
0.874118 | − | 0.485714i | \(-0.161440\pi\) | |||||||
\(44\) | −0.450476 | + | 0.450476i | −0.0679118 | + | 0.0679118i | ||||
\(45\) | 1.23628 | + | 1.23628i | 0.184293 | + | 0.184293i | ||||
\(46\) | −3.52924 | − | 3.52924i | −0.520359 | − | 0.520359i | ||||
\(47\) | 2.64599 | − | 2.64599i | 0.385957 | − | 0.385957i | −0.487285 | − | 0.873243i | \(-0.662013\pi\) |
0.873243 | + | 0.487285i | \(0.162013\pi\) | |||||||
\(48\) | 0.870270i | 0.125613i | ||||||||
\(49\) | 4.10376 | + | 5.67090i | 0.586252 | + | 0.810129i | ||||
\(50\) | −1.35179 | − | 1.35179i | −0.191173 | − | 0.191173i | ||||
\(51\) | − | 2.40676i | − | 0.337013i | ||||||
\(52\) | −2.79502 | + | 2.45720i | −0.387600 | + | 0.340752i | ||||
\(53\) | 6.46466 | 0.887990 | 0.443995 | − | 0.896029i | \(-0.353561\pi\) | ||||
0.443995 | + | 0.896029i | \(0.353561\pi\) | |||||||
\(54\) | −0.695639 | − | 0.695639i | −0.0946644 | − | 0.0946644i | ||||
\(55\) | − | 1.07911i | − | 0.145507i | ||||||
\(56\) | 2.43174 | + | 7.50830i | 0.324954 | + | 1.00334i | ||||
\(57\) | −3.04121 | + | 3.04121i | −0.402818 | + | 0.402818i | ||||
\(58\) | 0.116048 | − | 0.116048i | 0.0152378 | − | 0.0152378i | ||||
\(59\) | 6.95599 | − | 6.95599i | 0.905593 | − | 0.905593i | −0.0903198 | − | 0.995913i | \(-0.528789\pi\) |
0.995913 | + | 0.0903198i | \(0.0287889\pi\) | |||||||
\(60\) | 1.27605 | + | 1.27605i | 0.164738 | + | 0.164738i | ||||
\(61\) | 3.67293i | 0.470271i | 0.971963 | + | 0.235135i | \(0.0755533\pi\) | ||||
−0.971963 | + | 0.235135i | \(0.924447\pi\) | |||||||
\(62\) | −3.44001 | −0.436881 | ||||||||
\(63\) | −2.35624 | − | 1.20338i | −0.296859 | − | 0.151611i | ||||
\(64\) | 6.76750i | 0.845938i | ||||||||
\(65\) | 0.404620 | − | 6.29080i | 0.0501869 | − | 0.780278i | ||||
\(66\) | 0.607201i | 0.0747413i | ||||||||
\(67\) | −1.59968 | + | 1.59968i | −0.195433 | + | 0.195433i | −0.798039 | − | 0.602606i | \(-0.794129\pi\) |
0.602606 | + | 0.798039i | \(0.294129\pi\) | |||||||
\(68\) | − | 2.48419i | − | 0.301252i | ||||||
\(69\) | 5.07339 | 0.610764 | ||||||||
\(70\) | −4.05275 | − | 2.06981i | −0.484396 | − | 0.247390i | ||||
\(71\) | −1.65815 | + | 1.65815i | −0.196786 | + | 0.196786i | −0.798621 | − | 0.601835i | \(-0.794437\pi\) |
0.601835 | + | 0.798621i | \(0.294437\pi\) | |||||||
\(72\) | −2.10930 | − | 2.10930i | −0.248583 | − | 0.248583i | ||||
\(73\) | −4.88992 | + | 4.88992i | −0.572322 | + | 0.572322i | −0.932777 | − | 0.360455i | \(-0.882622\pi\) |
0.360455 | + | 0.932777i | \(0.382622\pi\) | |||||||
\(74\) | −7.79020 | −0.905592 | ||||||||
\(75\) | 1.94324 | 0.224386 | ||||||||
\(76\) | −3.13906 | + | 3.13906i | −0.360075 | + | 0.360075i | ||||
\(77\) | 0.503150 | + | 1.55354i | 0.0573393 | + | 0.177042i | ||||
\(78\) | −0.227675 | + | 3.53976i | −0.0257791 | + | 0.400799i | ||||
\(79\) | −9.79014 | −1.10148 | −0.550739 | − | 0.834678i | \(-0.685654\pi\) | ||||
−0.550739 | + | 0.834678i | \(0.685654\pi\) | |||||||
\(80\) | −1.07589 | − | 1.07589i | −0.120289 | − | 0.120289i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.71719 | −0.741789 | ||||||||
\(83\) | −4.07668 | − | 4.07668i | −0.447474 | − | 0.447474i | 0.447040 | − | 0.894514i | \(-0.352478\pi\) |
−0.894514 | + | 0.447040i | \(0.852478\pi\) | |||||||
\(84\) | −2.43205 | − | 1.24209i | −0.265359 | − | 0.135524i | ||||
\(85\) | 2.97542 | + | 2.97542i | 0.322729 | + | 0.322729i | ||||
\(86\) | −4.43127 | − | 4.43127i | −0.477836 | − | 0.477836i | ||||
\(87\) | 0.166822i | 0.0178852i | ||||||||
\(88\) | 1.84114i | 0.196266i | ||||||||
\(89\) | −11.9654 | + | 11.9654i | −1.26833 | + | 1.26833i | −0.321378 | + | 0.946951i | \(0.604146\pi\) |
−0.946951 | + | 0.321378i | \(0.895854\pi\) | |||||||
\(90\) | 1.72000 | 0.181304 | ||||||||
\(91\) | 2.35067 | + | 9.24523i | 0.246417 | + | 0.969164i | ||||
\(92\) | 5.23662 | 0.545955 | ||||||||
\(93\) | 2.47255 | − | 2.47255i | 0.256392 | − | 0.256392i | ||||
\(94\) | − | 3.68131i | − | 0.379698i | ||||||
\(95\) | − | 7.51956i | − | 0.771490i | ||||||
\(96\) | −3.61320 | − | 3.61320i | −0.368771 | − | 0.368771i | ||||
\(97\) | 1.41557 | + | 1.41557i | 0.143730 | + | 0.143730i | 0.775310 | − | 0.631580i | \(-0.217593\pi\) |
−0.631580 | + | 0.775310i | \(0.717593\pi\) | |||||||
\(98\) | 6.79963 | + | 1.09016i | 0.686867 | + | 0.110123i | ||||
\(99\) | −0.436434 | − | 0.436434i | −0.0438633 | − | 0.0438633i | ||||
\(100\) | 2.00576 | 0.200576 | ||||||||
\(101\) | 16.8635 | 1.67798 | 0.838992 | − | 0.544144i | \(-0.183145\pi\) | ||||
0.838992 | + | 0.544144i | \(0.183145\pi\) | |||||||
\(102\) | −1.67423 | − | 1.67423i | −0.165774 | − | 0.165774i | ||||
\(103\) | 14.7431 | 1.45268 | 0.726342 | − | 0.687333i | \(-0.241219\pi\) | ||||
0.726342 | + | 0.687333i | \(0.241219\pi\) | |||||||
\(104\) | −0.690350 | + | 10.7332i | −0.0676944 | + | 1.05247i | ||||
\(105\) | 4.40068 | − | 1.42526i | 0.429462 | − | 0.139091i | ||||
\(106\) | 4.49707 | − | 4.49707i | 0.436794 | − | 0.436794i | ||||
\(107\) | −11.0553 | −1.06876 | −0.534379 | − | 0.845245i | \(-0.679454\pi\) | ||||
−0.534379 | + | 0.845245i | \(0.679454\pi\) | |||||||
\(108\) | 1.03217 | 0.0993210 | ||||||||
\(109\) | 9.27976 | − | 9.27976i | 0.888840 | − | 0.888840i | −0.105572 | − | 0.994412i | \(-0.533667\pi\) |
0.994412 | + | 0.105572i | \(0.0336672\pi\) | |||||||
\(110\) | −0.750668 | − | 0.750668i | −0.0715734 | − | 0.0715734i | ||||
\(111\) | 5.59931 | − | 5.59931i | 0.531463 | − | 0.531463i | ||||
\(112\) | 2.05057 | + | 1.04726i | 0.193760 | + | 0.0989571i | ||||
\(113\) | 12.3107 | 1.15810 | 0.579048 | − | 0.815294i | \(-0.303425\pi\) | ||||
0.579048 | + | 0.815294i | \(0.303425\pi\) | |||||||
\(114\) | 4.23117i | 0.396285i | ||||||||
\(115\) | −6.27211 | + | 6.27211i | −0.584877 | + | 0.584877i | ||||
\(116\) | 0.172189i | 0.0159874i | ||||||||
\(117\) | −2.38061 | − | 2.70790i | −0.220087 | − | 0.250345i | ||||
\(118\) | − | 9.67771i | − | 0.890906i | ||||||
\(119\) | −5.67090 | − | 2.89624i | −0.519851 | − | 0.265498i | ||||
\(120\) | 5.21535 | 0.476094 | ||||||||
\(121\) | − | 10.6191i | − | 0.965368i | ||||||
\(122\) | 2.55503 | + | 2.55503i | 0.231322 | + | 0.231322i | ||||
\(123\) | 4.82807 | − | 4.82807i | 0.435333 | − | 0.435333i | ||||
\(124\) | 2.55210 | − | 2.55210i | 0.229186 | − | 0.229186i | ||||
\(125\) | −8.58377 | + | 8.58377i | −0.767755 | + | 0.767755i | ||||
\(126\) | −2.47621 | + | 0.801978i | −0.220598 | + | 0.0714459i | ||||
\(127\) | 17.7901i | 1.57862i | 0.613995 | + | 0.789310i | \(0.289562\pi\) | ||||
−0.613995 | + | 0.789310i | \(0.710438\pi\) | |||||||
\(128\) | −2.51866 | − | 2.51866i | −0.222621 | − | 0.222621i | ||||
\(129\) | 6.37008 | 0.560854 | ||||||||
\(130\) | −4.09465 | − | 4.65759i | −0.359125 | − | 0.408498i | ||||
\(131\) | − | 2.33242i | − | 0.203784i | −0.994795 | − | 0.101892i | \(-0.967510\pi\) | ||
0.994795 | − | 0.101892i | \(-0.0324896\pi\) | |||||||
\(132\) | −0.450476 | − | 0.450476i | −0.0392089 | − | 0.0392089i | ||||
\(133\) | 3.50611 | + | 10.8256i | 0.304018 | + | 0.938695i | ||||
\(134\) | 2.22560i | 0.192263i | ||||||||
\(135\) | −1.23628 | + | 1.23628i | −0.106402 | + | 0.106402i | ||||
\(136\) | −5.07656 | − | 5.07656i | −0.435312 | − | 0.435312i | ||||
\(137\) | 9.74888 | + | 9.74888i | 0.832903 | + | 0.832903i | 0.987913 | − | 0.155010i | \(-0.0495410\pi\) |
−0.155010 | + | 0.987913i | \(0.549541\pi\) | |||||||
\(138\) | 3.52924 | − | 3.52924i | 0.300429 | − | 0.300429i | ||||
\(139\) | − | 17.5778i | − | 1.49093i | −0.666546 | − | 0.745463i | \(-0.732228\pi\) | ||
0.666546 | − | 0.745463i | \(-0.267772\pi\) | |||||||
\(140\) | 4.54226 | − | 1.47112i | 0.383891 | − | 0.124332i | ||||
\(141\) | 2.64599 | + | 2.64599i | 0.222833 | + | 0.222833i | ||||
\(142\) | 2.30695i | 0.193595i | ||||||||
\(143\) | −0.142840 | + | 2.22080i | −0.0119449 | + | 0.185712i | ||||
\(144\) | −0.870270 | −0.0725225 | ||||||||
\(145\) | −0.206238 | − | 0.206238i | −0.0171272 | − | 0.0171272i | ||||
\(146\) | 6.80324i | 0.563040i | ||||||||
\(147\) | −5.67090 | + | 4.10376i | −0.467728 | + | 0.338473i | ||||
\(148\) | 5.77946 | − | 5.77946i | 0.475069 | − | 0.475069i | ||||
\(149\) | −0.269612 | + | 0.269612i | −0.0220875 | + | 0.0220875i | −0.718064 | − | 0.695977i | \(-0.754972\pi\) |
0.695977 | + | 0.718064i | \(0.254972\pi\) | |||||||
\(150\) | 1.35179 | − | 1.35179i | 0.110374 | − | 0.110374i | ||||
\(151\) | −3.72152 | − | 3.72152i | −0.302853 | − | 0.302853i | 0.539276 | − | 0.842129i | \(-0.318698\pi\) |
−0.842129 | + | 0.539276i | \(0.818698\pi\) | |||||||
\(152\) | 12.8296i | 1.04062i | ||||||||
\(153\) | 2.40676 | 0.194575 | ||||||||
\(154\) | 1.43071 | + | 0.730692i | 0.115290 | + | 0.0588809i | ||||
\(155\) | 6.11352i | 0.491050i | ||||||||
\(156\) | −2.45720 | − | 2.79502i | −0.196734 | − | 0.223781i | ||||
\(157\) | − | 17.5809i | − | 1.40311i | −0.712618 | − | 0.701553i | \(-0.752490\pi\) | ||
0.712618 | − | 0.701553i | \(-0.247510\pi\) | |||||||
\(158\) | −6.81040 | + | 6.81040i | −0.541807 | + | 0.541807i | ||||
