Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.a (trivial) |
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: | yes |
Analytic conductor: | \(21.2961022191\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} - 372 x^{4} + 146 x^{3} + 116 x^{2} - 12 x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.45503\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.45503 | 1.02886 | 0.514431 | − | 0.857532i | \(-0.328003\pi\) | ||||
0.514431 | + | 0.857532i | \(0.328003\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.117115 | 0.0585575 | ||||||||
\(5\) | −0.420019 | −0.187838 | −0.0939191 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939191 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(6\) | −1.45503 | −0.594014 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.73966 | −0.968615 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.611141 | −0.193260 | ||||||||
\(11\) | 4.09314 | 1.23413 | 0.617065 | − | 0.786912i | \(-0.288322\pi\) | ||||
0.617065 | + | 0.786912i | \(0.288322\pi\) | |||||||
\(12\) | −0.117115 | −0.0338082 | ||||||||
\(13\) | 5.95755 | 1.65233 | 0.826164 | − | 0.563430i | \(-0.190518\pi\) | ||||
0.826164 | + | 0.563430i | \(0.190518\pi\) | |||||||
\(14\) | 1.45503 | 0.388873 | ||||||||
\(15\) | 0.420019 | 0.108448 | ||||||||
\(16\) | −4.22051 | −1.05513 | ||||||||
\(17\) | −7.99832 | −1.93988 | −0.969939 | − | 0.243348i | \(-0.921754\pi\) | ||||
−0.969939 | + | 0.243348i | \(0.921754\pi\) | |||||||
\(18\) | 1.45503 | 0.342954 | ||||||||
\(19\) | 1.20264 | 0.275904 | 0.137952 | − | 0.990439i | \(-0.455948\pi\) | ||||
0.137952 | + | 0.990439i | \(0.455948\pi\) | |||||||
\(20\) | −0.0491906 | −0.0109993 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 5.95565 | 1.26975 | ||||||||
\(23\) | −0.806334 | −0.168132 | −0.0840661 | − | 0.996460i | \(-0.526791\pi\) | ||||
−0.0840661 | + | 0.996460i | \(0.526791\pi\) | |||||||
\(24\) | 2.73966 | 0.559230 | ||||||||
\(25\) | −4.82358 | −0.964717 | ||||||||
\(26\) | 8.66843 | 1.70002 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.117115 | 0.0221327 | ||||||||
\(29\) | 5.46630 | 1.01507 | 0.507533 | − | 0.861632i | \(-0.330558\pi\) | ||||
0.507533 | + | 0.861632i | \(0.330558\pi\) | |||||||
\(30\) | 0.611141 | 0.111579 | ||||||||
\(31\) | 3.58774 | 0.644376 | 0.322188 | − | 0.946676i | \(-0.395582\pi\) | ||||
0.322188 | + | 0.946676i | \(0.395582\pi\) | |||||||
\(32\) | −0.661667 | −0.116967 | ||||||||
\(33\) | −4.09314 | −0.712525 | ||||||||
\(34\) | −11.6378 | −1.99587 | ||||||||
\(35\) | −0.420019 | −0.0709962 | ||||||||
\(36\) | 0.117115 | 0.0195192 | ||||||||
\(37\) | −3.79745 | −0.624297 | −0.312149 | − | 0.950033i | \(-0.601049\pi\) | ||||
−0.312149 | + | 0.950033i | \(0.601049\pi\) | |||||||
\(38\) | 1.74988 | 0.283867 | ||||||||
\(39\) | −5.95755 | −0.953972 | ||||||||
\(40\) | 1.15071 | 0.181943 | ||||||||
\(41\) | 9.24830 | 1.44434 | 0.722171 | − | 0.691715i | \(-0.243145\pi\) | ||||
0.722171 | + | 0.691715i | \(0.243145\pi\) | |||||||
\(42\) | −1.45503 | −0.224516 | ||||||||
\(43\) | −4.78854 | −0.730245 | −0.365123 | − | 0.930959i | \(-0.618973\pi\) | ||||
−0.365123 | + | 0.930959i | \(0.618973\pi\) | |||||||
\(44\) | 0.479369 | 0.0722676 | ||||||||
\(45\) | −0.420019 | −0.0626128 | ||||||||
\(46\) | −1.17324 | −0.172985 | ||||||||
\(47\) | 10.3421 | 1.50855 | 0.754273 | − | 0.656561i | \(-0.227990\pi\) | ||||
0.754273 | + | 0.656561i | \(0.227990\pi\) | |||||||
\(48\) | 4.22051 | 0.609179 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.01846 | −0.992561 | ||||||||
\(51\) | 7.99832 | 1.11999 | ||||||||
\(52\) | 0.697719 | 0.0967563 | ||||||||
\(53\) | 3.29407 | 0.452475 | 0.226238 | − | 0.974072i | \(-0.427357\pi\) | ||||
0.226238 | + | 0.974072i | \(0.427357\pi\) | |||||||
\(54\) | −1.45503 | −0.198005 | ||||||||
\(55\) | −1.71920 | −0.231817 | ||||||||
\(56\) | −2.73966 | −0.366102 | ||||||||
\(57\) | −1.20264 | −0.159293 | ||||||||
\(58\) | 7.95363 | 1.04436 | ||||||||
\(59\) | 5.19779 | 0.676695 | 0.338347 | − | 0.941021i | \(-0.390132\pi\) | ||||
0.338347 | + | 0.941021i | \(0.390132\pi\) | |||||||
\(60\) | 0.0491906 | 0.00635048 | ||||||||
\(61\) | −4.46437 | −0.571605 | −0.285802 | − | 0.958289i | \(-0.592260\pi\) | ||||
−0.285802 | + | 0.958289i | \(0.592260\pi\) | |||||||
\(62\) | 5.22027 | 0.662974 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 7.47828 | 0.934785 | ||||||||
\(65\) | −2.50229 | −0.310371 | ||||||||
\(66\) | −5.95565 | −0.733090 | ||||||||
\(67\) | 10.1874 | 1.24459 | 0.622297 | − | 0.782781i | \(-0.286200\pi\) | ||||
0.622297 | + | 0.782781i | \(0.286200\pi\) | |||||||
\(68\) | −0.936724 | −0.113594 | ||||||||
\(69\) | 0.806334 | 0.0970712 | ||||||||
\(70\) | −0.611141 | −0.0730453 | ||||||||
\(71\) | 8.24577 | 0.978592 | 0.489296 | − | 0.872118i | \(-0.337254\pi\) | ||||
0.489296 | + | 0.872118i | \(0.337254\pi\) | |||||||
\(72\) | −2.73966 | −0.322872 | ||||||||
\(73\) | 8.96444 | 1.04921 | 0.524604 | − | 0.851346i | \(-0.324213\pi\) | ||||
0.524604 | + | 0.851346i | \(0.324213\pi\) | |||||||
\(74\) | −5.52541 | −0.642316 | ||||||||
\(75\) | 4.82358 | 0.556979 | ||||||||
\(76\) | 0.140847 | 0.0161563 | ||||||||
\(77\) | 4.09314 | 0.466457 | ||||||||
\(78\) | −8.66843 | −0.981506 | ||||||||
\(79\) | −11.1975 | −1.25982 | −0.629911 | − | 0.776667i | \(-0.716909\pi\) | ||||
−0.629911 | + | 0.776667i | \(0.716909\pi\) | |||||||
\(80\) | 1.77270 | 0.198194 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.4566 | 1.48603 | ||||||||
\(83\) | 14.0246 | 1.53940 | 0.769699 | − | 0.638407i | \(-0.220406\pi\) | ||||
0.769699 | + | 0.638407i | \(0.220406\pi\) | |||||||
\(84\) | −0.117115 | −0.0127783 | ||||||||
\(85\) | 3.35945 | 0.364383 | ||||||||
\(86\) | −6.96747 | −0.751322 | ||||||||
\(87\) | −5.46630 | −0.586049 | ||||||||
\(88\) | −11.2138 | −1.19540 | ||||||||
\(89\) | 12.7389 | 1.35032 | 0.675162 | − | 0.737669i | \(-0.264074\pi\) | ||||
0.675162 | + | 0.737669i | \(0.264074\pi\) | |||||||
\(90\) | −0.611141 | −0.0644199 | ||||||||
\(91\) | 5.95755 | 0.624521 | ||||||||
\(92\) | −0.0944338 | −0.00984540 | ||||||||
\(93\) | −3.58774 | −0.372031 | ||||||||
\(94\) | 15.0480 | 1.55209 | ||||||||
\(95\) | −0.505131 | −0.0518254 | ||||||||
\(96\) | 0.661667 | 0.0675311 | ||||||||
\(97\) | −8.63018 | −0.876262 | −0.438131 | − | 0.898911i | \(-0.644359\pi\) | ||||
−0.438131 | + | 0.898911i | \(0.644359\pi\) | |||||||
\(98\) | 1.45503 | 0.146980 | ||||||||
\(99\) | 4.09314 | 0.411376 | ||||||||
\(100\) | −0.564914 | −0.0564914 | ||||||||
\(101\) | −13.9999 | −1.39305 | −0.696523 | − | 0.717535i | \(-0.745270\pi\) | ||||
−0.696523 | + | 0.717535i | \(0.745270\pi\) | |||||||
\(102\) | 11.6378 | 1.15231 | ||||||||
\(103\) | 18.1046 | 1.78390 | 0.891950 | − | 0.452133i | \(-0.149337\pi\) | ||||
0.891950 | + | 0.452133i | \(0.149337\pi\) | |||||||
\(104\) | −16.3216 | −1.60047 | ||||||||
\(105\) | 0.420019 | 0.0409897 | ||||||||
\(106\) | 4.79297 | 0.465534 | ||||||||
\(107\) | −8.11725 | −0.784725 | −0.392362 | − | 0.919811i | \(-0.628342\pi\) | ||||
−0.392362 | + | 0.919811i | \(0.628342\pi\) | |||||||
\(108\) | −0.117115 | −0.0112694 | ||||||||
\(109\) | 5.74750 | 0.550511 | 0.275256 | − | 0.961371i | \(-0.411238\pi\) | ||||
