Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26x^{14} + 268x^{12} - 1395x^{10} + 3876x^{8} - 5635x^{6} + 4042x^{4} - 1272x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.08213\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.08213 | 1.47228 | 0.736142 | − | 0.676827i | \(-0.236645\pi\) | ||||
0.736142 | + | 0.676827i | \(0.236645\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.33525 | 1.16762 | ||||||||
\(5\) | −1.33222 | −0.595789 | −0.297894 | − | 0.954599i | \(-0.596284\pi\) | ||||
−0.297894 | + | 0.954599i | \(0.596284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.698024 | 0.246789 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.77386 | −0.877171 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.74691 | −1.59391 | −0.796953 | − | 0.604041i | \(-0.793556\pi\) | ||||
−0.796953 | + | 0.604041i | \(0.793556\pi\) | |||||||
\(14\) | −2.08213 | −0.556471 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.21712 | −0.804280 | ||||||||
\(17\) | 4.27240 | 1.03621 | 0.518105 | − | 0.855317i | \(-0.326638\pi\) | ||||
0.518105 | + | 0.855317i | \(0.326638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.162553 | −0.0372922 | −0.0186461 | − | 0.999826i | \(-0.505936\pi\) | ||||
−0.0186461 | + | 0.999826i | \(0.505936\pi\) | |||||||
\(20\) | −3.11107 | −0.695657 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.12680 | −0.234954 | −0.117477 | − | 0.993076i | \(-0.537481\pi\) | ||||
−0.117477 | + | 0.993076i | \(0.537481\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.22518 | −0.645036 | ||||||||
\(26\) | −11.9658 | −2.34668 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.33525 | −0.441320 | ||||||||
\(29\) | 9.83547 | 1.82640 | 0.913201 | − | 0.407510i | \(-0.133603\pi\) | ||||
0.913201 | + | 0.407510i | \(0.133603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.09480 | 1.63347 | 0.816737 | − | 0.577009i | \(-0.195780\pi\) | ||||
0.816737 | + | 0.577009i | \(0.195780\pi\) | |||||||
\(32\) | −8.09449 | −1.43092 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.89567 | 1.52559 | ||||||||
\(35\) | 1.33222 | 0.225187 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.42718 | −1.38542 | −0.692710 | − | 0.721217i | \(-0.743583\pi\) | ||||
−0.692710 | + | 0.721217i | \(0.743583\pi\) | |||||||
\(38\) | −0.338455 | −0.0549047 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.929924 | −0.147034 | ||||||||
\(41\) | 4.50712 | 0.703894 | 0.351947 | − | 0.936020i | \(-0.385520\pi\) | ||||
0.351947 | + | 0.936020i | \(0.385520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.02855 | 1.22434 | 0.612172 | − | 0.790725i | \(-0.290296\pi\) | ||||
0.612172 | + | 0.790725i | \(0.290296\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.34613 | −0.345919 | ||||||||
\(47\) | 2.79374 | 0.407510 | 0.203755 | − | 0.979022i | \(-0.434685\pi\) | ||||
0.203755 | + | 0.979022i | \(0.434685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.71523 | −0.949677 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.4204 | −1.86108 | ||||||||
\(53\) | 10.4883 | 1.44067 | 0.720336 | − | 0.693625i | \(-0.243987\pi\) | ||||
0.720336 | + | 0.693625i | \(0.243987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.698024 | −0.0932774 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 20.4787 | 2.68898 | ||||||||
\(59\) | 13.6125 | 1.77220 | 0.886099 | − | 0.463497i | \(-0.153405\pi\) | ||||
0.886099 | + | 0.463497i | \(0.153405\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.06786 | −1.03298 | −0.516492 | − | 0.856292i | \(-0.672762\pi\) | ||||
−0.516492 | + | 0.856292i | \(0.672762\pi\) | |||||||
\(62\) | 18.9365 | 2.40494 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.4195 | −1.30244 | ||||||||
\(65\) | 7.65617 | 0.949631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.10333 | 1.11215 | 0.556074 | − | 0.831133i | \(-0.312307\pi\) | ||||
0.556074 | + | 0.831133i | \(0.312307\pi\) | |||||||
\(68\) | 9.97710 | 1.20990 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.77386 | 0.331539 | ||||||||
\(71\) | −1.01904 | −0.120938 | −0.0604689 | − | 0.998170i | \(-0.519260\pi\) | ||||
−0.0604689 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.64824 | 0.895159 | 0.447579 | − | 0.894244i | \(-0.352286\pi\) | ||||
0.447579 | + | 0.894244i | \(0.352286\pi\) | |||||||
\(74\) | −17.5464 | −2.03973 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.379601 | −0.0435432 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.00547271 | 0.000615728 0 | 0.000307864 | − | 1.00000i | \(-0.499902\pi\) | ||||
0.000307864 | 1.00000i | \(0.499902\pi\) | ||||||||