\(159\) | 6.46466i | 0.512681i | ||||||||
\(160\) | 8.93383 | 0.706281 | ||||||||
\(161\) | 6.10520 | − | 11.9541i | 0.481157 | − | 0.942118i | ||||
\(162\) | 0.695639 | − | 0.695639i | 0.0546545 | − | 0.0546545i | ||||
\(163\) | −1.00752 | − | 1.00752i | −0.0789148 | − | 0.0789148i | 0.666548 | − | 0.745462i | \(-0.267771\pi\) |
−0.745462 | + | 0.666548i | \(0.767771\pi\) | |||||||
\(164\) | 4.98341 | − | 4.98341i | 0.389139 | − | 0.389139i | ||||
\(165\) | 1.07911 | 0.0840084 | ||||||||
\(166\) | −5.67180 | −0.440217 | ||||||||
\(167\) | −16.0507 | + | 16.0507i | −1.24204 | + | 1.24204i | −0.282889 | + | 0.959153i | \(0.591293\pi\) |
−0.959153 | + | 0.282889i | \(0.908707\pi\) | |||||||
\(168\) | −7.50830 | + | 2.43174i | −0.579278 | + | 0.187612i | ||||
\(169\) | −1.66541 | + | 12.8929i | −0.128109 | + | 0.991760i | ||||
\(170\) | 4.13963 | 0.317495 | ||||||||
\(171\) | −3.04121 | − | 3.04121i | −0.232567 | − | 0.232567i | ||||
\(172\) | 6.57503 | 0.501341 | ||||||||
\(173\) | −12.8330 | −0.975676 | −0.487838 | − | 0.872934i | \(-0.662214\pi\) | ||||
−0.487838 | + | 0.872934i | \(0.662214\pi\) | |||||||
\(174\) | 0.116048 | + | 0.116048i | 0.00879757 | + | 0.00879757i | ||||
\(175\) | 2.33845 | − | 4.57875i | 0.176770 | − | 0.346121i | ||||
\(176\) | 0.379816 | + | 0.379816i | 0.0286297 | + | 0.0286297i | ||||
\(177\) | 6.95599 | + | 6.95599i | 0.522844 | + | 0.522844i | ||||
\(178\) | 16.6472i | 1.24776i | ||||||||
\(179\) | − | 17.3893i | − | 1.29974i | −0.760046 | − | 0.649869i | \(-0.774824\pi\) | ||
0.760046 | − | 0.649869i | \(-0.225176\pi\) | |||||||
\(180\) | −1.27605 | + | 1.27605i | −0.0951113 | + | 0.0951113i | ||||
\(181\) | 14.1584 | 1.05238 | 0.526191 | − | 0.850366i | \(-0.323620\pi\) | ||||
0.526191 | + | 0.850366i | \(0.323620\pi\) | |||||||
\(182\) | 8.06656 | + | 4.79613i | 0.597933 | + | 0.355513i | ||||
\(183\) | −3.67293 | −0.271511 | ||||||||
\(184\) | 10.7013 | − | 10.7013i | 0.788909 | − | 0.788909i | ||||
\(185\) | 13.8446i | 1.01787i | ||||||||
\(186\) | − | 3.44001i | − | 0.252234i | ||||||
\(187\) | −1.05039 | − | 1.05039i | −0.0768122 | − | 0.0768122i | ||||
\(188\) | 2.73112 | + | 2.73112i | 0.199188 | + | 0.199188i | ||||
\(189\) | 1.20338 | − | 2.35624i | 0.0875329 | − | 0.171391i | ||||
\(190\) | −5.23090 | − | 5.23090i | −0.379489 | − | 0.379489i | ||||
\(191\) | −1.61029 | −0.116516 | −0.0582581 | − | 0.998302i | \(-0.518555\pi\) | ||||
−0.0582581 | + | 0.998302i | \(0.518555\pi\) | |||||||
\(192\) | −6.76750 | −0.488403 | ||||||||
\(193\) | 15.5701 | + | 15.5701i | 1.12076 | + | 1.12076i | 0.991627 | + | 0.129132i | \(0.0412190\pi\) |
0.129132 | + | 0.991627i | \(0.458781\pi\) | |||||||
\(194\) | 1.96946 | 0.141399 | ||||||||
\(195\) | 6.29080 | + | 0.404620i | 0.450493 | + | 0.0289754i | ||||
\(196\) | −5.85336 | + | 4.23580i | −0.418097 | + | 0.302557i | ||||
\(197\) | −12.8905 | + | 12.8905i | −0.918408 | + | 0.918408i | −0.996914 | − | 0.0785057i | \(-0.974985\pi\) |
0.0785057 | + | 0.996914i | \(0.474985\pi\) | |||||||
\(198\) | −0.607201 | −0.0431519 | ||||||||
\(199\) | −13.5710 | −0.962024 | −0.481012 | − | 0.876714i | \(-0.659731\pi\) | ||||
−0.481012 | + | 0.876714i | \(0.659731\pi\) | |||||||
\(200\) | 4.09887 | − | 4.09887i | 0.289834 | − | 0.289834i | ||||
\(201\) | −1.59968 | − | 1.59968i | −0.112833 | − | 0.112833i | ||||
\(202\) | 11.7309 | − | 11.7309i | 0.825385 | − | 0.825385i | ||||
\(203\) | 0.393073 | + | 0.200750i | 0.0275883 | + | 0.0140899i | ||||
\(204\) | 2.48419 | 0.173928 | ||||||||
\(205\) | 11.9377i | 0.833762i | ||||||||
\(206\) | 10.2559 | − | 10.2559i | 0.714562 | − | 0.714562i | ||||
\(207\) | 5.07339i | 0.352625i | ||||||||
\(208\) | 2.07177 | + | 2.35660i | 0.143651 | + | 0.163401i | ||||
\(209\) | 2.65458i | 0.183621i | ||||||||
\(210\) | 2.06981 | − | 4.05275i | 0.142831 | − | 0.279666i | ||||
\(211\) | −12.1333 | −0.835292 | −0.417646 | − | 0.908610i | \(-0.637145\pi\) | ||||
−0.417646 | + | 0.908610i | \(0.637145\pi\) | |||||||
\(212\) | 6.67266i | 0.458280i | ||||||||
\(213\) | −1.65815 | − | 1.65815i | −0.113615 | − | 0.113615i | ||||
\(214\) | −7.69050 | + | 7.69050i | −0.525712 | + | 0.525712i | ||||
\(215\) | −7.87518 | + | 7.87518i | −0.537083 | + | 0.537083i | ||||
\(216\) | 2.10930 | − | 2.10930i | 0.143519 | − | 0.143519i | ||||
\(217\) | −2.85052 | − | 8.80135i | −0.193506 | − | 0.597475i | ||||
\(218\) | − | 12.9107i | − | 0.874425i | ||||||
\(219\) | −4.88992 | − | 4.88992i | −0.330430 | − | 0.330430i | ||||
\(220\) | 1.11383 | 0.0750941 | ||||||||
\(221\) | −5.72954 | − | 6.51725i | −0.385411 | − | 0.438397i | ||||
\(222\) | − | 7.79020i | − | 0.522844i | ||||||
\(223\) | 4.74466 | + | 4.74466i | 0.317726 | + | 0.317726i | 0.847893 | − | 0.530167i | \(-0.177871\pi\) |
−0.530167 | + | 0.847893i | \(0.677871\pi\) | |||||||
\(224\) | −12.8616 | + | 4.16553i | −0.859354 | + | 0.278321i | ||||
\(225\) | 1.94324i | 0.129549i | ||||||||
\(226\) | 8.56381 | − | 8.56381i | 0.569656 | − | 0.569656i | ||||
\(227\) | −10.5233 | − | 10.5233i | −0.698454 | − | 0.698454i | 0.265623 | − | 0.964077i | \(-0.414422\pi\) |
−0.964077 | + | 0.265623i | \(0.914422\pi\) | |||||||
\(228\) | −3.13906 | − | 3.13906i | −0.207889 | − | 0.207889i | ||||
\(229\) | 20.7310 | − | 20.7310i | 1.36994 | − | 1.36994i | 0.509427 | − | 0.860514i | \(-0.329858\pi\) |
0.860514 | − | 0.509427i | \(-0.170142\pi\) | |||||||
\(230\) | 8.72624i | 0.575391i | ||||||||
\(231\) | −1.55354 | + | 0.503150i | −0.102215 | + | 0.0331048i | ||||
\(232\) | 0.351877 | + | 0.351877i | 0.0231019 | + | 0.0231019i | ||||
\(233\) | 6.37148i | 0.417409i | 0.977979 | + | 0.208705i | \(0.0669247\pi\) | ||||
−0.977979 | + | 0.208705i | \(0.933075\pi\) | |||||||
\(234\) | −3.53976 | − | 0.227675i | −0.231401 | − | 0.0148836i | ||||
\(235\) | −6.54235 | −0.426776 | ||||||||
\(236\) | 7.17979 | + | 7.17979i | 0.467365 | + | 0.467365i | ||||
\(237\) | − | 9.79014i | − | 0.635938i | ||||||
\(238\) | −5.95963 | + | 1.93016i | −0.386306 | + | 0.125114i | ||||
\(239\) | −18.6706 | + | 18.6706i | −1.20770 | + | 1.20770i | −0.235935 | + | 0.971769i | \(0.575815\pi\) |
−0.971769 | + | 0.235935i | \(0.924185\pi\) | |||||||
\(240\) | 1.07589 | − | 1.07589i | 0.0694487 | − | 0.0694487i | ||||
\(241\) | −2.22932 | + | 2.22932i | −0.143603 | + | 0.143603i | −0.775253 | − | 0.631650i | \(-0.782378\pi\) |
0.631650 | + | 0.775253i | \(0.282378\pi\) | |||||||
\(242\) | −7.38702 | − | 7.38702i | −0.474856 | − | 0.474856i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −3.79110 | −0.242700 | ||||||||
\(245\) | 1.93742 | − | 12.0842i | 0.123777 | − | 0.772030i | ||||
\(246\) | − | 6.71719i | − | 0.428272i | ||||||
\(247\) | −0.995356 | + | 15.4752i | −0.0633330 | + | 0.984665i | ||||
\(248\) | − | 10.4307i | − | 0.662350i | ||||||
\(249\) | 4.07668 | − | 4.07668i | 0.258349 | − | 0.258349i | ||||
\(250\) | 11.9424i | 0.755304i | ||||||||
\(251\) | −1.06046 | −0.0669356 | −0.0334678 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334678 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(252\) | 1.24209 | − | 2.43205i | 0.0782446 | − | 0.153205i | ||||
\(253\) | 2.21420 | − | 2.21420i | 0.139206 | − | 0.139206i | ||||
\(254\) | 12.3755 | + | 12.3755i | 0.776509 | + | 0.776509i | ||||
\(255\) | −2.97542 | + | 2.97542i | −0.186328 | + | 0.186328i | ||||
\(256\) | −17.0392 | −1.06495 | ||||||||
\(257\) | −7.75932 | −0.484013 | −0.242007 | − | 0.970275i | \(-0.577806\pi\) | ||||
−0.242007 | + | 0.970275i | \(0.577806\pi\) | |||||||
\(258\) | 4.43127 | − | 4.43127i | 0.275879 | − | 0.275879i | ||||
\(259\) | −6.45525 | − | 19.9314i | −0.401110 | − | 1.23848i | ||||
\(260\) | 6.49320 | + | 0.417638i | 0.402691 | + | 0.0259008i | ||||
\(261\) | −0.166822 | −0.0103260 | ||||||||
\(262\) | −1.62252 | − | 1.62252i | −0.100240 | − | 0.100240i | ||||
\(263\) | −5.08859 | −0.313776 | −0.156888 | − | 0.987616i | \(-0.550146\pi\) | ||||
−0.156888 | + | 0.987616i | \(0.550146\pi\) | |||||||
\(264\) | −1.84114 | −0.113314 | ||||||||
\(265\) | −7.99211 | − | 7.99211i | −0.490951 | − | 0.490951i | ||||
\(266\) | 9.96966 | + | 5.09170i | 0.611279 | + | 0.312192i | ||||
\(267\) | −11.9654 | − | 11.9654i | −0.732270 | − | 0.732270i | ||||
\(268\) | −1.65115 | − | 1.65115i | −0.100860 | − | 0.100860i | ||||
\(269\) | 12.9830i | 0.791585i | 0.918340 | + | 0.395793i | \(0.129530\pi\) | ||||
−0.918340 | + | 0.395793i | \(0.870470\pi\) | |||||||
\(270\) | 1.72000i | 0.104676i | ||||||||
\(271\) | 5.68824 | − | 5.68824i | 0.345536 | − | 0.345536i | −0.512908 | − | 0.858444i | \(-0.671432\pi\) |
0.858444 | + | 0.512908i | \(0.171432\pi\) | |||||||
\(272\) | −2.09453 | −0.126999 | ||||||||
\(273\) | −9.24523 | + | 2.35067i | −0.559547 | + | 0.142269i | ||||
\(274\) | 13.5634 | 0.819395 | ||||||||
\(275\) | 0.848097 | − | 0.848097i | 0.0511422 | − | 0.0511422i | ||||
\(276\) | 5.23662i | 0.315207i | ||||||||
\(277\) | 7.99926i | 0.480629i | 0.970695 | + | 0.240314i | \(0.0772505\pi\) | ||||