0.275256 | + | 0.961371i | \(0.411238\pi\) | |||||||
\(110\) | −2.50149 | −0.238507 | ||||||||
\(111\) | 3.79745 | 0.360438 | ||||||||
\(112\) | −4.22051 | −0.398801 | ||||||||
\(113\) | 14.6228 | 1.37559 | 0.687797 | − | 0.725903i | \(-0.258578\pi\) | ||||
0.687797 | + | 0.725903i | \(0.258578\pi\) | |||||||
\(114\) | −1.74988 | −0.163891 | ||||||||
\(115\) | 0.338676 | 0.0315817 | ||||||||
\(116\) | 0.640186 | 0.0594398 | ||||||||
\(117\) | 5.95755 | 0.550776 | ||||||||
\(118\) | 7.56294 | 0.696225 | ||||||||
\(119\) | −7.99832 | −0.733205 | ||||||||
\(120\) | −1.15071 | −0.105045 | ||||||||
\(121\) | 5.75383 | 0.523075 | ||||||||
\(122\) | −6.49580 | −0.588102 | ||||||||
\(123\) | −9.24830 | −0.833891 | ||||||||
\(124\) | 0.420178 | 0.0377331 | ||||||||
\(125\) | 4.12609 | 0.369049 | ||||||||
\(126\) | 1.45503 | 0.129624 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 12.2045 | 1.07873 | ||||||||
\(129\) | 4.78854 | 0.421607 | ||||||||
\(130\) | −3.64091 | −0.319329 | ||||||||
\(131\) | −8.56457 | −0.748290 | −0.374145 | − | 0.927370i | \(-0.622064\pi\) | ||||
−0.374145 | + | 0.927370i | \(0.622064\pi\) | |||||||
\(132\) | −0.479369 | −0.0417237 | ||||||||
\(133\) | 1.20264 | 0.104282 | ||||||||
\(134\) | 14.8230 | 1.28052 | ||||||||
\(135\) | 0.420019 | 0.0361495 | ||||||||
\(136\) | 21.9127 | 1.87899 | ||||||||
\(137\) | 11.6339 | 0.993952 | 0.496976 | − | 0.867764i | \(-0.334444\pi\) | ||||
0.496976 | + | 0.867764i | \(0.334444\pi\) | |||||||
\(138\) | 1.17324 | 0.0998728 | ||||||||
\(139\) | −5.36556 | −0.455101 | −0.227550 | − | 0.973766i | \(-0.573072\pi\) | ||||
−0.227550 | + | 0.973766i | \(0.573072\pi\) | |||||||
\(140\) | −0.0491906 | −0.00415736 | ||||||||
\(141\) | −10.3421 | −0.870959 | ||||||||
\(142\) | 11.9978 | 1.00684 | ||||||||
\(143\) | 24.3851 | 2.03919 | ||||||||
\(144\) | −4.22051 | −0.351710 | ||||||||
\(145\) | −2.29595 | −0.190668 | ||||||||
\(146\) | 13.0435 | 1.07949 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −0.444739 | −0.0365573 | ||||||||
\(149\) | −2.26030 | −0.185171 | −0.0925856 | − | 0.995705i | \(-0.529513\pi\) | ||||
−0.0925856 | + | 0.995705i | \(0.529513\pi\) | |||||||
\(150\) | 7.01846 | 0.573055 | ||||||||
\(151\) | 5.84583 | 0.475727 | 0.237863 | − | 0.971299i | \(-0.423553\pi\) | ||||
0.237863 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(152\) | −3.29482 | −0.267245 | ||||||||
\(153\) | −7.99832 | −0.646626 | ||||||||
\(154\) | 5.95565 | 0.479920 | ||||||||
\(155\) | −1.50692 | −0.121039 | ||||||||
\(156\) | −0.697719 | −0.0558622 | ||||||||
\(157\) | −2.77780 | −0.221692 | −0.110846 | − | 0.993838i | \(-0.535356\pi\) | ||||
−0.110846 | + | 0.993838i | \(0.535356\pi\) | |||||||
\(158\) | −16.2928 | −1.29618 | ||||||||
\(159\) | −3.29407 | −0.261237 | ||||||||
\(160\) | 0.277913 | 0.0219709 | ||||||||
\(161\) | −0.806334 | −0.0635480 | ||||||||
\(162\) | 1.45503 | 0.114318 | ||||||||
\(163\) | −7.22816 | −0.566153 | −0.283076 | − | 0.959097i | \(-0.591355\pi\) | ||||
−0.283076 | + | 0.959097i | \(0.591355\pi\) | |||||||
\(164\) | 1.08311 | 0.0845770 | ||||||||
\(165\) | 1.71920 | 0.133839 | ||||||||
\(166\) | 20.4062 | 1.58383 | ||||||||
\(167\) | 19.3352 | 1.49620 | 0.748102 | − | 0.663584i | \(-0.230965\pi\) | ||||
0.748102 | + | 0.663584i | \(0.230965\pi\) | |||||||
\(168\) | 2.73966 | 0.211369 | ||||||||
\(169\) | 22.4925 | 1.73019 | ||||||||
\(170\) | 4.88810 | 0.374900 | ||||||||
\(171\) | 1.20264 | 0.0919681 | ||||||||
\(172\) | −0.560810 | −0.0427614 | ||||||||
\(173\) | 10.9047 | 0.829067 | 0.414533 | − | 0.910034i | \(-0.363945\pi\) | ||||
0.414533 | + | 0.910034i | \(0.363945\pi\) | |||||||
\(174\) | −7.95363 | −0.602963 | ||||||||
\(175\) | −4.82358 | −0.364629 | ||||||||
\(176\) | −17.2752 | −1.30216 | ||||||||
\(177\) | −5.19779 | −0.390690 | ||||||||
\(178\) | 18.5355 | 1.38930 | ||||||||
\(179\) | −24.2428 | −1.81199 | −0.905995 | − | 0.423289i | \(-0.860876\pi\) | ||||
−0.905995 | + | 0.423289i | \(0.860876\pi\) | |||||||
\(180\) | −0.0491906 | −0.00366645 | ||||||||
\(181\) | −2.20670 | −0.164023 | −0.0820114 | − | 0.996631i | \(-0.526134\pi\) | ||||
−0.0820114 | + | 0.996631i | \(0.526134\pi\) | |||||||
\(182\) | 8.66843 | 0.642546 | ||||||||
\(183\) | 4.46437 | 0.330016 | ||||||||
\(184\) | 2.20908 | 0.162855 | ||||||||
\(185\) | 1.59500 | 0.117267 | ||||||||
\(186\) | −5.22027 | −0.382768 | ||||||||
\(187\) | −32.7383 | −2.39406 | ||||||||
\(188\) | 1.21121 | 0.0883367 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.734982 | −0.0533212 | ||||||||
\(191\) | −21.7204 | −1.57164 | −0.785818 | − | 0.618458i | \(-0.787758\pi\) | ||||
−0.785818 | + | 0.618458i | \(0.787758\pi\) | |||||||
\(192\) | −7.47828 | −0.539699 | ||||||||
\(193\) | −6.27244 | −0.451500 | −0.225750 | − | 0.974185i | \(-0.572483\pi\) | ||||
−0.225750 | + | 0.974185i | \(0.572483\pi\) | |||||||
\(194\) | −12.5572 | −0.901553 | ||||||||
\(195\) | 2.50229 | 0.179193 | ||||||||
\(196\) | 0.117115 | 0.00836536 | ||||||||
\(197\) | 20.0593 | 1.42917 | 0.714584 | − | 0.699550i | \(-0.246616\pi\) | ||||
0.714584 | + | 0.699550i | \(0.246616\pi\) | |||||||
\(198\) | 5.95565 | 0.423250 | ||||||||
\(199\) | −0.345721 | −0.0245075 | −0.0122538 | − | 0.999925i | \(-0.503901\pi\) | ||||
−0.0122538 | + | 0.999925i | \(0.503901\pi\) | |||||||
\(200\) | 13.2150 | 0.934439 | ||||||||
\(201\) | −10.1874 | −0.718567 | ||||||||
\(202\) | −20.3703 | −1.43325 | ||||||||
\(203\) | 5.46630 | 0.383659 | ||||||||
\(204\) | 0.936724 | 0.0655838 | ||||||||
\(205\) | −3.88446 | −0.271303 | ||||||||
\(206\) | 26.3428 | 1.83539 | ||||||||
\(207\) | −0.806334 | −0.0560441 | ||||||||
\(208\) | −25.1439 | −1.74342 | ||||||||
\(209\) | 4.92257 | 0.340501 | ||||||||
\(210\) | 0.611141 | 0.0421727 | ||||||||
\(211\) | −17.4577 | −1.20184 | −0.600919 | − | 0.799310i | \(-0.705199\pi\) | ||||
−0.600919 | + | 0.799310i | \(0.705199\pi\) | |||||||
\(212\) | 0.385785 | 0.0264958 | ||||||||
\(213\) | −8.24577 | −0.564991 | ||||||||
\(214\) | −11.8109 | −0.807374 | ||||||||
\(215\) | 2.01128 | 0.137168 | ||||||||
\(216\) | 2.73966 | 0.186410 | ||||||||
\(217\) | 3.58774 | 0.243551 | ||||||||
\(218\) | 8.36280 | 0.566400 | ||||||||
\(219\) | −8.96444 | −0.605761 | ||||||||
\(220\) | −0.201344 | −0.0135746 | ||||||||
\(221\) | −47.6504 | −3.20532 | ||||||||
\(222\) | 5.52541 | 0.370841 | ||||||||
\(223\) | −8.39861 | −0.562412 | −0.281206 | − | 0.959647i | \(-0.590734\pi\) | ||||
−0.281206 | + | 0.959647i | \(0.590734\pi\) | |||||||
\(224\) | −0.661667 | −0.0442095 | ||||||||
\(225\) | −4.82358 | −0.321572 | ||||||||
\(226\) | 21.2766 | 1.41530 | ||||||||
\(227\) | 7.77384 | 0.515968 | 0.257984 | − | 0.966149i | \(-0.416942\pi\) | ||||
0.257984 | + | 0.966149i | \(0.416942\pi\) | |||||||
\(228\) | −0.140847 | −0.00932782 | ||||||||
\(229\) | −25.0564 | −1.65577 | −0.827885 | − | 0.560897i | \(-0.810456\pi\) | ||||
−0.827885 | + | 0.560897i | \(0.810456\pi\) | |||||||
\(230\) | 0.492783 | 0.0324932 | ||||||||
\(231\) | −4.09314 | −0.269309 | ||||||||
\(232\) | −14.9758 | −0.983208 | ||||||||
\(233\) | −30.1760 | −1.97689 | −0.988446 | − | 0.151571i | \(-0.951567\pi\) | ||||
−0.988446 | + | 0.151571i | \(0.951567\pi\) | |||||||
\(234\) | 8.66843 | 0.566673 | ||||||||
\(235\) | −4.34387 | −0.283363 | ||||||||
\(236\) | 0.608739 | 0.0396256 | ||||||||
\(237\) | 11.1975 | 0.727359 | ||||||||
\(238\) | −11.6378 | −0.754367 | ||||||||
\(239\) | −5.76988 | −0.373222 | −0.186611 | − | 0.982434i | \(-0.559750\pi\) | ||||
−0.186611 | + | 0.982434i | \(0.559750\pi\) | |||||||
\(240\) | −1.77270 | −0.114427 | ||||||||
\(241\) | −11.9312 | −0.768559 | −0.384279 | − | 0.923217i | \(-0.625550\pi\) | ||||
−0.384279 | + | 0.923217i | \(0.625550\pi\) | |||||||
\(242\) | 8.37199 | 0.538172 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.522845 | −0.0334717 | ||||||||
\(245\) | −0.420019 | −0.0268340 | ||||||||
\(246\) | −13.4566 | −0.857959 | ||||||||
\(247\) | 7.16478 | 0.455884 | ||||||||
\(248\) | −9.82916 | −0.624152 | ||||||||
\(249\) | −14.0246 | −0.888772 | ||||||||
\(250\) | 6.00359 | 0.379701 | ||||||||
\(251\) | 27.8947 | 1.76070 | 0.880350 | − | 0.474325i | \(-0.157308\pi\) | ||||
0.880350 | + | 0.474325i | \(0.157308\pi\) | |||||||
\(252\) | 0.117115 | 0.00737755 | ||||||||
\(253\) | −3.30044 | −0.207497 | ||||||||
\(254\) | −1.45503 | −0.0912968 | ||||||||
\(255\) | −3.35945 | −0.210377 | ||||||||
\(256\) | 2.80131 | 0.175082 | ||||||||
\(257\) | −1.37008 | −0.0854634 | −0.0427317 | − | 0.999087i | \(-0.513606\pi\) | ||||
−0.0427317 | + | 0.999087i | \(0.513606\pi\) | |||||||
\(258\) | 6.96747 | 0.433776 | ||||||||
\(259\) | −3.79745 | −0.235962 | ||||||||
\(260\) | −0.293055 | −0.0181745 | ||||||||
\(261\) | 5.46630 | 0.338355 | ||||||||
\(262\) | −12.4617 | −0.769888 | ||||||||
\(263\) | 6.11351 | 0.376975 | 0.188488 | − | 0.982076i | \(-0.439642\pi\) | ||||
0.188488 | + | 0.982076i | \(0.439642\pi\) | |||||||
\(264\) | 11.2138 | 0.690162 | ||||||||
\(265\) | −1.38357 | −0.0849921 | ||||||||
\(266\) | 1.74988 | 0.107292 | ||||||||
\(267\) | −12.7389 | −0.779610 | ||||||||
\(268\) | 1.19310 | 0.0728803 | ||||||||
\(269\) | −14.3108 | −0.872547 | −0.436274 | − | 0.899814i | \(-0.643702\pi\) | ||||
−0.436274 | + | 0.899814i | \(0.643702\pi\) | |||||||
\(270\) | 0.611141 | 0.0371929 | ||||||||
\(271\) | −19.0355 | −1.15632 | −0.578162 | − | 0.815922i | \(-0.696230\pi\) | ||||
−0.578162 | + | 0.815922i | \(0.696230\pi\) | |||||||
\(272\) | 33.7570 | 2.04682 | ||||||||
\(273\) | −5.95755 | −0.360568 | ||||||||
\(274\) | 16.9277 | 1.02264 | ||||||||
\(275\) | −19.7436 | −1.19059 | ||||||||
\(276\) | 0.0944338 | 0.00568425 | ||||||||
\(277\) | 17.7110 | 1.06415 | 0.532076 | − | 0.846697i | \(-0.321412\pi\) | ||||
0.532076 | + | 0.846697i | \(0.321412\pi\) | |||||||
\(278\) | −7.80705 | −0.468236 | ||||||||
\(279\) | 3.58774 | 0.214792 | ||||||||
\(280\) | 1.15071 | 0.0687680 | ||||||||
\(281\) | −27.6078 | −1.64694 | −0.823472 | − | 0.567357i | \(-0.807966\pi\) | ||||
−0.823472 | + | 0.567357i | \(0.807966\pi\) | |||||||
\(282\) | −15.0480 | −0.896097 | ||||||||
\(283\) | 11.8324 | 0.703360 | 0.351680 | − | 0.936120i | \(-0.385610\pi\) | ||||
0.351680 | + | 0.936120i | \(0.385610\pi\) | |||||||
\(284\) | 0.965703 | 0.0573039 | ||||||||
\(285\) | 0.505131 | 0.0299214 | ||||||||
\(286\) | 35.4811 | 2.09804 | ||||||||
\(287\) | 9.24830 | 0.545910 | ||||||||
\(288\) | −0.661667 | −0.0389891 | ||||||||
\(289\) | 46.9732 | 2.76313 | ||||||||
\(290\) | −3.34068 | −0.196171 | ||||||||
\(291\) | 8.63018 | 0.505910 | ||||||||
\(292\) | 1.04987 | 0.0614390 | ||||||||
\(293\) | 17.9876 | 1.05085 | 0.525423 | − | 0.850841i | \(-0.323907\pi\) | ||||
0.525423 | + | 0.850841i | \(0.323907\pi\) | |||||||
\(294\) | −1.45503 | −0.0848591 | ||||||||
\(295\) | −2.18317 | −0.127109 | ||||||||
\(296\) | 10.4037 | 0.604703 | ||||||||
\(297\) | −4.09314 | −0.237508 | ||||||||
\(298\) | −3.28881 | −0.190516 | ||||||||
\(299\) | −4.80378 | −0.277810 | ||||||||
\(300\) | 0.564914 | 0.0326153 | ||||||||
\(301\) | −4.78854 | −0.276007 | ||||||||
\(302\) | 8.50586 | 0.489457 | ||||||||
\(303\) | 13.9999 | 0.804275 | ||||||||
\(304\) | −5.07575 | −0.291114 | ||||||||
\(305\) | 1.87512 | 0.107369 | ||||||||
\(306\) | −11.6378 | −0.665289 | ||||||||
\(307\) | 13.1148 | 0.748500 | 0.374250 | − | 0.927328i | \(-0.377900\pi\) | ||||
0.374250 | + | 0.927328i | \(0.377900\pi\) | |||||||
\(308\) | 0.479369 | 0.0273146 | ||||||||
\(309\) | −18.1046 | −1.02994 | ||||||||
\(310\) | −2.19261 | −0.124532 | ||||||||
\(311\) | −9.74688 | −0.552695 | −0.276347 | − | 0.961058i | \(-0.589124\pi\) | ||||
−0.276347 | + | 0.961058i | \(0.589124\pi\) | |||||||
\(312\) | 16.3216 | 0.924031 | ||||||||
\(313\) | 20.0884 | 1.13547 | 0.567733 | − | 0.823213i | \(-0.307821\pi\) | ||||
0.567733 | + | 0.823213i | \(0.307821\pi\) | |||||||
\(314\) | −4.04178 | −0.228091 | ||||||||
\(315\) | −0.420019 | −0.0236654 | ||||||||
\(316\) | −1.31140 | −0.0737721 | ||||||||
\(317\) | −23.1449 | −1.29995 | −0.649974 | − | 0.759956i | \(-0.725220\pi\) | ||||
−0.649974 | + | 0.759956i | \(0.725220\pi\) | |||||||
\(318\) | −4.79297 | −0.268776 | ||||||||
\(319\) | 22.3743 | 1.25272 | ||||||||
\(320\) | −3.14102 | −0.175588 | ||||||||
\(321\) | 8.11725 | 0.453061 | ||||||||
\(322\) | −1.17324 | −0.0653821 | ||||||||
\(323\) | −9.61909 | −0.535220 | ||||||||
\(324\) | 0.117115 | 0.00650639 | ||||||||
\(325\) | −28.7368 | −1.59403 | ||||||||
\(326\) | −10.5172 | −0.582493 | ||||||||
\(327\) | −5.74750 | −0.317838 | ||||||||
\(328\) | −25.3371 | −1.39901 | ||||||||
\(329\) | 10.3421 | 0.570177 | ||||||||
\(330\) | 2.50149 | 0.137702 | ||||||||
\(331\) | −12.8235 | −0.704842 | −0.352421 | − | 0.935841i | \(-0.614642\pi\) | ||||
−0.352421 | + | 0.935841i | \(0.614642\pi\) | |||||||
\(332\) | 1.64249 | 0.0901434 | ||||||||
\(333\) | −3.79745 | −0.208099 | ||||||||
\(334\) | 28.1333 | 1.53939 | ||||||||
\(335\) | −4.27892 | −0.233782 | ||||||||
\(336\) | 4.22051 | 0.230248 | ||||||||
\(337\) | 10.3028 | 0.561228 | 0.280614 | − | 0.959821i | \(-0.409462\pi\) | ||||
0.280614 | + | 0.959821i | \(0.409462\pi\) | |||||||
\(338\) | 32.7272 | 1.78013 | ||||||||
\(339\) | −14.6228 | −0.794200 | ||||||||
\(340\) | 0.393442 | 0.0213374 | ||||||||
\(341\) | 14.6851 | 0.795244 | ||||||||
\(342\) | 1.74988 | 0.0946225 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 13.1189 | 0.707326 | ||||||||
\(345\) | −0.338676 | −0.0182337 | ||||||||
\(346\) | 15.8666 | 0.852996 | ||||||||
\(347\) | 19.3807 | 1.04041 | 0.520206 | − | 0.854041i | \(-0.325855\pi\) | ||||
0.520206 | + | 0.854041i | \(0.325855\pi\) | |||||||
\(348\) | −0.640186 | −0.0343176 | ||||||||
\(349\) | 26.2455 | 1.40489 | 0.702446 | − | 0.711737i | \(-0.252091\pi\) | ||||
0.702446 | + | 0.711737i | \(0.252091\pi\) | |||||||
\(350\) | −7.01846 | −0.375153 | ||||||||
\(351\) | −5.95755 | −0.317991 | ||||||||
\(352\) | −2.70830 | −0.144353 | ||||||||
\(353\) | 22.3694 | 1.19060 | 0.595300 | − | 0.803503i | \(-0.297033\pi\) | ||||
0.595300 | + | 0.803503i | \(0.297033\pi\) | |||||||
\(354\) | −7.56294 | −0.401966 | ||||||||
\(355\) | −3.46338 | −0.183817 | ||||||||
\(356\) | 1.49192 | 0.0790716 | ||||||||
\(357\) | 7.99832 | 0.423316 | ||||||||
\(358\) | −35.2740 | −1.86429 | ||||||||
\(359\) | 26.1003 | 1.37752 | 0.688759 | − | 0.724990i | \(-0.258156\pi\) | ||||