−0.970695 | + | 0.240314i | \(0.922749\pi\) | |||||||
\(278\) | −12.2278 | − | 12.2278i | −0.733373 | − | 0.733373i | ||||
\(279\) | 2.47255 | + | 2.47255i | 0.148028 | + | 0.148028i | ||||
\(280\) | 6.27604 | − | 12.2886i | 0.375065 | − | 0.734386i | ||||
\(281\) | −12.1673 | − | 12.1673i | −0.725839 | − | 0.725839i | 0.243949 | − | 0.969788i | \(-0.421557\pi\) |
−0.969788 | + | 0.243949i | \(0.921557\pi\) | |||||||
\(282\) | 3.68131 | 0.219219 | ||||||||
\(283\) | 3.07612 | 0.182857 | 0.0914283 | − | 0.995812i | \(-0.470857\pi\) | ||||
0.0914283 | + | 0.995812i | \(0.470857\pi\) | |||||||
\(284\) | −1.71150 | − | 1.71150i | −0.101559 | − | 0.101559i | ||||
\(285\) | 7.51956 | 0.445420 | ||||||||
\(286\) | 1.44551 | + | 1.64424i | 0.0854747 | + | 0.0972258i | ||||
\(287\) | −5.56612 | − | 17.1861i | −0.328557 | − | 1.01446i | ||||
\(288\) | 3.61320 | − | 3.61320i | 0.212910 | − | 0.212910i | ||||
\(289\) | −11.2075 | −0.659266 | ||||||||
\(290\) | −0.286935 | −0.0168494 | ||||||||
\(291\) | −1.41557 | + | 1.41557i | −0.0829825 | + | 0.0829825i | ||||
\(292\) | −5.04725 | − | 5.04725i | −0.295368 | − | 0.295368i | ||||
\(293\) | −18.7336 | + | 18.7336i | −1.09443 | + | 1.09443i | −0.0993799 | + | 0.995050i | \(0.531686\pi\) |
−0.995050 | + | 0.0993799i | \(0.968314\pi\) | |||||||
\(294\) | −1.09016 | + | 6.79963i | −0.0635795 | + | 0.396563i | ||||
\(295\) | −17.1991 | −1.00137 | ||||||||
\(296\) | − | 23.6212i | − | 1.37296i | ||||||
\(297\) | 0.436434 | − | 0.436434i | 0.0253245 | − | 0.0253245i | ||||
\(298\) | 0.375105i | 0.0217293i | ||||||||
\(299\) | 13.7382 | − | 12.0777i | 0.794501 | − | 0.698474i | ||||
\(300\) | 2.00576i | 0.115803i | ||||||||
\(301\) | 7.66561 | − | 15.0095i | 0.441838 | − | 0.865130i | ||||
\(302\) | −5.17767 | −0.297942 | ||||||||
\(303\) | 16.8635i | 0.968784i | ||||||||
\(304\) | 2.64668 | + | 2.64668i | 0.151797 | + | 0.151797i | ||||
\(305\) | 4.54076 | − | 4.54076i | 0.260003 | − | 0.260003i | ||||
\(306\) | 1.67423 | − | 1.67423i | 0.0957095 | − | 0.0957095i | ||||
\(307\) | −4.74652 | + | 4.74652i | −0.270898 | + | 0.270898i | −0.829462 | − | 0.558563i | \(-0.811353\pi\) |
0.558563 | + | 0.829462i | \(0.311353\pi\) | |||||||
\(308\) | −1.60352 | + | 0.519338i | −0.0913693 | + | 0.0295920i | ||||
\(309\) | 14.7431i | 0.838708i | ||||||||
\(310\) | 4.25280 | + | 4.25280i | 0.241543 | + | 0.241543i | ||||
\(311\) | 25.2400 | 1.43123 | 0.715616 | − | 0.698494i | \(-0.246146\pi\) | ||||
0.715616 | + | 0.698494i | \(0.246146\pi\) | |||||||
\(312\) | −10.7332 | − | 0.690350i | −0.607646 | − | 0.0390834i | ||||
\(313\) | 4.80127i | 0.271384i | 0.990751 | + | 0.135692i | \(0.0433257\pi\) | ||||
−0.990751 | + | 0.135692i | \(0.956674\pi\) | |||||||
\(314\) | −12.2299 | − | 12.2299i | −0.690175 | − | 0.690175i | ||||
\(315\) | 1.42526 | + | 4.40068i | 0.0803043 | + | 0.247950i | ||||
\(316\) | − | 10.1051i | − | 0.568458i | ||||||
\(317\) | −12.4651 | + | 12.4651i | −0.700111 | + | 0.700111i | −0.964434 | − | 0.264324i | \(-0.914851\pi\) |
0.264324 | + | 0.964434i | \(0.414851\pi\) | |||||||
\(318\) | 4.49707 | + | 4.49707i | 0.252183 | + | 0.252183i | ||||
\(319\) | 0.0728069 | + | 0.0728069i | 0.00407640 | + | 0.00407640i | ||||
\(320\) | 8.36651 | − | 8.36651i | 0.467702 | − | 0.467702i | ||||
\(321\) | − | 11.0553i | − | 0.617047i | ||||||
\(322\) | −4.06874 | − | 12.5628i | −0.226742 | − | 0.700096i | ||||
\(323\) | −7.31945 | − | 7.31945i | −0.407265 | − | 0.407265i | ||||
\(324\) | 1.03217i | 0.0573430i | ||||||||
\(325\) | 5.26210 | − | 4.62610i | 0.291889 | − | 0.256610i | ||||
\(326\) | −1.40174 | −0.0776349 | ||||||||
\(327\) | 9.27976 | + | 9.27976i | 0.513172 | + | 0.513172i | ||||
\(328\) | − | 20.3677i | − | 1.12462i | ||||||
\(329\) | 9.41872 | − | 3.05047i | 0.519271 | − | 0.168178i | ||||
\(330\) | 0.750668 | − | 0.750668i | 0.0413229 | − | 0.0413229i | ||||
\(331\) | 4.48479 | − | 4.48479i | 0.246506 | − | 0.246506i | −0.573029 | − | 0.819535i | \(-0.694232\pi\) |
0.819535 | + | 0.573029i | \(0.194232\pi\) | |||||||
\(332\) | 4.20785 | − | 4.20785i | 0.230936 | − | 0.230936i | ||||
\(333\) | 5.59931 | + | 5.59931i | 0.306840 | + | 0.306840i | ||||
\(334\) | 22.3310i | 1.22190i | ||||||||
\(335\) | 3.95530 | 0.216101 | ||||||||
\(336\) | −1.04726 | + | 2.05057i | −0.0571329 | + | 0.111868i | ||||
\(337\) | 12.2741i | 0.668611i | 0.942465 | + | 0.334306i | \(0.108502\pi\) | ||||
−0.942465 | + | 0.334306i | \(0.891498\pi\) | |||||||
\(338\) | 7.81026 | + | 10.1273i | 0.424822 | + | 0.550853i | ||||
\(339\) | 12.3107i | 0.668627i | ||||||||
\(340\) | −3.07115 | + | 3.07115i | −0.166556 | + | 0.166556i | ||||
\(341\) | − | 2.15821i | − | 0.116874i | ||||||
\(342\) | −4.23117 | −0.228795 | ||||||||
\(343\) | 2.84523 | + | 18.3004i | 0.153628 | + | 0.988129i | ||||
\(344\) | 13.4364 | − | 13.4364i | 0.724442 | − | 0.724442i | ||||
\(345\) | −6.27211 | − | 6.27211i | −0.337679 | − | 0.337679i | ||||
\(346\) | −8.92714 | + | 8.92714i | −0.479926 | + | 0.479926i | ||||
\(347\) | 32.4407 | 1.74151 | 0.870754 | − | 0.491719i | \(-0.163631\pi\) | ||||
0.870754 | + | 0.491719i | \(0.163631\pi\) | |||||||
\(348\) | −0.172189 | −0.00923032 | ||||||||
\(349\) | −20.5692 | + | 20.5692i | −1.10104 | + | 1.10104i | −0.106760 | + | 0.994285i | \(0.534048\pi\) |
−0.994285 | + | 0.106760i | \(0.965952\pi\) | |||||||
\(350\) | −1.55844 | − | 4.81187i | −0.0833019 | − | 0.257205i | ||||
\(351\) | 2.70790 | − | 2.38061i | 0.144537 | − | 0.127067i | ||||
\(352\) | −3.15385 | −0.168101 | ||||||||
\(353\) | −9.10052 | − | 9.10052i | −0.484372 | − | 0.484372i | 0.422153 | − | 0.906525i | \(-0.361275\pi\) |
−0.906525 | + | 0.422153i | \(0.861275\pi\) | |||||||
\(354\) | 9.67771 | 0.514365 | ||||||||
\(355\) | 4.09987 | 0.217598 | ||||||||
\(356\) | −12.3504 | − | 12.3504i | −0.654568 | − | 0.654568i | ||||
\(357\) | 2.89624 | − | 5.67090i | 0.153285 | − | 0.300136i | ||||
\(358\) | −12.0967 | − | 12.0967i | −0.639329 | − | 0.639329i | ||||
\(359\) | 17.3029 | + | 17.3029i | 0.913215 | + | 0.913215i | 0.996524 | − | 0.0833092i | \(-0.0265489\pi\) |
−0.0833092 | + | 0.996524i | \(0.526549\pi\) | |||||||
\(360\) | 5.21535i | 0.274873i | ||||||||
\(361\) | − | 0.502056i | − | 0.0264240i | ||||||
\(362\) | 9.84910 | − | 9.84910i | 0.517657 | − | 0.517657i | ||||
\(363\) | 10.6191 | 0.557356 | ||||||||
\(364\) | −9.54269 | + | 2.42630i | −0.500173 | + | 0.127173i | ||||
\(365\) | 12.0906 | 0.632851 | ||||||||
\(366\) | −2.55503 | + | 2.55503i | −0.133554 | + | 0.133554i | ||||
\(367\) | 19.1370i | 0.998941i | 0.866331 | + | 0.499471i | \(0.166472\pi\) | ||||
−0.866331 | + | 0.499471i | \(0.833528\pi\) | |||||||
\(368\) | − | 4.41522i | − | 0.230159i | ||||||
\(369\) | 4.82807 | + | 4.82807i | 0.251339 | + | 0.251339i | ||||
\(370\) | 9.63083 | + | 9.63083i | 0.500683 | + | 0.500683i | ||||
\(371\) | 15.2323 | + | 7.77943i | 0.790823 | + | 0.403888i | ||||
\(372\) | 2.55210 | + | 2.55210i | 0.132320 | + | 0.132320i | ||||
\(373\) | 8.12926 | 0.420917 | 0.210459 | − | 0.977603i | \(-0.432504\pi\) | ||||
0.210459 | + | 0.977603i | \(0.432504\pi\) | |||||||
\(374\) | −1.46138 | −0.0755664 | ||||||||
\(375\) | −8.58377 | − | 8.58377i | −0.443264 | − | 0.443264i | ||||
\(376\) | 11.1624 | 0.575655 | ||||||||
\(377\) | 0.397138 | + | 0.451737i | 0.0204536 | + | 0.0232656i | ||||
\(378\) | −0.801978 | − | 2.47621i | −0.0412493 | − | 0.127362i | ||||
\(379\) | 10.0128 | − | 10.0128i | 0.514321 | − | 0.514321i | −0.401526 | − | 0.915848i | \(-0.631520\pi\) |
0.915848 | + | 0.401526i | \(0.131520\pi\) | |||||||
\(380\) | 7.76149 | 0.398156 | ||||||||
\(381\) | −17.7901 | −0.911417 | ||||||||
\(382\) | −1.12018 | + | 1.12018i | −0.0573133 | + | 0.0573133i | ||||
\(383\) | −27.1171 | − | 27.1171i | −1.38562 | − | 1.38562i | −0.834284 | − | 0.551334i | \(-0.814119\pi\) |
−0.551334 | − | 0.834284i | \(-0.685881\pi\) | |||||||
\(384\) | 2.51866 | − | 2.51866i | 0.128530 | − | 0.128530i | ||||
\(385\) | 1.29857 | − | 2.54264i | 0.0661814 | − | 0.129585i | ||||
\(386\) | 21.6623 | 1.10258 | ||||||||
\(387\) | 6.37008i | 0.323809i | ||||||||
\(388\) | −1.46112 | + | 1.46112i | −0.0741771 | + | 0.0741771i | ||||
\(389\) | 34.8952i | 1.76926i | 0.466297 | + | 0.884628i | \(0.345588\pi\) | ||||
−0.466297 | + | 0.884628i | \(0.654412\pi\) | |||||||
\(390\) | 4.65759 | − | 4.09465i | 0.235846 | − | 0.207341i | ||||
\(391\) | 12.2104i | 0.617506i | ||||||||
\(392\) | −3.30556 | + | 20.6177i | −0.166956 | + | 1.04135i | ||||
\(393\) | 2.33242 | 0.117655 | ||||||||
\(394\) | 17.9342i | 0.903513i | ||||||||
\(395\) | 12.1033 | + | 12.1033i | 0.608984 | + | 0.608984i | ||||
\(396\) | 0.450476 | − | 0.450476i | 0.0226373 | − | 0.0226373i | ||||
\(397\) | −21.8818 | + | 21.8818i | −1.09822 | + | 1.09822i | −0.103599 | + | 0.994619i | \(0.533036\pi\) |
−0.994619 | + | 0.103599i | \(0.966964\pi\) | |||||||
\(398\) | −9.44053 | + | 9.44053i | −0.473211 | + | 0.473211i | ||||