0.688759 | + | 0.724990i | \(0.258156\pi\) | |||||||
\(360\) | 1.15071 | 0.0606476 | ||||||||
\(361\) | −17.5537 | −0.923877 | ||||||||
\(362\) | −3.21082 | −0.168757 | ||||||||
\(363\) | −5.75383 | −0.301997 | ||||||||
\(364\) | 0.697719 | 0.0365704 | ||||||||
\(365\) | −3.76524 | −0.197081 | ||||||||
\(366\) | 6.49580 | 0.339541 | ||||||||
\(367\) | −34.4353 | −1.79751 | −0.898754 | − | 0.438454i | \(-0.855526\pi\) | ||||
−0.898754 | + | 0.438454i | \(0.855526\pi\) | |||||||
\(368\) | 3.40314 | 0.177401 | ||||||||
\(369\) | 9.24830 | 0.481447 | ||||||||
\(370\) | 2.32078 | 0.120652 | ||||||||
\(371\) | 3.29407 | 0.171019 | ||||||||
\(372\) | −0.420178 | −0.0217852 | ||||||||
\(373\) | 1.95485 | 0.101218 | 0.0506091 | − | 0.998719i | \(-0.483884\pi\) | ||||
0.0506091 | + | 0.998719i | \(0.483884\pi\) | |||||||
\(374\) | −47.6352 | −2.46316 | ||||||||
\(375\) | −4.12609 | −0.213071 | ||||||||
\(376\) | −28.3337 | −1.46120 | ||||||||
\(377\) | 32.5658 | 1.67722 | ||||||||
\(378\) | −1.45503 | −0.0748387 | ||||||||
\(379\) | −29.7272 | −1.52698 | −0.763492 | − | 0.645817i | \(-0.776517\pi\) | ||||
−0.763492 | + | 0.645817i | \(0.776517\pi\) | |||||||
\(380\) | −0.0591585 | −0.00303477 | ||||||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | −31.6039 | −1.61700 | ||||||||
\(383\) | −35.6298 | −1.82060 | −0.910300 | − | 0.413949i | \(-0.864149\pi\) | ||||
−0.910300 | + | 0.413949i | \(0.864149\pi\) | |||||||
\(384\) | −12.2045 | −0.622807 | ||||||||
\(385\) | −1.71920 | −0.0876185 | ||||||||
\(386\) | −9.12660 | −0.464532 | ||||||||
\(387\) | −4.78854 | −0.243415 | ||||||||
\(388\) | −1.01072 | −0.0513118 | ||||||||
\(389\) | −28.9904 | −1.46987 | −0.734935 | − | 0.678138i | \(-0.762787\pi\) | ||||
−0.734935 | + | 0.678138i | \(0.762787\pi\) | |||||||
\(390\) | 3.64091 | 0.184364 | ||||||||
\(391\) | 6.44932 | 0.326156 | ||||||||
\(392\) | −2.73966 | −0.138374 | ||||||||
\(393\) | 8.56457 | 0.432026 | ||||||||
\(394\) | 29.1869 | 1.47042 | ||||||||
\(395\) | 4.70318 | 0.236643 | ||||||||
\(396\) | 0.479369 | 0.0240892 | ||||||||
\(397\) | −3.59161 | −0.180258 | −0.0901289 | − | 0.995930i | \(-0.528728\pi\) | ||||
−0.0901289 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(398\) | −0.503035 | −0.0252149 | ||||||||
\(399\) | −1.20264 | −0.0602072 | ||||||||
\(400\) | 20.3580 | 1.01790 | ||||||||
\(401\) | 9.61960 | 0.480380 | 0.240190 | − | 0.970726i | \(-0.422790\pi\) | ||||
0.240190 | + | 0.970726i | \(0.422790\pi\) | |||||||
\(402\) | −14.8230 | −0.739306 | ||||||||
\(403\) | 21.3741 | 1.06472 | ||||||||
\(404\) | −1.63960 | −0.0815733 | ||||||||
\(405\) | −0.420019 | −0.0208709 | ||||||||
\(406\) | 7.95363 | 0.394732 | ||||||||
\(407\) | −15.5435 | −0.770464 | ||||||||
\(408\) | −21.9127 | −1.08484 | ||||||||
\(409\) | 31.7875 | 1.57179 | 0.785894 | − | 0.618361i | \(-0.212203\pi\) | ||||
0.785894 | + | 0.618361i | \(0.212203\pi\) | |||||||
\(410\) | −5.65201 | −0.279133 | ||||||||
\(411\) | −11.6339 | −0.573858 | ||||||||
\(412\) | 2.12032 | 0.104461 | ||||||||
\(413\) | 5.19779 | 0.255766 | ||||||||
\(414\) | −1.17324 | −0.0576616 | ||||||||
\(415\) | −5.89060 | −0.289158 | ||||||||
\(416\) | −3.94192 | −0.193268 | ||||||||
\(417\) | 5.36556 | 0.262753 | ||||||||
\(418\) | 7.16249 | 0.350329 | ||||||||
\(419\) | 21.3043 | 1.04078 | 0.520392 | − | 0.853928i | \(-0.325786\pi\) | ||||
0.520392 | + | 0.853928i | \(0.325786\pi\) | |||||||
\(420\) | 0.0491906 | 0.00240025 | ||||||||
\(421\) | −25.4806 | −1.24185 | −0.620924 | − | 0.783871i | \(-0.713242\pi\) | ||||
−0.620924 | + | 0.783871i | \(0.713242\pi\) | |||||||
\(422\) | −25.4015 | −1.23653 | ||||||||
\(423\) | 10.3421 | 0.502849 | ||||||||
\(424\) | −9.02461 | −0.438274 | ||||||||
\(425\) | 38.5806 | 1.87143 | ||||||||
\(426\) | −11.9978 | −0.581297 | ||||||||
\(427\) | −4.46437 | −0.216046 | ||||||||
\(428\) | −0.950653 | −0.0459515 | ||||||||
\(429\) | −24.3851 | −1.17732 | ||||||||
\(430\) | 2.92647 | 0.141127 | ||||||||
\(431\) | −27.6736 | −1.33299 | −0.666495 | − | 0.745510i | \(-0.732206\pi\) | ||||
−0.666495 | + | 0.745510i | \(0.732206\pi\) | |||||||
\(432\) | 4.22051 | 0.203060 | ||||||||
\(433\) | 28.1288 | 1.35178 | 0.675892 | − | 0.737000i | \(-0.263758\pi\) | ||||
0.675892 | + | 0.737000i | \(0.263758\pi\) | |||||||
\(434\) | 5.22027 | 0.250581 | ||||||||
\(435\) | 2.29595 | 0.110082 | ||||||||
\(436\) | 0.673119 | 0.0322366 | ||||||||
\(437\) | −0.969728 | −0.0463884 | ||||||||
\(438\) | −13.0435 | −0.623244 | ||||||||
\(439\) | 22.3769 | 1.06799 | 0.533995 | − | 0.845488i | \(-0.320690\pi\) | ||||
0.533995 | + | 0.845488i | \(0.320690\pi\) | |||||||
\(440\) | 4.71001 | 0.224541 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −69.3329 | −3.29783 | ||||||||
\(443\) | 27.7545 | 1.31866 | 0.659328 | − | 0.751856i | \(-0.270841\pi\) | ||||
0.659328 | + | 0.751856i | \(0.270841\pi\) | |||||||
\(444\) | 0.444739 | 0.0211064 | ||||||||
\(445\) | −5.35060 | −0.253643 | ||||||||
\(446\) | −12.2202 | −0.578645 | ||||||||
\(447\) | 2.26030 | 0.106909 | ||||||||
\(448\) | 7.47828 | 0.353316 | ||||||||
\(449\) | 0.741298 | 0.0349840 | 0.0174920 | − | 0.999847i | \(-0.494432\pi\) | ||||
0.0174920 | + | 0.999847i | \(0.494432\pi\) | |||||||
\(450\) | −7.01846 | −0.330854 | ||||||||
\(451\) | 37.8546 | 1.78250 | ||||||||
\(452\) | 1.71255 | 0.0805514 | ||||||||
\(453\) | −5.84583 | −0.274661 | ||||||||
\(454\) | 11.3112 | 0.530860 | ||||||||
\(455\) | −2.50229 | −0.117309 | ||||||||
\(456\) | 3.29482 | 0.154294 | ||||||||
\(457\) | 18.5086 | 0.865798 | 0.432899 | − | 0.901442i | \(-0.357491\pi\) | ||||
0.432899 | + | 0.901442i | \(0.357491\pi\) | |||||||
\(458\) | −36.4578 | −1.70356 | ||||||||
\(459\) | 7.99832 | 0.373330 | ||||||||
\(460\) | 0.0396640 | 0.00184934 | ||||||||
\(461\) | −40.2184 | −1.87316 | −0.936579 | − | 0.350456i | \(-0.886027\pi\) | ||||
−0.936579 | + | 0.350456i | \(0.886027\pi\) | |||||||
\(462\) | −5.95565 | −0.277082 | ||||||||
\(463\) | −33.6466 | −1.56369 | −0.781844 | − | 0.623474i | \(-0.785721\pi\) | ||||
−0.781844 | + | 0.623474i | \(0.785721\pi\) | |||||||
\(464\) | −23.0706 | −1.07103 | ||||||||
\(465\) | 1.50692 | 0.0698816 | ||||||||
\(466\) | −43.9070 | −2.03395 | ||||||||
\(467\) | 14.6853 | 0.679554 | 0.339777 | − | 0.940506i | \(-0.389648\pi\) | ||||
0.339777 | + | 0.940506i | \(0.389648\pi\) | |||||||
\(468\) | 0.697719 | 0.0322521 | ||||||||
\(469\) | 10.1874 | 0.470412 | ||||||||
\(470\) | −6.32046 | −0.291541 | ||||||||
\(471\) | 2.77780 | 0.127994 | ||||||||
\(472\) | −14.2402 | −0.655456 | ||||||||
\(473\) | −19.6002 | −0.901217 | ||||||||
\(474\) | 16.2928 | 0.748352 | ||||||||
\(475\) | −5.80103 | −0.266169 | ||||||||
\(476\) | −0.936724 | −0.0429347 | ||||||||
\(477\) | 3.29407 | 0.150825 | ||||||||
\(478\) | −8.39535 | −0.383994 | ||||||||
\(479\) | 10.4227 | 0.476227 | 0.238113 | − | 0.971237i | \(-0.423471\pi\) | ||||
0.238113 | + | 0.971237i | \(0.423471\pi\) | |||||||
\(480\) | −0.277913 | −0.0126849 | ||||||||
\(481\) | −22.6235 | −1.03154 | ||||||||
\(482\) | −17.3603 | −0.790741 | ||||||||
\(483\) | 0.806334 | 0.0366894 | ||||||||
\(484\) | 0.673859 | 0.0306300 | ||||||||
\(485\) | 3.62484 | 0.164596 | ||||||||
\(486\) | −1.45503 | −0.0660015 | ||||||||