\(399\) | −10.8256 | + | 3.50611i | −0.541956 | + | 0.175525i | ||||
\(400\) | − | 1.69114i | − | 0.0845572i | ||||||
\(401\) | 7.79276 | + | 7.79276i | 0.389152 | + | 0.389152i | 0.874385 | − | 0.485233i | \(-0.161265\pi\) |
−0.485233 | + | 0.874385i | \(0.661265\pi\) | |||||||
\(402\) | −2.22560 | −0.111003 | ||||||||
\(403\) | 0.809240 | − | 12.5816i | 0.0403111 | − | 0.626734i | ||||
\(404\) | 17.4061i | 0.865985i | ||||||||
\(405\) | −1.23628 | − | 1.23628i | −0.0614311 | − | 0.0614311i | ||||
\(406\) | 0.413087 | − | 0.133788i | 0.0205011 | − | 0.00663977i | ||||
\(407\) | − | 4.88746i | − | 0.242263i | ||||||
\(408\) | 5.07656 | − | 5.07656i | 0.251327 | − | 0.251327i | ||||
\(409\) | −22.4425 | − | 22.4425i | −1.10971 | − | 1.10971i | −0.993188 | − | 0.116524i | \(-0.962825\pi\) |
−0.116524 | − | 0.993188i | \(-0.537175\pi\) | |||||||
\(410\) | 8.30430 | + | 8.30430i | 0.410120 | + | 0.410120i | ||||
\(411\) | −9.74888 | + | 9.74888i | −0.480877 | + | 0.480877i | ||||
\(412\) | 15.2175i | 0.749711i | ||||||||
\(413\) | 24.7607 | − | 8.01932i | 1.21839 | − | 0.394605i | ||||
\(414\) | 3.52924 | + | 3.52924i | 0.173453 | + | 0.173453i | ||||
\(415\) | 10.0798i | 0.494799i | ||||||||
\(416\) | −18.3858 | − | 1.18256i | −0.901438 | − | 0.0579799i | ||||
\(417\) | 17.5778 | 0.860787 | ||||||||
\(418\) | 1.84663 | + | 1.84663i | 0.0903215 | + | 0.0903215i | ||||
\(419\) | − | 31.2454i | − | 1.52644i | −0.646141 | − | 0.763218i | \(-0.723618\pi\) | ||
0.646141 | − | 0.763218i | \(-0.276382\pi\) | |||||||
\(420\) | 1.47112 | + | 4.54226i | 0.0717831 | + | 0.221640i | ||||
\(421\) | 17.2565 | − | 17.2565i | 0.841029 | − | 0.841029i | −0.147964 | − | 0.988993i | \(-0.547272\pi\) |
0.988993 | + | 0.147964i | \(0.0472720\pi\) | |||||||
\(422\) | −8.44041 | + | 8.44041i | −0.410873 | + | 0.410873i | ||||
\(423\) | −2.64599 | + | 2.64599i | −0.128652 | + | 0.128652i | ||||
\(424\) | 13.6359 | + | 13.6359i | 0.662218 | + | 0.662218i | ||||
\(425\) | 4.67691i | 0.226863i | ||||||||
\(426\) | −2.30695 | −0.111772 | ||||||||
\(427\) | −4.41992 | + | 8.65432i | −0.213895 | + | 0.418812i | ||||
\(428\) | − | 11.4110i | − | 0.551571i | ||||||
\(429\) | −2.22080 | − | 0.142840i | −0.107221 | − | 0.00689639i | ||||
\(430\) | 10.9566i | 0.528372i | ||||||||
\(431\) | −11.9765 | + | 11.9765i | −0.576886 | + | 0.576886i | −0.934044 | − | 0.357158i | \(-0.883746\pi\) |
0.357158 | + | 0.934044i | \(0.383746\pi\) | |||||||
\(432\) | − | 0.870270i | − | 0.0418709i | ||||||
\(433\) | 17.0143 | 0.817655 | 0.408827 | − | 0.912612i | \(-0.365938\pi\) | ||||
0.408827 | + | 0.912612i | \(0.365938\pi\) | |||||||
\(434\) | −8.10549 | − | 4.13963i | −0.389076 | − | 0.198708i | ||||
\(435\) | 0.206238 | − | 0.206238i | 0.00988837 | − | 0.00988837i | ||||
\(436\) | 9.57833 | + | 9.57833i | 0.458719 | + | 0.458719i | ||||
\(437\) | 15.4292 | − | 15.4292i | 0.738081 | − | 0.738081i | ||||
\(438\) | −6.80324 | −0.325071 | ||||||||
\(439\) | −28.1092 | −1.34158 | −0.670790 | − | 0.741648i | \(-0.734045\pi\) | ||||
−0.670790 | + | 0.741648i | \(0.734045\pi\) | |||||||
\(440\) | 2.27616 | − | 2.27616i | 0.108512 | − | 0.108512i | ||||
\(441\) | −4.10376 | − | 5.67090i | −0.195417 | − | 0.270043i | ||||
\(442\) | −8.51934 | − | 0.547958i | −0.405224 | − | 0.0260637i | ||||
\(443\) | 19.0605 | 0.905591 | 0.452795 | − | 0.891614i | \(-0.350427\pi\) | ||||
0.452795 | + | 0.891614i | \(0.350427\pi\) | |||||||
\(444\) | 5.77946 | + | 5.77946i | 0.274281 | + | 0.274281i | ||||
\(445\) | 29.5851 | 1.40247 | ||||||||
\(446\) | 6.60114 | 0.312573 | ||||||||
\(447\) | −0.269612 | − | 0.269612i | −0.0127522 | − | 0.0127522i | ||||
\(448\) | −8.14386 | + | 15.9459i | −0.384761 | + | 0.753372i | ||||
\(449\) | −10.1856 | − | 10.1856i | −0.480690 | − | 0.480690i | 0.424662 | − | 0.905352i | \(-0.360393\pi\) |
−0.905352 | + | 0.424662i | \(0.860393\pi\) | |||||||
\(450\) | 1.35179 | + | 1.35179i | 0.0637242 | + | 0.0637242i | ||||
\(451\) | − | 4.21427i | − | 0.198442i | ||||||
\(452\) | 12.7068i | 0.597678i | ||||||||
\(453\) | 3.72152 | − | 3.72152i | 0.174852 | − | 0.174852i | ||||
\(454\) | −14.6408 | −0.687126 | ||||||||
\(455\) | 8.52359 | − | 14.3357i | 0.399592 | − | 0.672070i | ||||
\(456\) | −12.8296 | −0.600803 | ||||||||
\(457\) | 7.05936 | − | 7.05936i | 0.330223 | − | 0.330223i | −0.522448 | − | 0.852671i | \(-0.674981\pi\) |
0.852671 | + | 0.522448i | \(0.174981\pi\) | |||||||
\(458\) | − | 28.8425i | − | 1.34772i | ||||||
\(459\) | 2.40676i | 0.112338i | ||||||||
\(460\) | −6.47390 | − | 6.47390i | −0.301847 | − | 0.301847i | ||||
\(461\) | 29.3823 | + | 29.3823i | 1.36847 | + | 1.36847i | 0.862623 | + | 0.505847i | \(0.168820\pi\) |
0.505847 | + | 0.862623i | \(0.331180\pi\) | |||||||
\(462\) | −0.730692 | + | 1.43071i | −0.0339949 | + | 0.0665628i | ||||
\(463\) | −5.98784 | − | 5.98784i | −0.278278 | − | 0.278278i | 0.554143 | − | 0.832421i | \(-0.313046\pi\) |
−0.832421 | + | 0.554143i | \(0.813046\pi\) | |||||||
\(464\) | 0.145180 | 0.00673982 | ||||||||
\(465\) | −6.11352 | −0.283508 | ||||||||
\(466\) | 4.43224 | + | 4.43224i | 0.205320 | + | 0.205320i | ||||
\(467\) | 26.7048 | 1.23575 | 0.617875 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617875 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(468\) | 2.79502 | − | 2.45720i | 0.129200 | − | 0.113584i | ||||
\(469\) | −5.69427 | + | 1.84422i | −0.262937 | + | 0.0851582i | ||||
\(470\) | −4.55111 | + | 4.55111i | −0.209927 | + | 0.209927i | ||||
\(471\) | 17.5809 | 0.810083 | ||||||||
\(472\) | 29.3445 | 1.35069 | ||||||||
\(473\) | 2.78012 | − | 2.78012i | 0.127830 | − | 0.127830i | ||||
\(474\) | −6.81040 | − | 6.81040i | −0.312812 | − | 0.312812i | ||||
\(475\) | 5.90981 | − | 5.90981i | 0.271161 | − | 0.271161i | ||||
\(476\) | 2.98942 | − | 5.85336i | 0.137020 | − | 0.268288i | ||||
\(477\) | −6.46466 | −0.295997 | ||||||||
\(478\) | 25.9760i | 1.18812i | ||||||||
\(479\) | 9.06708 | − | 9.06708i | 0.414285 | − | 0.414285i | −0.468943 | − | 0.883228i | \(-0.655365\pi\) |
0.883228 | + | 0.468943i | \(0.155365\pi\) | |||||||
\(480\) | 8.93383i | 0.407772i | ||||||||
\(481\) | 1.83259 | − | 28.4921i | 0.0835591 | − | 1.29913i | ||||
\(482\) | 3.10160i | 0.141274i | ||||||||
\(483\) | 11.9541 | + | 6.10520i | 0.543932 | + | 0.277796i | ||||
\(484\) | 10.9607 | 0.498214 | ||||||||
\(485\) | − | 3.50008i | − | 0.158931i | ||||||
\(486\) | 0.695639 | + | 0.695639i | 0.0315548 | + | 0.0315548i | ||||
\(487\) | 10.1182 | − | 10.1182i | 0.458500 | − | 0.458500i | −0.439663 | − | 0.898163i | \(-0.644902\pi\) |
0.898163 | + | 0.439663i | \(0.144902\pi\) | |||||||
\(488\) | −7.74730 | + | 7.74730i | −0.350704 | + | 0.350704i | ||||
\(489\) | 1.00752 | − | 1.00752i | 0.0455615 | − | 0.0455615i | ||||
\(490\) | −7.05849 | − | 9.75397i | −0.318870 | − | 0.440639i | ||||
\(491\) | − | 33.4254i | − | 1.50847i | −0.656607 | − | 0.754233i | \(-0.728009\pi\) | ||
0.656607 | − | 0.754233i | \(-0.271991\pi\) | |||||||
\(492\) | 4.98341 | + | 4.98341i | 0.224669 | + | 0.224669i | ||||
\(493\) | −0.401500 | −0.0180827 | ||||||||
\(494\) | 10.0728 | + | 11.4576i | 0.453195 | + | 0.515501i | ||||
\(495\) | 1.07911i | 0.0485022i | ||||||||
\(496\) | −2.15179 | − | 2.15179i | −0.0966181 | − | 0.0966181i | ||||
\(497\) | −5.90239 | + | 1.91162i | −0.264758 | + | 0.0857481i | ||||
\(498\) | − | 5.67180i | − | 0.254159i | ||||||
\(499\) | −6.16674 | + | 6.16674i | −0.276061 | + | 0.276061i | −0.831535 | − | 0.555473i | \(-0.812537\pi\) |
0.555473 | + | 0.831535i | \(0.312537\pi\) | |||||||
\(500\) | −8.85994 | − | 8.85994i | −0.396228 | − | 0.396228i | ||||
\(501\) | −16.0507 | − | 16.0507i | −0.717093 | − | 0.717093i | ||||
\(502\) | −0.737697 | + | 0.737697i | −0.0329250 | + | 0.0329250i | ||||
\(503\) | − | 24.5304i | − | 1.09376i | −0.837212 | − | 0.546878i | \(-0.815816\pi\) | ||
0.837212 | − | 0.546878i | \(-0.184184\pi\) | |||||||
\(504\) | −2.43174 | − | 7.50830i | −0.108318 | − | 0.334446i | ||||
\(505\) | −20.8480 | − | 20.8480i | −0.927723 | − | 0.927723i | ||||
\(506\) | − | 3.08057i | − | 0.136948i | ||||||
\(507\) | −12.8929 | − | 1.66541i | −0.572593 | − | 0.0739636i | ||||
\(508\) | −18.3625 | −0.814705 | ||||||||
\(509\) | 2.00075 | + | 2.00075i | 0.0886819 | + | 0.0886819i | 0.750056 | − | 0.661374i | \(-0.230026\pi\) |
−0.661374 | + | 0.750056i | \(0.730026\pi\) | |||||||
\(510\) | 4.13963i | 0.183306i | ||||||||
\(511\) | −17.4063 | + | 5.63742i | −0.770008 | + | 0.249385i | ||||
\(512\) | −6.81578 | + | 6.81578i | −0.301218 | + | 0.301218i | ||||
\(513\) | 3.04121 | − | 3.04121i | 0.134273 | − | 0.134273i | ||||
\(514\) | −5.39768 | + | 5.39768i | −0.238082 | + | 0.238082i | ||||
\(515\) | −18.2266 | − | 18.2266i | −0.803160 | − | 0.803160i | ||||
\(516\) | 6.57503i | 0.289449i | ||||||||
\(517\) | 2.30960 | 0.101576 | ||||||||
\(518\) | −18.3556 | − | 9.37455i | −0.806499 | − | 0.411894i | ||||
\(519\) | − | 12.8330i | − | 0.563307i | ||||||