\(487\) | −33.8424 | −1.53355 | −0.766773 | − | 0.641918i | \(-0.778139\pi\) | ||||
−0.766773 | + | 0.641918i | \(0.778139\pi\) | |||||||
\(488\) | 12.2308 | 0.553665 | ||||||||
\(489\) | 7.22816 | 0.326869 | ||||||||
\(490\) | −0.611141 | −0.0276085 | ||||||||
\(491\) | 23.3096 | 1.05195 | 0.525975 | − | 0.850500i | \(-0.323701\pi\) | ||||
0.525975 | + | 0.850500i | \(0.323701\pi\) | |||||||
\(492\) | −1.08311 | −0.0488306 | ||||||||
\(493\) | −43.7212 | −1.96910 | ||||||||
\(494\) | 10.4250 | 0.469042 | ||||||||
\(495\) | −1.71920 | −0.0772722 | ||||||||
\(496\) | −15.1421 | −0.679900 | ||||||||
\(497\) | 8.24577 | 0.369873 | ||||||||
\(498\) | −20.4062 | −0.914424 | ||||||||
\(499\) | −0.990923 | −0.0443598 | −0.0221799 | − | 0.999754i | \(-0.507061\pi\) | ||||
−0.0221799 | + | 0.999754i | \(0.507061\pi\) | |||||||
\(500\) | 0.483228 | 0.0216106 | ||||||||
\(501\) | −19.3352 | −0.863834 | ||||||||
\(502\) | 40.5877 | 1.81152 | ||||||||
\(503\) | 12.6071 | 0.562124 | 0.281062 | − | 0.959690i | \(-0.409313\pi\) | ||||
0.281062 | + | 0.959690i | \(0.409313\pi\) | |||||||
\(504\) | −2.73966 | −0.122034 | ||||||||
\(505\) | 5.88024 | 0.261667 | ||||||||
\(506\) | −4.80224 | −0.213486 | ||||||||
\(507\) | −22.4925 | −0.998925 | ||||||||
\(508\) | −0.117115 | −0.00519614 | ||||||||
\(509\) | 32.4113 | 1.43661 | 0.718303 | − | 0.695730i | \(-0.244919\pi\) | ||||
0.718303 | + | 0.695730i | \(0.244919\pi\) | |||||||
\(510\) | −4.88810 | −0.216449 | ||||||||
\(511\) | 8.96444 | 0.396563 | ||||||||
\(512\) | −20.3329 | −0.898597 | ||||||||
\(513\) | −1.20264 | −0.0530978 | ||||||||
\(514\) | −1.99351 | −0.0879300 | ||||||||
\(515\) | −7.60429 | −0.335085 | ||||||||
\(516\) | 0.560810 | 0.0246883 | ||||||||
\(517\) | 42.3316 | 1.86174 | ||||||||
\(518\) | −5.52541 | −0.242773 | ||||||||
\(519\) | −10.9047 | −0.478662 | ||||||||
\(520\) | 6.85541 | 0.300629 | ||||||||
\(521\) | 7.88673 | 0.345524 | 0.172762 | − | 0.984964i | \(-0.444731\pi\) | ||||
0.172762 | + | 0.984964i | \(0.444731\pi\) | |||||||
\(522\) | 7.95363 | 0.348121 | ||||||||
\(523\) | −5.81467 | −0.254258 | −0.127129 | − | 0.991886i | \(-0.540576\pi\) | ||||
−0.127129 | + | 0.991886i | \(0.540576\pi\) | |||||||
\(524\) | −1.00304 | −0.0438180 | ||||||||
\(525\) | 4.82358 | 0.210518 | ||||||||
\(526\) | 8.89534 | 0.387855 | ||||||||
\(527\) | −28.6959 | −1.25001 | ||||||||
\(528\) | 17.2752 | 0.751805 | ||||||||
\(529\) | −22.3498 | −0.971732 | ||||||||
\(530\) | −2.01314 | −0.0874452 | ||||||||
\(531\) | 5.19779 | 0.225565 | ||||||||
\(532\) | 0.140847 | 0.00610649 | ||||||||
\(533\) | 55.0972 | 2.38653 | ||||||||
\(534\) | −18.5355 | −0.802111 | ||||||||
\(535\) | 3.40940 | 0.147401 | ||||||||
\(536\) | −27.9101 | −1.20553 | ||||||||
\(537\) | 24.2428 | 1.04615 | ||||||||
\(538\) | −20.8227 | −0.897731 | ||||||||
\(539\) | 4.09314 | 0.176304 | ||||||||
\(540\) | 0.0491906 | 0.00211683 | ||||||||
\(541\) | 11.4384 | 0.491777 | 0.245889 | − | 0.969298i | \(-0.420920\pi\) | ||||
0.245889 | + | 0.969298i | \(0.420920\pi\) | |||||||
\(542\) | −27.6972 | −1.18970 | ||||||||
\(543\) | 2.20670 | 0.0946986 | ||||||||
\(544\) | 5.29223 | 0.226902 | ||||||||
\(545\) | −2.41406 | −0.103407 | ||||||||
\(546\) | −8.66843 | −0.370974 | ||||||||
\(547\) | −11.5776 | −0.495021 | −0.247510 | − | 0.968885i | \(-0.579612\pi\) | ||||
−0.247510 | + | 0.968885i | \(0.579612\pi\) | |||||||
\(548\) | 1.36251 | 0.0582034 | ||||||||
\(549\) | −4.46437 | −0.190535 | ||||||||
\(550\) | −28.7276 | −1.22495 | ||||||||
\(551\) | 6.57398 | 0.280061 | ||||||||
\(552\) | −2.20908 | −0.0940245 | ||||||||
\(553\) | −11.1975 | −0.476168 | ||||||||
\(554\) | 25.7701 | 1.09486 | ||||||||
\(555\) | −1.59500 | −0.0677041 | ||||||||
\(556\) | −0.628388 | −0.0266496 | ||||||||
\(557\) | −4.77210 | −0.202201 | −0.101100 | − | 0.994876i | \(-0.532236\pi\) | ||||
−0.101100 | + | 0.994876i | \(0.532236\pi\) | |||||||
\(558\) | 5.22027 | 0.220991 | ||||||||
\(559\) | −28.5280 | −1.20660 | ||||||||
\(560\) | 1.77270 | 0.0749101 | ||||||||
\(561\) | 32.7383 | 1.38221 | ||||||||
\(562\) | −40.1702 | −1.69448 | ||||||||
\(563\) | −24.0710 | −1.01447 | −0.507236 | − | 0.861807i | \(-0.669333\pi\) | ||||
−0.507236 | + | 0.861807i | \(0.669333\pi\) | |||||||
\(564\) | −1.21121 | −0.0510012 | ||||||||
\(565\) | −6.14184 | −0.258389 | ||||||||
\(566\) | 17.2164 | 0.723661 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −22.5906 | −0.947879 | ||||||||
\(569\) | −29.5305 | −1.23798 | −0.618991 | − | 0.785398i | \(-0.712458\pi\) | ||||
−0.618991 | + | 0.785398i | \(0.712458\pi\) | |||||||
\(570\) | 0.734982 | 0.0307850 | ||||||||
\(571\) | −10.5476 | −0.441402 | −0.220701 | − | 0.975342i | \(-0.570834\pi\) | ||||
−0.220701 | + | 0.975342i | \(0.570834\pi\) | |||||||
\(572\) | 2.85587 | 0.119410 | ||||||||
\(573\) | 21.7204 | 0.907384 | ||||||||
\(574\) | 13.4566 | 0.561666 | ||||||||
\(575\) | 3.88942 | 0.162200 | ||||||||
\(576\) | 7.47828 | 0.311595 | ||||||||
\(577\) | −23.4100 | −0.974573 | −0.487286 | − | 0.873242i | \(-0.662013\pi\) | ||||
−0.487286 | + | 0.873242i | \(0.662013\pi\) | |||||||
\(578\) | 68.3474 | 2.84288 | ||||||||
\(579\) | 6.27244 | 0.260674 | ||||||||
\(580\) | −0.268890 | −0.0111651 | ||||||||
\(581\) | 14.0246 | 0.581838 | ||||||||
\(582\) | 12.5572 | 0.520512 | ||||||||
\(583\) | 13.4831 | 0.558413 | ||||||||
\(584\) | −24.5595 | −1.01628 | ||||||||
\(585\) | −2.50229 | −0.103457 | ||||||||
\(586\) | 26.1725 | 1.08118 | ||||||||
\(587\) | −37.0926 | −1.53098 | −0.765488 | − | 0.643451i | \(-0.777502\pi\) | ||||
−0.765488 | + | 0.643451i | \(0.777502\pi\) | |||||||
\(588\) | −0.117115 | −0.00482974 | ||||||||
\(589\) | 4.31475 | 0.177786 | ||||||||
\(590\) | −3.17658 | −0.130778 | ||||||||
\(591\) | −20.0593 | −0.825130 | ||||||||
\(592\) | 16.0272 | 0.658714 | ||||||||
\(593\) | −13.9145 | −0.571400 | −0.285700 | − | 0.958319i | \(-0.592226\pi\) | ||||
−0.285700 | + | 0.958319i | \(0.592226\pi\) | |||||||
\(594\) | −5.95565 | −0.244363 | ||||||||
\(595\) | 3.35945 | 0.137724 | ||||||||
\(596\) | −0.264715 | −0.0108432 | ||||||||
\(597\) | 0.345721 | 0.0141494 | ||||||||
\(598\) | −6.98964 | −0.285828 | ||||||||
\(599\) | 21.8080 | 0.891051 | 0.445526 | − | 0.895269i | \(-0.353017\pi\) | ||||
0.445526 | + | 0.895269i | \(0.353017\pi\) | |||||||
\(600\) | −13.2150 | −0.539498 | ||||||||
\(601\) | 17.0329 | 0.694785 | 0.347393 | − | 0.937720i | \(-0.387067\pi\) | ||||
0.347393 | + | 0.937720i | \(0.387067\pi\) | |||||||
\(602\) | −6.96747 | −0.283973 | ||||||||
\(603\) | 10.1874 | 0.414865 | ||||||||
\(604\) | 0.684635 | 0.0278574 | ||||||||
\(605\) | −2.41672 | −0.0982535 | ||||||||
\(606\) | 20.3703 | 0.827488 | ||||||||
\(607\) | −38.0454 | −1.54422 | −0.772108 | − | 0.635491i | \(-0.780798\pi\) | ||||
−0.772108 | + | 0.635491i | \(0.780798\pi\) | |||||||
\(608\) | −0.795746 | −0.0322718 | ||||||||
\(609\) | −5.46630 | −0.221506 | ||||||||
\(610\) | 2.72836 | 0.110468 | ||||||||
\(611\) | 61.6134 | 2.49261 | ||||||||
\(612\) | −0.936724 | −0.0378648 | ||||||||
\(613\) | 16.0498 | 0.648245 | 0.324123 | − | 0.946015i | \(-0.394931\pi\) | ||||
0.324123 | + | 0.946015i | \(0.394931\pi\) | |||||||