\(520\) | 14.1226 | − | 12.4157i | 0.619318 | − | 0.544464i | ||||
\(521\) | 23.3476i | 1.02288i | 0.859320 | + | 0.511438i | \(0.170887\pi\) | ||||
−0.859320 | + | 0.511438i | \(0.829113\pi\) | |||||||
\(522\) | −0.116048 | + | 0.116048i | −0.00507928 | + | 0.00507928i | ||||
\(523\) | 14.2481i | 0.623026i | 0.950242 | + | 0.311513i | \(0.100836\pi\) | ||||
−0.950242 | + | 0.311513i | \(0.899164\pi\) | |||||||
\(524\) | 2.40746 | 0.105170 | ||||||||
\(525\) | 4.57875 | + | 2.33845i | 0.199833 | + | 0.102058i | ||||
\(526\) | −3.53982 | + | 3.53982i | −0.154343 | + | 0.154343i | ||||
\(527\) | 5.95083 | + | 5.95083i | 0.259222 | + | 0.259222i | ||||
\(528\) | −0.379816 | + | 0.379816i | −0.0165294 | + | 0.0165294i | ||||
\(529\) | −2.73925 | −0.119098 | ||||||||
\(530\) | −11.1192 | −0.482989 | ||||||||
\(531\) | −6.95599 | + | 6.95599i | −0.301864 | + | 0.301864i | ||||
\(532\) | −11.1739 | + | 3.61891i | −0.484448 | + | 0.156900i | ||||
\(533\) | 1.58018 | − | 24.5677i | 0.0684450 | − | 1.06414i | ||||
\(534\) | −16.6472 | −0.720394 | ||||||||
\(535\) | 13.6674 | + | 13.6674i | 0.590894 | + | 0.590894i | ||||
\(536\) | −6.74842 | −0.291487 | ||||||||
\(537\) | 17.3893 | 0.750404 | ||||||||
\(538\) | 9.03145 | + | 9.03145i | 0.389373 | + | 0.389373i | ||||
\(539\) | −0.683953 | + | 4.26600i | −0.0294599 | + | 0.183750i | ||||
\(540\) | −1.27605 | − | 1.27605i | −0.0549125 | − | 0.0549125i | ||||
\(541\) | 9.94575 | + | 9.94575i | 0.427601 | + | 0.427601i | 0.887811 | − | 0.460209i | \(-0.152226\pi\) |
−0.460209 | + | 0.887811i | \(0.652226\pi\) | |||||||
\(542\) | − | 7.91392i | − | 0.339932i | ||||||
\(543\) | 14.1584i | 0.607593i | ||||||||
\(544\) | 8.69609 | − | 8.69609i | 0.372842 | − | 0.372842i | ||||
\(545\) | −22.9447 | −0.982843 | ||||||||
\(546\) | −4.79613 | + | 8.06656i | −0.205255 | + | 0.345217i | ||||
\(547\) | −23.3108 | −0.996700 | −0.498350 | − | 0.866976i | \(-0.666061\pi\) | ||||
−0.498350 | + | 0.866976i | \(0.666061\pi\) | |||||||
\(548\) | −10.0625 | + | 10.0625i | −0.429850 | + | 0.429850i | ||||
\(549\) | − | 3.67293i | − | 0.156757i | ||||||
\(550\) | − | 1.17994i | − | 0.0503127i | ||||||
\(551\) | 0.507341 | + | 0.507341i | 0.0216135 | + | 0.0216135i | ||||
\(552\) | 10.7013 | + | 10.7013i | 0.455477 | + | 0.455477i | ||||
\(553\) | −23.0680 | − | 11.7812i | −0.980949 | − | 0.500989i | ||||
\(554\) | 5.56459 | + | 5.56459i | 0.236417 | + | 0.236417i | ||||
\(555\) | −13.8446 | −0.587670 | ||||||||
\(556\) | 18.1433 | 0.769448 | ||||||||
\(557\) | 12.9583 | + | 12.9583i | 0.549061 | + | 0.549061i | 0.926169 | − | 0.377108i | \(-0.123082\pi\) |
−0.377108 | + | 0.926169i | \(0.623082\pi\) | |||||||
\(558\) | 3.44001 | 0.145627 | ||||||||
\(559\) | 17.2495 | − | 15.1647i | 0.729577 | − | 0.641397i | ||||
\(560\) | −1.24036 | − | 3.82978i | −0.0524148 | − | 0.161838i | ||||
\(561\) | 1.05039 | − | 1.05039i | 0.0443475 | − | 0.0443475i | ||||
\(562\) | −16.9280 | −0.714067 | ||||||||
\(563\) | −1.17695 | −0.0496027 | −0.0248013 | − | 0.999692i | \(-0.507895\pi\) | ||||
−0.0248013 | + | 0.999692i | \(0.507895\pi\) | |||||||
\(564\) | −2.73112 | + | 2.73112i | −0.115001 | + | 0.115001i | ||||
\(565\) | −15.2195 | − | 15.2195i | −0.640287 | − | 0.640287i | ||||
\(566\) | 2.13987 | − | 2.13987i | 0.0899455 | − | 0.0899455i | ||||
\(567\) | 2.35624 | + | 1.20338i | 0.0989529 | + | 0.0505371i | ||||
\(568\) | −6.99507 | −0.293506 | ||||||||
\(569\) | − | 21.1294i | − | 0.885791i | −0.896573 | − | 0.442895i | \(-0.853951\pi\) | ||
0.896573 | − | 0.442895i | \(-0.146049\pi\) | |||||||
\(570\) | 5.23090 | − | 5.23090i | 0.219098 | − | 0.219098i | ||||
\(571\) | − | 41.5084i | − | 1.73707i | −0.495626 | − | 0.868536i | \(-0.665061\pi\) | ||
0.495626 | − | 0.868536i | \(-0.334939\pi\) | |||||||
\(572\) | −2.29225 | − | 0.147436i | −0.0958438 | − | 0.00616461i | ||||
\(573\) | − | 1.61029i | − | 0.0672707i | ||||||
\(574\) | −15.8273 | − | 8.08331i | −0.660620 | − | 0.337391i | ||||
\(575\) | −9.85881 | −0.411141 | ||||||||
\(576\) | − | 6.76750i | − | 0.281979i | ||||||
\(577\) | 23.3813 | + | 23.3813i | 0.973375 | + | 0.973375i | 0.999655 | − | 0.0262795i | \(-0.00836600\pi\) |
−0.0262795 | + | 0.999655i | \(0.508366\pi\) | |||||||
\(578\) | −7.79639 | + | 7.79639i | −0.324287 | + | 0.324287i | ||||
\(579\) | −15.5701 | + | 15.5701i | −0.647071 | + | 0.647071i | ||||
\(580\) | 0.212874 | − | 0.212874i | 0.00883910 | − | 0.00883910i | ||||
\(581\) | −4.69987 | − | 14.5114i | −0.194983 | − | 0.602036i | ||||
\(582\) | 1.96946i | 0.0816366i | ||||||||
\(583\) | 2.82140 | + | 2.82140i | 0.116850 | + | 0.116850i | ||||
\(584\) | −20.6286 | −0.853618 | ||||||||
\(585\) | −0.404620 | + | 6.29080i | −0.0167290 | + | 0.260093i | ||||
\(586\) | 26.0637i | 1.07668i | ||||||||
\(587\) | 8.99127 | + | 8.99127i | 0.371109 | + | 0.371109i | 0.867881 | − | 0.496772i | \(-0.165481\pi\) |
−0.496772 | + | 0.867881i | \(0.665481\pi\) | |||||||
\(588\) | −4.23580 | − | 5.85336i | −0.174681 | − | 0.241388i | ||||
\(589\) | − | 15.0391i | − | 0.619676i | ||||||
\(590\) | −11.9643 | + | 11.9643i | −0.492564 | + | 0.492564i | ||||
\(591\) | −12.8905 | − | 12.8905i | −0.530243 | − | 0.530243i | ||||
\(592\) | −4.87291 | − | 4.87291i | −0.200275 | − | 0.200275i | ||||
\(593\) | −3.14300 | + | 3.14300i | −0.129068 | + | 0.129068i | −0.768690 | − | 0.639622i | \(-0.779091\pi\) |
0.639622 | + | 0.768690i | \(0.279091\pi\) | |||||||
\(594\) | − | 0.607201i | − | 0.0249138i | ||||||
\(595\) | 3.43025 | + | 10.5914i | 0.140627 | + | 0.434203i | ||||
\(596\) | −0.278287 | − | 0.278287i | −0.0113991 | − | 0.0113991i | ||||
\(597\) | − | 13.5710i | − | 0.555425i | ||||||
\(598\) | 1.15508 | − | 17.9586i | 0.0472349 | − | 0.734381i | ||||
\(599\) | −3.89314 | −0.159069 | −0.0795347 | − | 0.996832i | \(-0.525343\pi\) | ||||
−0.0795347 | + | 0.996832i | \(0.525343\pi\) | |||||||
\(600\) | 4.09887 | + | 4.09887i | 0.167336 | + | 0.167336i | ||||
\(601\) | − | 17.2457i | − | 0.703467i | −0.936100 | − | 0.351733i | \(-0.885592\pi\) | ||
0.936100 | − | 0.351733i | \(-0.114408\pi\) | |||||||
\(602\) | −5.10866 | − | 15.7737i | −0.208213 | − | 0.642886i | ||||
\(603\) | 1.59968 | − | 1.59968i | 0.0651442 | − | 0.0651442i | ||||
\(604\) | 3.84126 | − | 3.84126i | 0.156299 | − | 0.156299i | ||||
\(605\) | −13.1281 | + | 13.1281i | −0.533732 | + | 0.533732i | ||||
\(606\) | 11.7309 | + | 11.7309i | 0.476536 | + | 0.476536i | ||||
\(607\) | − | 29.7179i | − | 1.20621i | −0.797661 | − | 0.603106i | \(-0.793930\pi\) | ||
0.797661 | − | 0.603106i | \(-0.206070\pi\) | |||||||
\(608\) | −21.9770 | −0.891286 | ||||||||
\(609\) | −0.200750 | + | 0.393073i | −0.00813480 | + | 0.0159281i | ||||
\(610\) | − | 6.31745i | − | 0.255786i | ||||||
\(611\) | 13.4641 | + | 0.866004i | 0.544701 | + | 0.0350348i | ||||
\(612\) | 2.48419i | 0.100417i | ||||||||
\(613\) | −31.5296 | + | 31.5296i | −1.27347 | + | 1.27347i | −0.329210 | + | 0.944257i | \(0.606782\pi\) |
−0.944257 | + | 0.329210i | \(0.893218\pi\) | |||||||
\(614\) | 6.60373i | 0.266505i | ||||||||
\(615\) | −11.9377 | −0.481373 | ||||||||
\(616\) | −2.21559 | + | 4.33817i | −0.0892685 | + | 0.174790i | ||||
\(617\) | −22.1403 | + | 22.1403i | −0.891336 | + | 0.891336i | −0.994649 | − | 0.103313i | \(-0.967056\pi\) |
0.103313 | + | 0.994649i | \(0.467056\pi\) | |||||||
\(618\) | 10.2559 | + | 10.2559i | 0.412553 | + | 0.412553i | ||||
\(619\) | 3.28951 | − | 3.28951i | 0.132216 | − | 0.132216i | −0.637902 | − | 0.770118i | \(-0.720197\pi\) |
0.770118 | + | 0.637902i | \(0.220197\pi\) | |||||||
\(620\) | −6.31021 | −0.253424 | ||||||||
\(621\) | −5.07339 | −0.203588 | ||||||||
\(622\) | 17.5580 | − | 17.5580i | 0.704010 | − | 0.704010i | ||||
\(623\) | −42.5923 | + | 13.7945i | −1.70642 | + | 0.552664i | ||||
\(624\) | −2.35660 | + | 2.07177i | −0.0943396 | + | 0.0829372i | ||||
\(625\) | 11.5076 | 0.460304 | ||||||||
\(626\) | 3.33995 | + | 3.33995i | 0.133491 | + | 0.133491i | ||||
\(627\) | −2.65458 | −0.106014 | ||||||||
\(628\) | 18.1465 | 0.724124 | ||||||||
\(629\) | 13.4762 | + | 13.4762i | 0.537330 | + | 0.537330i | ||||
\(630\) | 4.05275 | + | 2.06981i | 0.161465 | + | 0.0824634i | ||||
\(631\) | 17.0276 | + | 17.0276i | 0.677858 | + | 0.677858i | 0.959515 | − | 0.281657i | \(-0.0908840\pi\) |
−0.281657 | + | 0.959515i | \(0.590884\pi\) | |||||||
\(632\) | −20.6503 | − | 20.6503i | −0.821426 | − | 0.821426i | ||||
\(633\) | − | 12.1333i | − | 0.482256i | ||||||
\(634\) | 17.3424i | 0.688756i | ||||||||
\(635\) | 21.9935 | − | 21.9935i | 0.872787 | − | 0.872787i | ||||
\(636\) | −6.67266 | −0.264588 | ||||||||
\(637\) | −5.58677 | + | 24.6128i | −0.221356 | + | 0.975193i | ||||
\(638\) | 0.101295 | 0.00401029 | ||||||||
\(639\) | 1.65815 | − | 1.65815i | 0.0655954 | − | 0.0655954i | ||||
\(640\) | 6.22753i | 0.246165i | ||||||||
\(641\) | − | 25.5087i | − | 1.00753i | −0.863840 | − | 0.503766i | \(-0.831947\pi\) | ||
0.863840 | − | 0.503766i | \(-0.168053\pi\) | |||||||