\(614\) | 19.0824 | 0.770103 | ||||||||
\(615\) | 3.88446 | 0.156637 | ||||||||
\(616\) | −11.2138 | −0.451817 | ||||||||
\(617\) | 28.5918 | 1.15106 | 0.575532 | − | 0.817779i | \(-0.304795\pi\) | ||||
0.575532 | + | 0.817779i | \(0.304795\pi\) | |||||||
\(618\) | −26.3428 | −1.05966 | ||||||||
\(619\) | −0.179381 | −0.00720994 | −0.00360497 | − | 0.999994i | \(-0.501148\pi\) | ||||
−0.00360497 | + | 0.999994i | \(0.501148\pi\) | |||||||
\(620\) | −0.176483 | −0.00708772 | ||||||||
\(621\) | 0.806334 | 0.0323571 | ||||||||
\(622\) | −14.1820 | −0.568647 | ||||||||
\(623\) | 12.7389 | 0.510375 | ||||||||
\(624\) | 25.1439 | 1.00656 | ||||||||
\(625\) | 22.3849 | 0.895395 | ||||||||
\(626\) | 29.2293 | 1.16824 | ||||||||
\(627\) | −4.92257 | −0.196589 | ||||||||
\(628\) | −0.325322 | −0.0129818 | ||||||||
\(629\) | 30.3732 | 1.21106 | ||||||||
\(630\) | −0.611141 | −0.0243484 | ||||||||
\(631\) | −29.5538 | −1.17652 | −0.588258 | − | 0.808673i | \(-0.700186\pi\) | ||||
−0.588258 | + | 0.808673i | \(0.700186\pi\) | |||||||
\(632\) | 30.6774 | 1.22028 | ||||||||
\(633\) | 17.4577 | 0.693882 | ||||||||
\(634\) | −33.6766 | −1.33747 | ||||||||
\(635\) | 0.420019 | 0.0166680 | ||||||||
\(636\) | −0.385785 | −0.0152974 | ||||||||
\(637\) | 5.95755 | 0.236047 | ||||||||
\(638\) | 32.5554 | 1.28888 | ||||||||
\(639\) | 8.24577 | 0.326197 | ||||||||
\(640\) | −5.12611 | −0.202627 | ||||||||
\(641\) | −4.17299 | −0.164823 | −0.0824116 | − | 0.996598i | \(-0.526262\pi\) | ||||
−0.0824116 | + | 0.996598i | \(0.526262\pi\) | |||||||
\(642\) | 11.8109 | 0.466137 | ||||||||
\(643\) | −0.715991 | −0.0282359 | −0.0141180 | − | 0.999900i | \(-0.504494\pi\) | ||||
−0.0141180 | + | 0.999900i | \(0.504494\pi\) | |||||||
\(644\) | −0.0944338 | −0.00372121 | ||||||||
\(645\) | −2.01128 | −0.0791940 | ||||||||
\(646\) | −13.9961 | −0.550668 | ||||||||
\(647\) | 18.4983 | 0.727245 | 0.363622 | − | 0.931546i | \(-0.381540\pi\) | ||||
0.363622 | + | 0.931546i | \(0.381540\pi\) | |||||||
\(648\) | −2.73966 | −0.107624 | ||||||||
\(649\) | 21.2753 | 0.835129 | ||||||||
\(650\) | −41.8129 | −1.64004 | ||||||||
\(651\) | −3.58774 | −0.140614 | ||||||||
\(652\) | −0.846526 | −0.0331525 | ||||||||
\(653\) | 24.6148 | 0.963251 | 0.481626 | − | 0.876377i | \(-0.340046\pi\) | ||||
0.481626 | + | 0.876377i | \(0.340046\pi\) | |||||||
\(654\) | −8.36280 | −0.327011 | ||||||||
\(655\) | 3.59728 | 0.140558 | ||||||||
\(656\) | −39.0326 | −1.52397 | ||||||||
\(657\) | 8.96444 | 0.349736 | ||||||||
\(658\) | 15.0480 | 0.586633 | ||||||||
\(659\) | −29.6799 | −1.15616 | −0.578082 | − | 0.815979i | \(-0.696199\pi\) | ||||
−0.578082 | + | 0.815979i | \(0.696199\pi\) | |||||||
\(660\) | 0.201344 | 0.00783731 | ||||||||
\(661\) | 0.127223 | 0.00494841 | 0.00247420 | − | 0.999997i | \(-0.499212\pi\) | ||||
0.00247420 | + | 0.999997i | \(0.499212\pi\) | |||||||
\(662\) | −18.6586 | −0.725186 | ||||||||
\(663\) | 47.6504 | 1.85059 | ||||||||
\(664\) | −38.4225 | −1.49108 | ||||||||
\(665\) | −0.505131 | −0.0195881 | ||||||||
\(666\) | −5.52541 | −0.214105 | ||||||||
\(667\) | −4.40766 | −0.170665 | ||||||||
\(668\) | 2.26445 | 0.0876140 | ||||||||
\(669\) | 8.39861 | 0.324709 | ||||||||
\(670\) | −6.22596 | −0.240530 | ||||||||
\(671\) | −18.2733 | −0.705434 | ||||||||
\(672\) | 0.661667 | 0.0255244 | ||||||||
\(673\) | 18.7015 | 0.720891 | 0.360445 | − | 0.932780i | \(-0.382625\pi\) | ||||
0.360445 | + | 0.932780i | \(0.382625\pi\) | |||||||
\(674\) | 14.9908 | 0.577426 | ||||||||
\(675\) | 4.82358 | 0.185660 | ||||||||
\(676\) | 2.63420 | 0.101316 | ||||||||
\(677\) | 37.6012 | 1.44513 | 0.722567 | − | 0.691301i | \(-0.242962\pi\) | ||||
0.722567 | + | 0.691301i | \(0.242962\pi\) | |||||||
\(678\) | −21.2766 | −0.817122 | ||||||||
\(679\) | −8.63018 | −0.331196 | ||||||||
\(680\) | −9.20373 | −0.352947 | ||||||||
\(681\) | −7.77384 | −0.297894 | ||||||||
\(682\) | 21.3673 | 0.818196 | ||||||||
\(683\) | 1.76839 | 0.0676657 | 0.0338328 | − | 0.999428i | \(-0.489229\pi\) | ||||
0.0338328 | + | 0.999428i | \(0.489229\pi\) | |||||||
\(684\) | 0.140847 | 0.00538542 | ||||||||
\(685\) | −4.88647 | −0.186702 | ||||||||
\(686\) | 1.45503 | 0.0555533 | ||||||||
\(687\) | 25.0564 | 0.955960 | ||||||||
\(688\) | 20.2101 | 0.770503 | ||||||||
\(689\) | 19.6246 | 0.747637 | ||||||||
\(690\) | −0.492783 | −0.0187599 | ||||||||
\(691\) | −6.84776 | −0.260501 | −0.130250 | − | 0.991481i | \(-0.541578\pi\) | ||||
−0.130250 | + | 0.991481i | \(0.541578\pi\) | |||||||
\(692\) | 1.27710 | 0.0485481 | ||||||||
\(693\) | 4.09314 | 0.155486 | ||||||||
\(694\) | 28.1996 | 1.07044 | ||||||||
\(695\) | 2.25364 | 0.0854854 | ||||||||
\(696\) | 14.9758 | 0.567655 | ||||||||
\(697\) | −73.9708 | −2.80185 | ||||||||
\(698\) | 38.1881 | 1.44544 | ||||||||
\(699\) | 30.1760 | 1.14136 | ||||||||
\(700\) | −0.564914 | −0.0213518 | ||||||||
\(701\) | −27.6613 | −1.04475 | −0.522376 | − | 0.852715i | \(-0.674954\pi\) | ||||
−0.522376 | + | 0.852715i | \(0.674954\pi\) | |||||||
\(702\) | −8.66843 | −0.327169 | ||||||||
\(703\) | −4.56696 | −0.172246 | ||||||||
\(704\) | 30.6097 | 1.15365 | ||||||||
\(705\) | 4.34387 | 0.163600 | ||||||||
\(706\) | 32.5481 | 1.22496 | ||||||||
\(707\) | −13.9999 | −0.526522 | ||||||||
\(708\) | −0.608739 | −0.0228778 | ||||||||
\(709\) | 45.0037 | 1.69015 | 0.845075 | − | 0.534648i | \(-0.179556\pi\) | ||||
0.845075 | + | 0.534648i | \(0.179556\pi\) | |||||||
\(710\) | −5.03932 | −0.189122 | ||||||||
\(711\) | −11.1975 | −0.419941 | ||||||||
\(712\) | −34.9003 | −1.30794 | ||||||||
\(713\) | −2.89291 | −0.108340 | ||||||||
\(714\) | 11.6378 | 0.435534 | ||||||||
\(715\) | −10.2422 | −0.383037 | ||||||||
\(716\) | −2.83919 | −0.106106 | ||||||||
\(717\) | 5.76988 | 0.215480 | ||||||||
\(718\) | 37.9767 | 1.41728 | ||||||||
\(719\) | 0.0406017 | 0.00151419 | 0.000757094 | − | 1.00000i | \(-0.499759\pi\) | ||||
0.000757094 | 1.00000i | \(0.499759\pi\) | ||||||||
\(720\) | 1.77270 | 0.0660645 | ||||||||
\(721\) | 18.1046 | 0.674251 | ||||||||
\(722\) | −25.5411 | −0.950542 | ||||||||
\(723\) | 11.9312 | 0.443728 | ||||||||
\(724\) | −0.258438 | −0.00960477 | ||||||||
\(725\) | −26.3671 | −0.979251 | ||||||||
\(726\) | −8.37199 | −0.310714 | ||||||||
\(727\) | −29.7498 | −1.10336 | −0.551679 | − | 0.834056i | \(-0.686013\pi\) | ||||
−0.551679 | + | 0.834056i | \(0.686013\pi\) | |||||||
\(728\) | −16.3216 | −0.604921 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.47853 | −0.202770 | ||||||||
\(731\) | 38.3003 | 1.41659 | ||||||||
\(732\) | 0.522845 | 0.0193249 | ||||||||
\(733\) | −3.84361 | −0.141967 | −0.0709835 | − | 0.997477i | \(-0.522614\pi\) | ||||
−0.0709835 | + | 0.997477i | \(0.522614\pi\) | |||||||
\(734\) | −50.1044 | −1.84939 | ||||||||
\(735\) | 0.420019 | 0.0154926 | ||||||||
\(736\) | 0.533524 | 0.0196660 | ||||||||
\(737\) | 41.6987 | 1.53599 | ||||||||
\(738\) | 13.4566 | 0.495343 | ||||||||
\(739\) | −13.5757 | −0.499391 | −0.249695 | − | 0.968324i | \(-0.580331\pi\) | ||||
−0.249695 | + | 0.968324i | \(0.580331\pi\) | |||||||
\(740\) | 0.186799 | 0.00686686 | ||||||||
\(741\) | −7.16478 | −0.263205 | ||||||||
\(742\) | 4.79297 | 0.175955 | ||||||||