\(642\) | −7.69050 | − | 7.69050i | −0.303520 | − | 0.303520i | ||||
\(643\) | 32.2837 | + | 32.2837i | 1.27314 | + | 1.27314i | 0.944430 | + | 0.328714i | \(0.106615\pi\) |
0.328714 | + | 0.944430i | \(0.393385\pi\) | |||||||
\(644\) | 12.3387 | + | 6.30163i | 0.486214 | + | 0.248319i | ||||
\(645\) | −7.87518 | − | 7.87518i | −0.310085 | − | 0.310085i | ||||
\(646\) | −10.1834 | −0.400660 | ||||||||
\(647\) | −3.98609 | −0.156709 | −0.0783547 | − | 0.996926i | \(-0.524967\pi\) | ||||
−0.0783547 | + | 0.996926i | \(0.524967\pi\) | |||||||
\(648\) | 2.10930 | + | 2.10930i | 0.0828610 | + | 0.0828610i | ||||
\(649\) | 6.07167 | 0.238334 | ||||||||
\(650\) | 0.442428 | − | 6.87861i | 0.0173534 | − | 0.269801i | ||||
\(651\) | 8.80135 | − | 2.85052i | 0.344952 | − | 0.111721i | ||||
\(652\) | 1.03993 | − | 1.03993i | 0.0407269 | − | 0.0407269i | ||||
\(653\) | −16.3776 | −0.640903 | −0.320452 | − | 0.947265i | \(-0.603835\pi\) | ||||
−0.320452 | + | 0.947265i | \(0.603835\pi\) | |||||||
\(654\) | 12.9107 | 0.504849 | ||||||||
\(655\) | −2.88351 | + | 2.88351i | −0.112668 | + | 0.112668i | ||||
\(656\) | −4.20172 | − | 4.20172i | −0.164050 | − | 0.164050i | ||||
\(657\) | 4.88992 | − | 4.88992i | 0.190774 | − | 0.190774i | ||||
\(658\) | 4.43000 | − | 8.67405i | 0.172699 | − | 0.338150i | ||||
\(659\) | 23.6671 | 0.921939 | 0.460970 | − | 0.887416i | \(-0.347502\pi\) | ||||
0.460970 | + | 0.887416i | \(0.347502\pi\) | |||||||
\(660\) | 1.11383i | 0.0433556i | ||||||||
\(661\) | 22.3640 | − | 22.3640i | 0.869858 | − | 0.869858i | −0.122598 | − | 0.992456i | \(-0.539123\pi\) |
0.992456 | + | 0.122598i | \(0.0391226\pi\) | |||||||
\(662\) | − | 6.23958i | − | 0.242508i | ||||||
\(663\) | 6.51725 | − | 5.72954i | 0.253109 | − | 0.222517i | ||||
\(664\) | − | 17.1979i | − | 0.667407i | ||||||
\(665\) | 9.04887 | − | 17.7179i | 0.350900 | − | 0.687071i | ||||
\(666\) | 7.79020 | 0.301864 | ||||||||
\(667\) | − | 0.846353i | − | 0.0327709i | ||||||
\(668\) | −16.5671 | − | 16.5671i | −0.641001 | − | 0.641001i | ||||
\(669\) | −4.74466 | + | 4.74466i | −0.183439 | + | 0.183439i | ||||
\(670\) | 2.75146 | − | 2.75146i | 0.106298 | − | 0.106298i | ||||
\(671\) | −1.60299 | + | 1.60299i | −0.0618828 | + | 0.0618828i | ||||
\(672\) | −4.16553 | − | 12.8616i | −0.160689 | − | 0.496148i | ||||
\(673\) | 15.2079i | 0.586222i | 0.956078 | + | 0.293111i | \(0.0946905\pi\) | ||||
−0.956078 | + | 0.293111i | \(0.905309\pi\) | |||||||
\(674\) | 8.53832 | + | 8.53832i | 0.328884 | + | 0.328884i | ||||
\(675\) | −1.94324 | −0.0747954 | ||||||||
\(676\) | −13.3077 | − | 1.71900i | −0.511834 | − | 0.0661152i | ||||
\(677\) | 37.3151i | 1.43414i | 0.697003 | + | 0.717068i | \(0.254516\pi\) | ||||
−0.697003 | + | 0.717068i | \(0.745484\pi\) | |||||||
\(678\) | 8.56381 | + | 8.56381i | 0.328891 | + | 0.328891i | ||||
\(679\) | 1.63197 | + | 5.03891i | 0.0626291 | + | 0.193376i | ||||
\(680\) | 12.5521i | 0.481350i | ||||||||
\(681\) | 10.5233 | − | 10.5233i | 0.403253 | − | 0.403253i | ||||
\(682\) | −1.50134 | − | 1.50134i | −0.0574892 | − | 0.0574892i | ||||
\(683\) | −10.3303 | − | 10.3303i | −0.395280 | − | 0.395280i | 0.481285 | − | 0.876564i | \(-0.340170\pi\) |
−0.876564 | + | 0.481285i | \(0.840170\pi\) | |||||||
\(684\) | 3.13906 | − | 3.13906i | 0.120025 | − | 0.120025i | ||||
\(685\) | − | 24.1046i | − | 0.920990i | ||||||
\(686\) | 14.7097 | + | 10.7512i | 0.561620 | + | 0.410483i | ||||
\(687\) | 20.7310 | + | 20.7310i | 0.790936 | + | 0.790936i | ||||
\(688\) | − | 5.54369i | − | 0.211351i | ||||||
\(689\) | 15.3898 | + | 17.5056i | 0.586306 | + | 0.666912i | ||||
\(690\) | −8.72624 | −0.332202 | ||||||||
\(691\) | −1.69742 | − | 1.69742i | −0.0645730 | − | 0.0645730i | 0.674083 | − | 0.738656i | \(-0.264539\pi\) |
−0.738656 | + | 0.674083i | \(0.764539\pi\) | |||||||
\(692\) | − | 13.2459i | − | 0.503533i | ||||||
\(693\) | −0.503150 | − | 1.55354i | −0.0191131 | − | 0.0590141i | ||||
\(694\) | 22.5670 | − | 22.5670i | 0.856632 | − | 0.856632i | ||||
\(695\) | −21.7310 | + | 21.7310i | −0.824303 | + | 0.824303i | ||||
\(696\) | −0.351877 | + | 0.351877i | −0.0133379 | + | 0.0133379i | ||||
\(697\) | 11.6200 | + | 11.6200i | 0.440138 | + | 0.440138i | ||||
\(698\) | 28.6175i | 1.08319i | ||||||||
\(699\) | −6.37148 | −0.240991 | ||||||||
\(700\) | 4.72606 | + | 2.41369i | 0.178628 | + | 0.0912289i | ||||
\(701\) | 26.1912i | 0.989227i | 0.869113 | + | 0.494613i | \(0.164690\pi\) | ||||
−0.869113 | + | 0.494613i | \(0.835310\pi\) | |||||||
\(702\) | 0.227675 | − | 3.53976i | 0.00859304 | − | 0.133600i | ||||
\(703\) | − | 34.0574i | − | 1.28450i | ||||||
\(704\) | −2.95357 | + | 2.95357i | −0.111317 | + | 0.111317i | ||||
\(705\) | − | 6.54235i | − | 0.246399i | ||||||
\(706\) | −12.6613 | −0.476516 | ||||||||
\(707\) | 39.7346 | + | 20.2932i | 1.49437 | + | 0.763204i | ||||
\(708\) | −7.17979 | + | 7.17979i | −0.269833 | + | 0.269833i | ||||
\(709\) | −29.5289 | − | 29.5289i | −1.10898 | − | 1.10898i | −0.993285 | − | 0.115697i | \(-0.963090\pi\) |
−0.115697 | − | 0.993285i | \(-0.536910\pi\) | |||||||
\(710\) | 2.85202 | − | 2.85202i | 0.107035 | − | 0.107035i | ||||
\(711\) | 9.79014 | 0.367159 | ||||||||
\(712\) | −50.4771 | −1.89171 | ||||||||
\(713\) | −12.5442 | + | 12.5442i | −0.469785 | + | 0.469785i | ||||
\(714\) | −1.93016 | − | 5.95963i | −0.0722346 | − | 0.223034i | ||||
\(715\) | 2.92211 | − | 2.56893i | 0.109281 | − | 0.0960725i | ||||
\(716\) | 17.9488 | 0.670778 | ||||||||
\(717\) | −18.6706 | − | 18.6706i | −0.697268 | − | 0.697268i | ||||
\(718\) | 24.0732 | 0.898404 | ||||||||
\(719\) | 19.7112 | 0.735104 | 0.367552 | − | 0.930003i | \(-0.380196\pi\) | ||||
0.367552 | + | 0.930003i | \(0.380196\pi\) | |||||||
\(720\) | 1.07589 | + | 1.07589i | 0.0400962 | + | 0.0400962i | ||||
\(721\) | 34.7384 | + | 17.7416i | 1.29373 | + | 0.660730i | ||||
\(722\) | −0.349249 | − | 0.349249i | −0.0129977 | − | 0.0129977i | ||||
\(723\) | −2.22932 | − | 2.22932i | −0.0829092 | − | 0.0829092i | ||||
\(724\) | 14.6139i | 0.543121i | ||||||||
\(725\) | − | 0.324176i | − | 0.0120396i | ||||||
\(726\) | 7.38702 | − | 7.38702i | 0.274158 | − | 0.274158i | ||||
\(727\) | −34.0497 | −1.26283 | −0.631417 | − | 0.775443i | \(-0.717526\pi\) | ||||
−0.631417 | + | 0.775443i | \(0.717526\pi\) | |||||||
\(728\) | −14.5427 | + | 24.4592i | −0.538988 | + | 0.906518i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.41068 | − | 8.41068i | 0.311293 | − | 0.311293i | ||||
\(731\) | 15.3312i | 0.567046i | ||||||||
\(732\) | − | 3.79110i | − | 0.140123i | ||||||
\(733\) | −0.266410 | − | 0.266410i | −0.00984010 | − | 0.00984010i | 0.702170 | − | 0.712010i | \(-0.252215\pi\) |
−0.712010 | + | 0.702170i | \(0.752215\pi\) | |||||||
\(734\) | 13.3124 | + | 13.3124i | 0.491370 | + | 0.491370i | ||||
\(735\) | 12.0842 | + | 1.93742i | 0.445732 | + | 0.0714627i | ||||
\(736\) | 18.3312 | + | 18.3312i | 0.675696 | + | 0.675696i | ||||
\(737\) | −1.39631 | −0.0514339 | ||||||||
\(738\) | 6.71719 | 0.247263 | ||||||||
\(739\) | −18.9905 | − | 18.9905i | −0.698578 | − | 0.698578i | 0.265526 | − | 0.964104i | \(-0.414454\pi\) |
−0.964104 | + | 0.265526i | \(0.914454\pi\) | |||||||
\(740\) | −14.2900 | −0.525312 | ||||||||
\(741\) | −15.4752 | − | 0.995356i | −0.568497 | − | 0.0365653i | ||||
\(742\) | 16.0079 | − | 5.18452i | 0.587667 | − | 0.190330i | ||||
\(743\) | −1.44435 | + | 1.44435i | −0.0529882 | + | 0.0529882i | −0.733104 | − | 0.680116i | \(-0.761929\pi\) |
0.680116 | + | 0.733104i | \(0.261929\pi\) | |||||||
\(744\) | 10.4307 | 0.382408 | ||||||||
\(745\) | 0.666630 | 0.0244234 | ||||||||
\(746\) | 5.65503 | − | 5.65503i | 0.207045 | − | 0.207045i | ||||
\(747\) | 4.07668 | + | 4.07668i | 0.149158 | + | 0.149158i | ||||
\(748\) | 1.08419 | − | 1.08419i | 0.0396418 | − | 0.0396418i | ||||
\(749\) | −26.0490 | − | 13.3037i | −0.951810 | − | 0.486107i | ||||
\(750\) | −11.9424 | −0.436075 | ||||||||
\(751\) | 13.5207i | 0.493377i | 0.969095 | + | 0.246688i | \(0.0793424\pi\) | ||||
−0.969095 | + | 0.246688i | \(0.920658\pi\) | |||||||
\(752\) | 2.30273 | − | 2.30273i | 0.0839718 | − | 0.0839718i | ||||
\(753\) | − | 1.06046i | − | 0.0386453i | ||||||
\(754\) | 0.590510 | + | 0.0379812i | 0.0215051 | + | 0.00138320i | ||||
\(755\) | 9.20167i | 0.334883i | ||||||||
\(756\) | 2.43205 | + | 1.24209i | 0.0884529 | + | 0.0451746i | ||||
\(757\) | 11.6360 | 0.422916 | 0.211458 | − | 0.977387i | \(-0.432179\pi\) | ||||
0.211458 | + | 0.977387i | \(0.432179\pi\) | |||||||
\(758\) | − | 13.9305i | − | 0.505980i | ||||||
\(759\) | 2.21420 | + | 2.21420i | 0.0803704 | + | 0.0803704i | ||||
\(760\) | 15.8610 | − | 15.8610i | 0.575338 | − | 0.575338i | ||||
\(761\) | −24.6474 | + | 24.6474i | −0.893469 | + | 0.893469i | −0.994848 | − | 0.101379i | \(-0.967675\pi\) |
0.101379 | + | 0.994848i | \(0.467675\pi\) | |||||||
\(762\) | −12.3755 | + | 12.3755i | −0.448317 | + | 0.448317i | ||||
\(763\) | 33.0324 | − | 10.6983i | 1.19585 | − | 0.387305i | ||||
\(764\) | − | 1.66210i | − | 0.0601325i | ||||||
\(765\) | −2.97542 | − | 2.97542i | −0.107576 | − | 0.107576i | ||||
\(766\) | −37.7274 | −1.36315 | ||||||||
\(767\) | 35.3956 | + | 2.27662i | 1.27806 | + | 0.0822041i | ||||
\(768\) | − | 17.0392i | − | 0.614848i | ||||||
\(769\) | −19.3743 | − | 19.3743i | −0.698654 | − | 0.698654i | 0.265466 | − | 0.964120i | \(-0.414474\pi\) |
−0.964120 | + | 0.265466i | \(0.914474\pi\) | |||||||
\(770\) | −0.865420 | − | 2.67210i | −0.0311876 | − | 0.0962956i | ||||
\(771\) | − | 7.75932i | − | 0.279445i | ||||||
\(772\) | −16.0710 | + | 16.0710i | −0.578409 | + | 0.578409i | ||||
\(773\) | 2.08951 | + | 2.08951i | 0.0751544 | + | 0.0751544i | 0.743685 | − | 0.668530i | \(-0.233076\pi\) |
−0.668530 | + | 0.743685i | \(0.733076\pi\) | |||||||
\(774\) | 4.43127 | + | 4.43127i | 0.159279 | + | 0.159279i | ||||
\(775\) | −4.80477 | + | 4.80477i | −0.172592 | + | 0.172592i | ||||
\(776\) | 5.97174i | 0.214373i | ||||||||
\(777\) | 19.9314 | − | 6.45525i | 0.715036 | − | 0.231581i | ||||
\(778\) | 24.2744 | + | 24.2744i | 0.870281 | + | 0.870281i | ||||
\(779\) | − | 29.3664i | − | 1.05216i | ||||||
\(780\) | −0.417638 | + | 6.49320i | −0.0149538 | + | 0.232494i | ||||
\(781\) | −1.44735 | −0.0517902 | ||||||||
\(782\) | 8.49403 | + | 8.49403i | 0.303746 | + | 0.303746i | ||||
\(783\) | − | 0.166822i | − | 0.00596174i | ||||||
\(784\) | 3.57138 | + | 4.93521i | 0.127549 | + | 0.176258i | ||||
\(785\) | −21.7348 | + | 21.7348i | −0.775748 | + | 0.775748i | ||||
\(786\) | 1.62252 | − | 1.62252i | 0.0578733 | − | 0.0578733i | ||||
\(787\) | 1.65961 | − | 1.65961i | 0.0591588 | − | 0.0591588i | −0.676908 | − | 0.736067i | \(-0.736681\pi\) |
0.736067 | + | 0.676908i | \(0.236681\pi\) | |||||||
\(788\) | −13.3052 | − | 13.3052i | −0.473978 | − | 0.473978i | ||||
\(789\) | − | 5.08859i | − | 0.181159i | ||||||
\(790\) | 16.8391 | 0.599108 | ||||||||
\(791\) | 29.0071 | + | 14.8144i | 1.03137 | + | 0.526741i | ||||
\(792\) | − | 1.84114i | − | 0.0654220i | ||||||
\(793\) | −9.94592 | + | 8.74381i | −0.353190 | + | 0.310502i | ||||
\(794\) | 30.4437i | 1.08041i | ||||||||
\(795\) | 7.99211 | − | 7.99211i | 0.283451 | − | 0.283451i | ||||
\(796\) | − | 14.0077i | − | 0.496488i | ||||||
\(797\) | 11.8936 | 0.421294 | 0.210647 | − | 0.977562i | \(-0.432443\pi\) | ||||
0.210647 | + | 0.977562i | \(0.432443\pi\) | |||||||
\(798\) | −5.09170 | + | 9.96966i | −0.180244 | + | 0.352922i | ||||
\(799\) | −6.36825 | + | 6.36825i | −0.225293 | + | 0.225293i | ||||
\(800\) | 7.02132 | + | 7.02132i | 0.248241 | + | 0.248241i | ||||
\(801\) | 11.9654 | − | 11.9654i | 0.422776 | − | 0.422776i | ||||
\(802\) | 10.8419 | 0.382841 | ||||||||
\(803\) | −4.26826 | −0.150624 | ||||||||
\(804\) | 1.65115 | − | 1.65115i | 0.0582316 | − | 0.0582316i | ||||
\(805\) | −22.3263 | + | 7.23090i | −0.786900 | + | 0.254856i | ||||
\(806\) | −8.18931 | − | 9.31518i | −0.288456 | − | 0.328113i | ||||
\(807\) | −12.9830 | −0.457022 | ||||||||
\(808\) | 35.5702 | + | 35.5702i | 1.25136 | + | 1.25136i | ||||
\(809\) | −44.3950 | −1.56084 | −0.780422 | − | 0.625253i | \(-0.784996\pi\) | ||||
−0.780422 | + | 0.625253i | \(0.784996\pi\) | |||||||
\(810\) | −1.72000 | −0.0604348 | ||||||||
\(811\) | 6.35365 | + | 6.35365i | 0.223107 | + | 0.223107i | 0.809805 | − | 0.586699i | \(-0.199573\pi\) |
−0.586699 | + | 0.809805i | \(0.699573\pi\) | |||||||
\(812\) | −0.207209 | + | 0.405720i | −0.00727161 | + | 0.0142380i | ||||
\(813\) | 5.68824 | + | 5.68824i | 0.199495 | + | 0.199495i | ||||
\(814\) | −3.39991 | − | 3.39991i | −0.119167 | − | 0.119167i | ||||
\(815\) | 2.49114i | 0.0872608i | ||||||||
\(816\) | − | 2.09453i | − | 0.0733231i | ||||||
\(817\) | 19.3728 | − | 19.3728i | 0.677767 | − | 0.677767i | ||||
\(818\) | −31.2238 | −1.09171 | ||||||||
\(819\) | −2.35067 | − | 9.24523i | −0.0821390 | − | 0.323055i | ||||
\(820\) | −12.3217 | −0.430294 | ||||||||
\(821\) | 7.24883 | − | 7.24883i | 0.252986 | − | 0.252986i | −0.569208 | − | 0.822194i | \(-0.692750\pi\) |
0.822194 | + | 0.569208i | \(0.192750\pi\) | |||||||
\(822\) | 13.5634i | 0.473078i | ||||||||
\(823\) | 13.7328i | 0.478694i | 0.970934 | + | 0.239347i | \(0.0769333\pi\) | ||||
−0.970934 | + | 0.239347i | \(0.923067\pi\) | |||||||
\(824\) | 31.0977 | + | 31.0977i | 1.08334 | + | 1.08334i | ||||
\(825\) | 0.848097 | + | 0.848097i | 0.0295270 | + | 0.0295270i | ||||
\(826\) | 11.6459 | − | 22.8030i | 0.405214 | − | 0.793419i | ||||
\(827\) | 30.3908 | + | 30.3908i | 1.05679 | + | 1.05679i | 0.998287 | + | 0.0585057i | \(0.0186336\pi\) |
0.0585057 | + | 0.998287i | \(0.481366\pi\) | |||||||
\(828\) | −5.23662 | −0.181985 | ||||||||
\(829\) | 4.89544 | 0.170026 | 0.0850128 | − | 0.996380i | \(-0.472907\pi\) | ||||
0.0850128 | + | 0.996380i | \(0.472907\pi\) | |||||||
\(830\) | 7.01191 | + | 7.01191i | 0.243387 | + | 0.243387i | ||||
\(831\) | −7.99926 | −0.277491 | ||||||||
\(832\) | −18.3257 | + | 16.1108i | −0.635330 | + | 0.558541i | ||||
\(833\) | −9.87676 | − | 13.6485i | −0.342209 | − | 0.472892i | ||||
\(834\) | 12.2278 | − | 12.2278i | 0.423413 | − | 0.423413i | ||||
\(835\) | 39.6862 | 1.37340 | ||||||||
\(836\) | −2.73999 | −0.0947644 | ||||||||
\(837\) | −2.47255 | + | 2.47255i | −0.0854639 | + | 0.0854639i | ||||
\(838\) | −21.7355 | − | 21.7355i | −0.750840 | − | 0.750840i | ||||
\(839\) | 20.0820 | − | 20.0820i | 0.693306 | − | 0.693306i | −0.269652 | − | 0.962958i | \(-0.586909\pi\) |
0.962958 | + | 0.269652i | \(0.0869086\pi\) | |||||||
\(840\) | 12.2886 | + | 6.27604i | 0.423998 | + | 0.216544i | ||||
\(841\) | −28.9722 | −0.999040 | ||||||||
\(842\) | − | 24.0085i | − | 0.827388i | ||||||
\(843\) | 12.1673 | − | 12.1673i | 0.419063 | − | 0.419063i | ||||
\(844\) | − | 12.5237i | − | 0.431083i | ||||||
\(845\) | 17.9981 | − | 13.8803i | 0.619153 | − | 0.477495i | ||||
\(846\) | 3.68131i | 0.126566i | ||||||||
\(847\) | 12.7787 | − | 25.0211i | 0.439082 | − | 0.859734i | ||||
\(848\) | 5.62600 | 0.193198 | ||||||||
\(849\) | 3.07612i | 0.105572i | ||||||||
\(850\) | 3.25344 | + | 3.25344i | 0.111592 | + | 0.111592i | ||||
\(851\) | −28.4075 | + | 28.4075i | −0.973796 | + | 0.973796i | ||||
\(852\) | 1.71150 | − | 1.71150i | 0.0586350 | − | 0.0586350i | ||||
\(853\) | −24.0164 | + | 24.0164i | −0.822307 | + | 0.822307i | −0.986438 | − | 0.164132i | \(-0.947518\pi\) |
0.164132 | + | 0.986438i | \(0.447518\pi\) | |||||||
\(854\) | 2.94561 | + | 9.09495i | 0.100797 | + | 0.311223i | ||||
\(855\) | 7.51956i | 0.257163i | ||||||||
\(856\) | −23.3189 | − | 23.3189i | −0.797025 | − | 0.797025i | ||||
\(857\) | −11.2917 | −0.385718 | −0.192859 | − | 0.981226i | \(-0.561776\pi\) | ||||
−0.192859 | + | 0.981226i | \(0.561776\pi\) | |||||||
\(858\) | −1.64424 | + | 1.44551i | −0.0561334 | + | 0.0493488i | ||||
\(859\) | 46.2098i | 1.57666i | 0.615254 | + | 0.788329i | \(0.289053\pi\) | ||||
−0.615254 | + | 0.788329i | \(0.710947\pi\) | |||||||
\(860\) | −8.12855 | − | 8.12855i | −0.277181 | − | 0.277181i | ||||
\(861\) | 17.1861 | − | 5.56612i | 0.585701 | − | 0.189693i | ||||
\(862\) | 16.6626i | 0.567529i | ||||||||
\(863\) | 11.2107 | − | 11.2107i | 0.381616 | − | 0.381616i | −0.490068 | − | 0.871684i | \(-0.663028\pi\) |
0.871684 | + | 0.490068i | \(0.163028\pi\) | |||||||
\(864\) | 3.61320 | + | 3.61320i | 0.122924 | + | 0.122924i | ||||
\(865\) | 15.8651 | + | 15.8651i | 0.539431 | + | 0.539431i | ||||
\(866\) | 11.8358 | − | 11.8358i | 0.402197 | − | 0.402197i | ||||
\(867\) | − | 11.2075i | − | 0.380628i | ||||||
\(868\) | 9.08452 | − | 2.94223i | 0.308349 | − | 0.0998659i | ||||
\(869\) | −4.27275 | − | 4.27275i | −0.144943 | − | 0.144943i | ||||
\(870\) | − | 0.286935i | − | 0.00972799i | ||||||
\(871\) | −8.14000 | − | 0.523560i | −0.275813 | − | 0.0177401i | ||||
\(872\) | 39.1476 | 1.32570 | ||||||||
\(873\) | −1.41557 | − | 1.41557i | −0.0479099 | − | 0.0479099i | ||||
\(874\) | − | 21.4664i | − | 0.726110i | ||||||
\(875\) | −30.5550 | + | 9.89593i | −1.03295 | + | 0.334543i | ||||
\(876\) | 5.04725 | − | 5.04725i | 0.170531 | − | 0.170531i | ||||
\(877\) | 5.66466 | − | 5.66466i | 0.191282 | − | 0.191282i | −0.604968 | − | 0.796250i | \(-0.706814\pi\) |
0.796250 | + | 0.604968i | \(0.206814\pi\) | |||||||
\(878\) | −19.5539 | + | 19.5539i | −0.659911 | + | 0.659911i | ||||
\(879\) | −18.7336 | − | 18.7336i | −0.631869 | − | 0.631869i | ||||
\(880\) | − | 0.939114i | − | 0.0316575i | ||||||
\(881\) | 52.6930 | 1.77527 | 0.887636 | − | 0.460546i | \(-0.152346\pi\) | ||||
0.887636 | + | 0.460546i | \(0.152346\pi\) | |||||||
\(882\) | −6.79963 | − | 1.09016i | −0.228956 | − | 0.0367077i | ||||
\(883\) | 2.48665i | 0.0836824i | 0.999124 | + | 0.0418412i | \(0.0133224\pi\) | ||||
−0.999124 | + | 0.0418412i | \(0.986678\pi\) | |||||||
\(884\) | 6.72693 | − | 5.91388i | 0.226251 | − | 0.198905i | ||||
\(885\) | − | 17.1991i | − | 0.578140i | ||||||
\(886\) | 13.2592 | − | 13.2592i | 0.445452 | − | 0.445452i | ||||