\(743\) | 7.62422 | 0.279706 | 0.139853 | − | 0.990172i | \(-0.455337\pi\) | ||||
0.139853 | + | 0.990172i | \(0.455337\pi\) | |||||||
\(744\) | 9.82916 | 0.360354 | ||||||||
\(745\) | 0.949370 | 0.0347822 | ||||||||
\(746\) | 2.84437 | 0.104140 | ||||||||
\(747\) | 14.0246 | 0.513133 | ||||||||
\(748\) | −3.83415 | −0.140190 | ||||||||
\(749\) | −8.11725 | −0.296598 | ||||||||
\(750\) | −6.00359 | −0.219220 | ||||||||
\(751\) | −38.7369 | −1.41353 | −0.706765 | − | 0.707449i | \(-0.749846\pi\) | ||||
−0.706765 | + | 0.707449i | \(0.749846\pi\) | |||||||
\(752\) | −43.6488 | −1.59171 | ||||||||
\(753\) | −27.8947 | −1.01654 | ||||||||
\(754\) | 47.3842 | 1.72563 | ||||||||
\(755\) | −2.45536 | −0.0893597 | ||||||||
\(756\) | −0.117115 | −0.00425943 | ||||||||
\(757\) | 13.7525 | 0.499841 | 0.249921 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249921 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(758\) | −43.2540 | −1.57106 | ||||||||
\(759\) | 3.30044 | 0.119798 | ||||||||
\(760\) | 1.38389 | 0.0501988 | ||||||||
\(761\) | 29.3366 | 1.06345 | 0.531725 | − | 0.846917i | \(-0.321544\pi\) | ||||
0.531725 | + | 0.846917i | \(0.321544\pi\) | |||||||
\(762\) | 1.45503 | 0.0527102 | ||||||||
\(763\) | 5.74750 | 0.208074 | ||||||||
\(764\) | −2.54379 | −0.0920311 | ||||||||
\(765\) | 3.35945 | 0.121461 | ||||||||
\(766\) | −51.8425 | −1.87315 | ||||||||
\(767\) | 30.9661 | 1.11812 | ||||||||
\(768\) | −2.80131 | −0.101084 | ||||||||
\(769\) | −29.4417 | −1.06170 | −0.530848 | − | 0.847467i | \(-0.678127\pi\) | ||||
−0.530848 | + | 0.847467i | \(0.678127\pi\) | |||||||
\(770\) | −2.50149 | −0.0901474 | ||||||||
\(771\) | 1.37008 | 0.0493423 | ||||||||
\(772\) | −0.734598 | −0.0264387 | ||||||||
\(773\) | −14.9074 | −0.536180 | −0.268090 | − | 0.963394i | \(-0.586392\pi\) | ||||
−0.268090 | + | 0.963394i | \(0.586392\pi\) | |||||||
\(774\) | −6.96747 | −0.250441 | ||||||||
\(775\) | −17.3057 | −0.621641 | ||||||||
\(776\) | 23.6437 | 0.848760 | ||||||||
\(777\) | 3.79745 | 0.136233 | ||||||||
\(778\) | −42.1819 | −1.51229 | ||||||||
\(779\) | 11.1224 | 0.398500 | ||||||||
\(780\) | 0.293055 | 0.0104931 | ||||||||
\(781\) | 33.7511 | 1.20771 | ||||||||
\(782\) | 9.38395 | 0.335570 | ||||||||
\(783\) | −5.46630 | −0.195350 | ||||||||
\(784\) | −4.22051 | −0.150733 | ||||||||
\(785\) | 1.16673 | 0.0416423 | ||||||||
\(786\) | 12.4617 | 0.444495 | ||||||||
\(787\) | −52.7973 | −1.88202 | −0.941010 | − | 0.338379i | \(-0.890121\pi\) | ||||
−0.941010 | + | 0.338379i | \(0.890121\pi\) | |||||||
\(788\) | 2.34925 | 0.0836885 | ||||||||
\(789\) | −6.11351 | −0.217647 | ||||||||
\(790\) | 6.84328 | 0.243473 | ||||||||
\(791\) | 14.6228 | 0.519926 | ||||||||
\(792\) | −11.2138 | −0.398465 | ||||||||
\(793\) | −26.5968 | −0.944478 | ||||||||
\(794\) | −5.22590 | −0.185460 | ||||||||
\(795\) | 1.38357 | 0.0490702 | ||||||||
\(796\) | −0.0404891 | −0.00143510 | ||||||||
\(797\) | −19.3955 | −0.687023 | −0.343511 | − | 0.939148i | \(-0.611616\pi\) | ||||
−0.343511 | + | 0.939148i | \(0.611616\pi\) | |||||||
\(798\) | −1.74988 | −0.0619449 | ||||||||
\(799\) | −82.7192 | −2.92639 | ||||||||
\(800\) | 3.19161 | 0.112840 | ||||||||
\(801\) | 12.7389 | 0.450108 | ||||||||
\(802\) | 13.9968 | 0.494245 | ||||||||
\(803\) | 36.6927 | 1.29486 | ||||||||
\(804\) | −1.19310 | −0.0420775 | ||||||||
\(805\) | 0.338676 | 0.0119367 | ||||||||
\(806\) | 31.1000 | 1.09545 | ||||||||
\(807\) | 14.3108 | 0.503765 | ||||||||
\(808\) | 38.3550 | 1.34932 | ||||||||
\(809\) | 16.1411 | 0.567490 | 0.283745 | − | 0.958900i | \(-0.408423\pi\) | ||||
0.283745 | + | 0.958900i | \(0.408423\pi\) | |||||||
\(810\) | −0.611141 | −0.0214733 | ||||||||
\(811\) | −29.7370 | −1.04421 | −0.522104 | − | 0.852882i | \(-0.674853\pi\) | ||||
−0.522104 | + | 0.852882i | \(0.674853\pi\) | |||||||
\(812\) | 0.640186 | 0.0224661 | ||||||||
\(813\) | 19.0355 | 0.667604 | ||||||||
\(814\) | −22.6163 | −0.792701 | ||||||||
\(815\) | 3.03596 | 0.106345 | ||||||||
\(816\) | −33.7570 | −1.18173 | ||||||||
\(817\) | −5.75888 | −0.201478 | ||||||||
\(818\) | 46.2517 | 1.61715 | ||||||||
\(819\) | 5.95755 | 0.208174 | ||||||||
\(820\) | −0.454929 | −0.0158868 | ||||||||
\(821\) | 13.5406 | 0.472570 | 0.236285 | − | 0.971684i | \(-0.424070\pi\) | ||||
0.236285 | + | 0.971684i | \(0.424070\pi\) | |||||||
\(822\) | −16.9277 | −0.590421 | ||||||||
\(823\) | −20.0304 | −0.698216 | −0.349108 | − | 0.937083i | \(-0.613515\pi\) | ||||
−0.349108 | + | 0.937083i | \(0.613515\pi\) | |||||||
\(824\) | −49.6004 | −1.72791 | ||||||||
\(825\) | 19.7436 | 0.687385 | ||||||||
\(826\) | 7.56294 | 0.263148 | ||||||||
\(827\) | −40.3235 | −1.40219 | −0.701094 | − | 0.713069i | \(-0.747304\pi\) | ||||
−0.701094 | + | 0.713069i | \(0.747304\pi\) | |||||||
\(828\) | −0.0944338 | −0.00328180 | ||||||||
\(829\) | −49.5541 | −1.72108 | −0.860542 | − | 0.509379i | \(-0.829875\pi\) | ||||
−0.860542 | + | 0.509379i | \(0.829875\pi\) | |||||||
\(830\) | −8.57100 | −0.297504 | ||||||||
\(831\) | −17.7110 | −0.614388 | ||||||||
\(832\) | 44.5523 | 1.54457 | ||||||||
\(833\) | −7.99832 | −0.277125 | ||||||||
\(834\) | 7.80705 | 0.270336 | ||||||||
\(835\) | −8.12116 | −0.281044 | ||||||||
\(836\) | 0.576507 | 0.0199389 | ||||||||
\(837\) | −3.58774 | −0.124010 | ||||||||
\(838\) | 30.9984 | 1.07082 | ||||||||
\(839\) | −34.0265 | −1.17473 | −0.587363 | − | 0.809324i | \(-0.699834\pi\) | ||||
−0.587363 | + | 0.809324i | \(0.699834\pi\) | |||||||
\(840\) | −1.15071 | −0.0397032 | ||||||||
\(841\) | 0.880417 | 0.0303592 | ||||||||
\(842\) | −37.0750 | −1.27769 | ||||||||
\(843\) | 27.6078 | 0.950863 | ||||||||
\(844\) | −2.04456 | −0.0703767 | ||||||||
\(845\) | −9.44726 | −0.324996 | ||||||||
\(846\) | 15.0480 | 0.517362 | ||||||||
\(847\) | 5.75383 | 0.197704 | ||||||||
\(848\) | −13.9027 | −0.477419 | ||||||||
\(849\) | −11.8324 | −0.406085 | ||||||||
\(850\) | 56.1359 | 1.92545 | ||||||||
\(851\) | 3.06201 | 0.104964 | ||||||||
\(852\) | −0.965703 | −0.0330844 | ||||||||
\(853\) | 27.8105 | 0.952213 | 0.476107 | − | 0.879388i | \(-0.342048\pi\) | ||||
0.476107 | + | 0.879388i | \(0.342048\pi\) | |||||||
\(854\) | −6.49580 | −0.222282 | ||||||||
\(855\) | −0.505131 | −0.0172751 | ||||||||
\(856\) | 22.2385 | 0.760096 | ||||||||
\(857\) | −55.1687 | −1.88453 | −0.942263 | − | 0.334874i | \(-0.891306\pi\) | ||||
−0.942263 | + | 0.334874i | \(0.891306\pi\) | |||||||
\(858\) | −35.4811 | −1.21131 | ||||||||
\(859\) | 14.0090 | 0.477980 | 0.238990 | − | 0.971022i | \(-0.423184\pi\) | ||||
0.238990 | + | 0.971022i | \(0.423184\pi\) | |||||||
\(860\) | 0.235551 | 0.00803222 | ||||||||
\(861\) | −9.24830 | −0.315181 | ||||||||
\(862\) | −40.2659 | −1.37146 | ||||||||
\(863\) | −7.64204 | −0.260138 | −0.130069 | − | 0.991505i | \(-0.541520\pi\) | ||||
−0.130069 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(864\) | 0.661667 | 0.0225104 | ||||||||
\(865\) | −4.58017 | −0.155731 | ||||||||
\(866\) | 40.9283 | 1.39080 | ||||||||
\(867\) | −46.9732 | −1.59529 | ||||||||
\(868\) | 0.420178 | 0.0142618 | ||||||||
\(869\) | −45.8332 | −1.55478 | ||||||||
\(870\) | 3.34068 | 0.113260 | ||||||||
\(871\) | 60.6922 | 2.05648 | ||||||||
\(872\) | −15.7462 | −0.533233 | ||||||||