\(887\) | − | 4.40886i | − | 0.148035i | −0.997257 | − | 0.0740175i | \(-0.976418\pi\) | ||
0.997257 | − | 0.0740175i | \(-0.0235821\pi\) | |||||||
\(888\) | 23.6212 | 0.792676 | ||||||||
\(889\) | −21.4083 | + | 41.9179i | −0.718010 | + | 1.40588i | ||||
\(890\) | 20.5805 | − | 20.5805i | 0.689860 | − | 0.689860i | ||||
\(891\) | 0.436434 | + | 0.436434i | 0.0146211 | + | 0.0146211i | ||||
\(892\) | −4.89731 | + | 4.89731i | −0.163974 | + | 0.163974i | ||||
\(893\) | 16.0940 | 0.538566 | ||||||||
\(894\) | −0.375105 | −0.0125454 | ||||||||
\(895\) | −21.4980 | + | 21.4980i | −0.718598 | + | 0.718598i | ||||
\(896\) | −2.90368 | − | 8.96549i | −0.0970052 | − | 0.299516i | ||||
\(897\) | 12.0777 | + | 13.7382i | 0.403264 | + | 0.458705i | ||||
\(898\) | −14.1710 | −0.472894 | ||||||||
\(899\) | −0.412476 | − | 0.412476i | −0.0137569 | − | 0.0137569i | ||||
\(900\) | −2.00576 | −0.0668588 | ||||||||
\(901\) | −15.5589 | −0.518341 | ||||||||
\(902\) | −2.93161 | − | 2.93161i | −0.0976119 | − | 0.0976119i | ||||
\(903\) | 15.0095 | + | 7.66561i | 0.499483 | + | 0.255096i | ||||
\(904\) | 25.9670 | + | 25.9670i | 0.863649 | + | 0.863649i | ||||
\(905\) | −17.5036 | − | 17.5036i | −0.581841 | − | 0.581841i | ||||
\(906\) | − | 5.17767i | − | 0.172017i | ||||||
\(907\) | − | 49.1741i | − | 1.63280i | −0.577487 | − | 0.816400i | \(-0.695966\pi\) | ||
0.577487 | − | 0.816400i | \(-0.304034\pi\) | |||||||
\(908\) | 10.8618 | − | 10.8618i | 0.360463 | − | 0.360463i | ||||
\(909\) | −16.8635 | −0.559328 | ||||||||
\(910\) | −4.04316 | − | 15.9018i | −0.134029 | − | 0.527141i | ||||
\(911\) | −2.22608 | −0.0737535 | −0.0368767 | − | 0.999320i | \(-0.511741\pi\) | ||||
−0.0368767 | + | 0.999320i | \(0.511741\pi\) | |||||||
\(912\) | −2.64668 | + | 2.64668i | −0.0876402 | + | 0.0876402i | ||||
\(913\) | − | 3.55841i | − | 0.117766i | ||||||
\(914\) | − | 9.82152i | − | 0.324867i | ||||||
\(915\) | 4.54076 | + | 4.54076i | 0.150113 | + | 0.150113i | ||||
\(916\) | 21.3980 | + | 21.3980i | 0.707008 | + | 0.707008i | ||||
\(917\) | 2.80678 | − | 5.49574i | 0.0926880 | − | 0.181485i | ||||
\(918\) | 1.67423 | + | 1.67423i | 0.0552579 | + | 0.0552579i | ||||
\(919\) | 27.8737 | 0.919469 | 0.459734 | − | 0.888056i | \(-0.347945\pi\) | ||||
0.459734 | + | 0.888056i | \(0.347945\pi\) | |||||||
\(920\) | −26.4595 | −0.872343 | ||||||||
\(921\) | −4.74652 | − | 4.74652i | −0.156403 | − | 0.156403i | ||||
\(922\) | 40.8789 | 1.34628 | ||||||||
\(923\) | −8.43751 | − | 0.542695i | −0.277724 | − | 0.0178630i | ||||
\(924\) | −0.519338 | − | 1.60352i | −0.0170850 | − | 0.0527521i | ||||
\(925\) | −10.8808 | + | 10.8808i | −0.357759 | + | 0.357759i | ||||
\(926\) | −8.33074 | −0.273765 | ||||||||
\(927\) | −14.7431 | −0.484228 | ||||||||
\(928\) | −0.602762 | + | 0.602762i | −0.0197866 | + | 0.0197866i | ||||
\(929\) | −29.7110 | − | 29.7110i | −0.974785 | − | 0.974785i | 0.0249045 | − | 0.999690i | \(-0.492072\pi\) |
−0.999690 | + | 0.0249045i | \(0.992072\pi\) | |||||||
\(930\) | −4.25280 | + | 4.25280i | −0.139455 | + | 0.139455i | ||||
\(931\) | −4.76600 | + | 29.7268i | −0.156199 | + | 0.974258i | ||||
\(932\) | −6.57647 | −0.215419 | ||||||||
\(933\) | 25.2400i | 0.826322i | ||||||||
\(934\) | 18.5769 | − | 18.5769i | 0.607854 | − | 0.607854i | ||||
\(935\) | 2.59715i | 0.0849358i | ||||||||
\(936\) | 0.690350 | − | 10.7332i | 0.0225648 | − | 0.350825i | ||||
\(937\) | 11.3062i | 0.369357i | 0.982799 | + | 0.184678i | \(0.0591243\pi\) | ||||
−0.982799 | + | 0.184678i | \(0.940876\pi\) | |||||||
\(938\) | −2.67824 | + | 5.24406i | −0.0874477 | + | 0.171225i | ||||
\(939\) | −4.80127 | −0.156683 | ||||||||
\(940\) | − | 6.75284i | − | 0.220253i | ||||||
\(941\) | 19.9739 | + | 19.9739i | 0.651129 | + | 0.651129i | 0.953265 | − | 0.302136i | \(-0.0976996\pi\) |
−0.302136 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(942\) | 12.2299 | − | 12.2299i | 0.398473 | − | 0.398473i | ||||
\(943\) | −24.4947 | + | 24.4947i | −0.797656 | + | 0.797656i | ||||
\(944\) | 6.05359 | − | 6.05359i | 0.197028 | − | 0.197028i | ||||
\(945\) | −4.40068 | + | 1.42526i | −0.143154 | + | 0.0463637i | ||||
\(946\) | − | 3.86792i | − | 0.125757i | ||||||
\(947\) | −2.51571 | − | 2.51571i | −0.0817495 | − | 0.0817495i | 0.665050 | − | 0.746799i | \(-0.268410\pi\) |
−0.746799 | + | 0.665050i | \(0.768410\pi\) | |||||||
\(948\) | 10.1051 | 0.328199 | ||||||||
\(949\) | −24.8824 | − | 1.60042i | −0.807717 | − | 0.0519518i | ||||
\(950\) | − | 8.22218i | − | 0.266763i | ||||||
\(951\) | −12.4651 | − | 12.4651i | −0.404209 | − | 0.404209i | ||||
\(952\) | −5.85259 | − | 18.0706i | −0.189684 | − | 0.585673i | ||||
\(953\) | 44.6048i | 1.44489i | 0.691427 | + | 0.722446i | \(0.256982\pi\) | ||||
−0.691427 | + | 0.722446i | \(0.743018\pi\) | |||||||
\(954\) | −4.49707 | + | 4.49707i | −0.145598 | + | 0.145598i | ||||
\(955\) | 1.99076 | + | 1.99076i | 0.0644194 | + | 0.0644194i | ||||
\(956\) | −19.2714 | − | 19.2714i | −0.623280 | − | 0.623280i | ||||
\(957\) | −0.0728069 | + | 0.0728069i | −0.00235351 | + | 0.00235351i | ||||
\(958\) | − | 12.6148i | − | 0.407566i | ||||||
\(959\) | 11.2391 | + | 34.7023i | 0.362931 | + | 1.12060i | ||||
\(960\) | 8.36651 | + | 8.36651i | 0.270028 | + | 0.270028i | ||||
\(961\) | − | 18.7730i | − | 0.605580i | ||||||
\(962\) | −18.5454 | − | 21.0950i | −0.597928 | − | 0.680132i | ||||
\(963\) | 11.0553 | 0.356252 | ||||||||
\(964\) | −2.30104 | − | 2.30104i | −0.0741116 | − | 0.0741116i | ||||
\(965\) | − | 38.4979i | − | 1.23929i | ||||||
\(966\) | 12.5628 | − | 4.06874i | 0.404200 | − | 0.130910i | ||||
\(967\) | −14.7534 | + | 14.7534i | −0.474437 | + | 0.474437i | −0.903347 | − | 0.428910i | \(-0.858898\pi\) |
0.428910 | + | 0.903347i | \(0.358898\pi\) | |||||||
\(968\) | 22.3987 | − | 22.3987i | 0.719923 | − | 0.719923i | ||||
\(969\) | 7.31945 | − | 7.31945i | 0.235135 | − | 0.235135i | ||||
\(970\) | −2.43479 | − | 2.43479i | −0.0781765 | − | 0.0781765i | ||||
\(971\) | − | 6.72360i | − | 0.215770i | −0.994163 | − | 0.107885i | \(-0.965592\pi\) | ||
0.994163 | − | 0.107885i | \(-0.0344079\pi\) | |||||||
\(972\) | −1.03217 | −0.0331070 | ||||||||
\(973\) | 21.1527 | − | 41.4175i | 0.678124 | − | 1.32778i | ||||
\(974\) | − | 14.0773i | − | 0.451064i | ||||||
\(975\) | 4.62610 | + | 5.26210i | 0.148154 | + | 0.168522i | ||||
\(976\) | 3.19644i | 0.102316i | ||||||||
\(977\) | 28.0472 | − | 28.0472i | 0.897311 | − | 0.897311i | −0.0978869 | − | 0.995198i | \(-0.531208\pi\) |
0.995198 | + | 0.0978869i | \(0.0312083\pi\) | |||||||
\(978\) | − | 1.40174i | − | 0.0448226i | ||||||
\(979\) | −10.4442 | −0.333799 | ||||||||
\(980\) | 12.4730 | + | 1.99975i | 0.398435 | + | 0.0638797i | ||||
\(981\) | −9.27976 | + | 9.27976i | −0.296280 | + | 0.296280i | ||||
\(982\) | −23.2520 | − | 23.2520i | −0.742001 | − | 0.742001i | ||||
\(983\) | −31.8528 | + | 31.8528i | −1.01595 | + | 1.01595i | −0.0160758 | + | 0.999871i | \(0.505117\pi\) |
−0.999871 | + | 0.0160758i | \(0.994883\pi\) | |||||||
\(984\) | 20.3677 | 0.649298 | ||||||||
\(985\) | 31.8724 | 1.01554 | ||||||||
\(986\) | −0.279299 | + | 0.279299i | −0.00889469 | + | 0.00889469i | ||||
\(987\) | 3.05047 | + | 9.41872i | 0.0970975 | + | 0.299801i | ||||
\(988\) | −15.9731 | − | 1.02738i | −0.508173 | − | 0.0326853i | ||||
\(989\) | −32.3179 | −1.02765 | ||||||||
\(990\) | 0.750668 | + | 0.750668i | 0.0238578 | + | 0.0238578i | ||||
\(991\) | −10.7436 | −0.341282 | −0.170641 | − | 0.985333i | \(-0.554584\pi\) | ||||
−0.170641 | + | 0.985333i | \(0.554584\pi\) | |||||||
\(992\) | 17.8677 | 0.567299 | ||||||||
\(993\) | 4.48479 | + | 4.48479i | 0.142320 | + | 0.142320i | ||||
\(994\) | −2.77613 | + | 5.43573i | −0.0880535 | + | 0.172411i | ||||
\(995\) | 16.7775 | + | 16.7775i | 0.531884 | + | 0.531884i | ||||
\(996\) | 4.20785 | + | 4.20785i | 0.133331 | + | 0.133331i | ||||
\(997\) | − | 12.5550i | − | 0.397622i | −0.980038 | − | 0.198811i | \(-0.936292\pi\) | ||
0.980038 | − | 0.198811i | \(-0.0637079\pi\) | |||||||
\(998\) | 8.57965i | 0.271584i | ||||||||
\(999\) | −5.59931 | + | 5.59931i | −0.177154 | + | 0.177154i |
(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 | 273.2.p.e.265.4 | yes | 12 | |
3.2 | odd | 2 | 819.2.y.g.811.3 | 12 | |||
7.6 | odd | 2 | 273.2.p.f.265.4 | yes | 12 | ||
13.8 | odd | 4 | 273.2.p.f.34.4 | yes | 12 | ||
21.20 | even | 2 | 819.2.y.f.811.3 | 12 | |||
39.8 | even | 4 | 819.2.y.f.307.3 | 12 | |||
91.34 | even | 4 | inner | 273.2.p.e.34.4 | ✓ | 12 | |
273.125 | odd | 4 | 819.2.y.g.307.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.p.e.34.4 | ✓ | 12 | 91.34 | even | 4 | inner | |
273.2.p.e.265.4 | yes | 12 | 1.1 | even | 1 | trivial | |
273.2.p.f.34.4 | yes | 12 | 13.8 | odd | 4 | ||
273.2.p.f.265.4 | yes | 12 | 7.6 | odd | 2 | ||
819.2.y.f.307.3 | 12 | 39.8 | even | 4 | |||
819.2.y.f.811.3 | 12 | 21.20 | even | 2 | |||
819.2.y.g.307.3 | 12 | 273.125 | odd | 4 | |||
819.2.y.g.811.3 | 12 | 3.2 | odd | 2 |