\(873\) | −8.63018 | −0.292087 | ||||||||
\(874\) | −1.41098 | −0.0477272 | ||||||||
\(875\) | 4.12609 | 0.139487 | ||||||||
\(876\) | −1.04987 | −0.0354718 | ||||||||
\(877\) | 0.769283 | 0.0259768 | 0.0129884 | − | 0.999916i | \(-0.495866\pi\) | ||||
0.0129884 | + | 0.999916i | \(0.495866\pi\) | |||||||
\(878\) | 32.5590 | 1.09881 | ||||||||
\(879\) | −17.9876 | −0.606706 | ||||||||
\(880\) | 7.25590 | 0.244596 | ||||||||
\(881\) | −3.94890 | −0.133042 | −0.0665209 | − | 0.997785i | \(-0.521190\pi\) | ||||
−0.0665209 | + | 0.997785i | \(0.521190\pi\) | |||||||
\(882\) | 1.45503 | 0.0489934 | ||||||||
\(883\) | 37.5238 | 1.26278 | 0.631388 | − | 0.775467i | \(-0.282486\pi\) | ||||
0.631388 | + | 0.775467i | \(0.282486\pi\) | |||||||
\(884\) | −5.58058 | −0.187695 | ||||||||
\(885\) | 2.18317 | 0.0733865 | ||||||||
\(886\) | 40.3836 | 1.35671 | ||||||||
\(887\) | 23.7485 | 0.797397 | 0.398698 | − | 0.917082i | \(-0.369462\pi\) | ||||
0.398698 | + | 0.917082i | \(0.369462\pi\) | |||||||
\(888\) | −10.4037 | −0.349126 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −7.78528 | −0.260963 | ||||||||
\(891\) | 4.09314 | 0.137125 | ||||||||
\(892\) | −0.983604 | −0.0329335 | ||||||||
\(893\) | 12.4378 | 0.416214 | ||||||||
\(894\) | 3.28881 | 0.109994 | ||||||||
\(895\) | 10.1824 | 0.340361 | ||||||||
\(896\) | 12.2045 | 0.407723 | ||||||||
\(897\) | 4.80378 | 0.160393 | ||||||||
\(898\) | 1.07861 | 0.0359937 | ||||||||
\(899\) | 19.6116 | 0.654085 | ||||||||
\(900\) | −0.564914 | −0.0188305 | ||||||||
\(901\) | −26.3470 | −0.877746 | ||||||||
\(902\) | 55.0796 | 1.83395 | ||||||||
\(903\) | 4.78854 | 0.159353 | ||||||||
\(904\) | −40.0614 | −1.33242 | ||||||||
\(905\) | 0.926857 | 0.0308098 | ||||||||
\(906\) | −8.50586 | −0.282588 | ||||||||
\(907\) | −25.2818 | −0.839468 | −0.419734 | − | 0.907647i | \(-0.637877\pi\) | ||||
−0.419734 | + | 0.907647i | \(0.637877\pi\) | |||||||
\(908\) | 0.910434 | 0.0302138 | ||||||||
\(909\) | −13.9999 | −0.464348 | ||||||||
\(910\) | −3.64091 | −0.120695 | ||||||||
\(911\) | 3.77037 | 0.124918 | 0.0624589 | − | 0.998048i | \(-0.480106\pi\) | ||||
0.0624589 | + | 0.998048i | \(0.480106\pi\) | |||||||
\(912\) | 5.07575 | 0.168075 | ||||||||
\(913\) | 57.4047 | 1.89982 | ||||||||
\(914\) | 26.9306 | 0.890787 | ||||||||
\(915\) | −1.87512 | −0.0619897 | ||||||||
\(916\) | −2.93448 | −0.0969578 | ||||||||
\(917\) | −8.56457 | −0.282827 | ||||||||
\(918\) | 11.6378 | 0.384105 | ||||||||
\(919\) | 31.0902 | 1.02557 | 0.512785 | − | 0.858517i | \(-0.328614\pi\) | ||||
0.512785 | + | 0.858517i | \(0.328614\pi\) | |||||||
\(920\) | −0.927855 | −0.0305905 | ||||||||
\(921\) | −13.1148 | −0.432146 | ||||||||
\(922\) | −58.5190 | −1.92722 | ||||||||
\(923\) | 49.1246 | 1.61696 | ||||||||
\(924\) | −0.479369 | −0.0157701 | ||||||||
\(925\) | 18.3173 | 0.602270 | ||||||||
\(926\) | −48.9568 | −1.60882 | ||||||||
\(927\) | 18.1046 | 0.594634 | ||||||||
\(928\) | −3.61687 | −0.118730 | ||||||||
\(929\) | 29.7655 | 0.976574 | 0.488287 | − | 0.872683i | \(-0.337622\pi\) | ||||
0.488287 | + | 0.872683i | \(0.337622\pi\) | |||||||
\(930\) | 2.19261 | 0.0718986 | ||||||||
\(931\) | 1.20264 | 0.0394149 | ||||||||
\(932\) | −3.53406 | −0.115762 | ||||||||
\(933\) | 9.74688 | 0.319098 | ||||||||
\(934\) | 21.3676 | 0.699168 | ||||||||
\(935\) | 13.7507 | 0.449696 | ||||||||
\(936\) | −16.3216 | −0.533490 | ||||||||
\(937\) | 31.5815 | 1.03172 | 0.515862 | − | 0.856672i | \(-0.327472\pi\) | ||||
0.515862 | + | 0.856672i | \(0.327472\pi\) | |||||||
\(938\) | 14.8230 | 0.483989 | ||||||||
\(939\) | −20.0884 | −0.655562 | ||||||||
\(940\) | −0.508732 | −0.0165930 | ||||||||
\(941\) | −7.00125 | −0.228234 | −0.114117 | − | 0.993467i | \(-0.536404\pi\) | ||||
−0.114117 | + | 0.993467i | \(0.536404\pi\) | |||||||
\(942\) | 4.04178 | 0.131688 | ||||||||
\(943\) | −7.45721 | −0.242840 | ||||||||
\(944\) | −21.9373 | −0.714000 | ||||||||
\(945\) | 0.420019 | 0.0136632 | ||||||||
\(946\) | −28.5189 | −0.927228 | ||||||||
\(947\) | 34.3629 | 1.11664 | 0.558322 | − | 0.829624i | \(-0.311445\pi\) | ||||
0.558322 | + | 0.829624i | \(0.311445\pi\) | |||||||
\(948\) | 1.31140 | 0.0425923 | ||||||||
\(949\) | 53.4061 | 1.73364 | ||||||||
\(950\) | −8.44067 | −0.273852 | ||||||||
\(951\) | 23.1449 | 0.750526 | ||||||||
\(952\) | 21.9127 | 0.710193 | ||||||||
\(953\) | 1.56016 | 0.0505386 | 0.0252693 | − | 0.999681i | \(-0.491956\pi\) | ||||
0.0252693 | + | 0.999681i | \(0.491956\pi\) | |||||||
\(954\) | 4.79297 | 0.155178 | ||||||||
\(955\) | 9.12300 | 0.295213 | ||||||||
\(956\) | −0.675739 | −0.0218550 | ||||||||
\(957\) | −22.3743 | −0.723260 | ||||||||
\(958\) | 15.1654 | 0.489972 | ||||||||
\(959\) | 11.6339 | 0.375679 | ||||||||
\(960\) | 3.14102 | 0.101376 | ||||||||
\(961\) | −18.1282 | −0.584779 | ||||||||
\(962\) | −32.9179 | −1.06132 | ||||||||
\(963\) | −8.11725 | −0.261575 | ||||||||
\(964\) | −1.39733 | −0.0450049 | ||||||||
\(965\) | 2.63455 | 0.0848091 | ||||||||
\(966\) | 1.17324 | 0.0377484 | ||||||||
\(967\) | 30.5017 | 0.980868 | 0.490434 | − | 0.871478i | \(-0.336838\pi\) | ||||
0.490434 | + | 0.871478i | \(0.336838\pi\) | |||||||
\(968\) | −15.7635 | −0.506658 | ||||||||
\(969\) | 9.61909 | 0.309010 | ||||||||
\(970\) | 5.27426 | 0.169346 | ||||||||
\(971\) | −25.2755 | −0.811131 | −0.405565 | − | 0.914066i | \(-0.632925\pi\) | ||||
−0.405565 | + | 0.914066i | \(0.632925\pi\) | |||||||
\(972\) | −0.117115 | −0.00375647 | ||||||||
\(973\) | −5.36556 | −0.172012 | ||||||||
\(974\) | −49.2418 | −1.57781 | ||||||||
\(975\) | 28.7368 | 0.920313 | ||||||||
\(976\) | 18.8420 | 0.603116 | ||||||||
\(977\) | 32.0198 | 1.02440 | 0.512202 | − | 0.858865i | \(-0.328830\pi\) | ||||
0.512202 | + | 0.858865i | \(0.328830\pi\) | |||||||
\(978\) | 10.5172 | 0.336303 | ||||||||
\(979\) | 52.1423 | 1.66647 | ||||||||
\(980\) | −0.0491906 | −0.00157134 | ||||||||
\(981\) | 5.74750 | 0.183504 | ||||||||
\(982\) | 33.9162 | 1.08231 | ||||||||
\(983\) | 44.6458 | 1.42398 | 0.711989 | − | 0.702190i | \(-0.247794\pi\) | ||||
0.711989 | + | 0.702190i | \(0.247794\pi\) | |||||||
\(984\) | 25.3371 | 0.807719 | ||||||||
\(985\) | −8.42530 | −0.268452 | ||||||||
\(986\) | −63.6157 | −2.02594 | ||||||||
\(987\) | −10.3421 | −0.329192 | ||||||||
\(988\) | 0.839104 | 0.0266955 | ||||||||
\(989\) | 3.86116 | 0.122778 | ||||||||
\(990\) | −2.50149 | −0.0795025 | ||||||||
\(991\) | 23.0161 | 0.731129 | 0.365565 | − | 0.930786i | \(-0.380876\pi\) | ||||
0.365565 | + | 0.930786i | \(0.380876\pi\) | |||||||
\(992\) | −2.37389 | −0.0753710 | ||||||||
\(993\) | 12.8235 | 0.406941 | ||||||||
\(994\) | 11.9978 | 0.380548 | ||||||||
\(995\) | 0.145209 | 0.00460345 | ||||||||
\(996\) | −1.64249 | −0.0520443 | ||||||||
\(997\) | 31.6803 | 1.00333 | 0.501663 | − | 0.865063i | \(-0.332722\pi\) | ||||
0.501663 | + | 0.865063i | \(0.332722\pi\) | |||||||
\(998\) | −1.44182 | −0.0456401 | ||||||||
\(999\) | 3.79745 | 0.120146 |
(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 | 2667.2.a.l.1.10 | ✓ | 13 | |
3.2 | odd | 2 | 8001.2.a.o.1.4 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.10 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8001.2.a.o.1.4 | 13 | 3.2 | odd | 2 |