\(80\) | 4.28592 | 0.479181 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.38438 | 1.03633 | ||||||||
\(83\) | 2.83233 | 0.310888 | 0.155444 | − | 0.987845i | \(-0.450319\pi\) | ||||
0.155444 | + | 0.987845i | \(0.450319\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.69179 | −0.617362 | ||||||||
\(86\) | 16.7165 | 1.80258 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5254 | −1.11569 | −0.557845 | − | 0.829945i | \(-0.688372\pi\) | ||||
−0.557845 | + | 0.829945i | \(0.688372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.74691 | 0.602440 | ||||||||
\(92\) | −2.63135 | −0.274337 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.81693 | 0.599970 | ||||||||
\(95\) | 0.216557 | 0.0222182 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1613 | 1.23479 | 0.617396 | − | 0.786652i | \(-0.288188\pi\) | ||||
0.617396 | + | 0.786652i | \(0.288188\pi\) | |||||||
\(98\) | 2.08213 | 0.210326 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.53159 | −0.753159 | ||||||||
\(101\) | 1.52188 | 0.151433 | 0.0757164 | − | 0.997129i | \(-0.475876\pi\) | ||||
0.0757164 | + | 0.997129i | \(0.475876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4665 | 1.52396 | 0.761979 | − | 0.647602i | \(-0.224228\pi\) | ||||
0.761979 | + | 0.647602i | \(0.224228\pi\) | |||||||
\(104\) | −4.01148 | −0.393358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.8379 | 2.12108 | ||||||||
\(107\) | −8.25043 | −0.797599 | −0.398799 | − | 0.917038i | \(-0.630573\pi\) | ||||
−0.398799 | + | 0.917038i | \(0.630573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.305943 | −0.0293040 | −0.0146520 | − | 0.999893i | \(-0.504664\pi\) | ||||
−0.0146520 | + | 0.999893i | \(0.504664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.21712 | 0.303989 | ||||||||
\(113\) | −10.1503 | −0.954857 | −0.477428 | − | 0.878671i | \(-0.658431\pi\) | ||||
−0.477428 | + | 0.878671i | \(0.658431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50115 | 0.139983 | ||||||||
\(116\) | 22.9682 | 2.13255 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 28.3429 | 2.60918 | ||||||||
\(119\) | −4.27240 | −0.391650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.7983 | −1.52085 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 21.2386 | 1.90728 | ||||||||
\(125\) | 10.9578 | 0.980094 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.80774 | −0.337882 | −0.168941 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168941 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(128\) | −5.50574 | −0.486643 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.9411 | 1.39813 | ||||||||
\(131\) | −14.6612 | −1.28096 | −0.640479 | − | 0.767976i | \(-0.721264\pi\) | ||||
−0.640479 | + | 0.767976i | \(0.721264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.162553 | 0.0140951 | ||||||||
\(134\) | 18.9543 | 1.63740 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.98224 | 0.255725 | ||||||||
\(137\) | −16.8306 | −1.43794 | −0.718968 | − | 0.695043i | \(-0.755385\pi\) | ||||
−0.718968 | + | 0.695043i | \(0.755385\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.79467 | 0.661135 | 0.330568 | − | 0.943782i | \(-0.392760\pi\) | ||||
0.330568 | + | 0.943782i | \(0.392760\pi\) | |||||||
\(140\) | 3.11107 | 0.262933 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.12177 | −0.178055 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.1031 | −1.08815 | ||||||||
\(146\) | 15.9246 | 1.31793 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.6795 | −1.61765 | ||||||||
\(149\) | 9.71989 | 0.796284 | 0.398142 | − | 0.917324i | \(-0.369655\pi\) | ||||
0.398142 | + | 0.917324i | \(0.369655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1015 | −0.822051 | −0.411026 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411026 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(152\) | −0.113466 | −0.00920328 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.1163 | −0.973206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.94915 | −0.394985 | −0.197493 | − | 0.980304i | \(-0.563280\pi\) | ||||
−0.197493 | + | 0.980304i | \(0.563280\pi\) | |||||||
\(158\) | 0.0113949 | 0.000906526 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.7837 | 0.852524 | ||||||||
\(161\) | 1.12680 | 0.0888041 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.73297 | 0.527367 | 0.263683 | − | 0.964609i | \(-0.415063\pi\) | ||||
0.263683 | + | 0.964609i | \(0.415063\pi\) | |||||||
\(164\) | 10.5252 | 0.821882 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.89726 | 0.457716 | ||||||||
\(167\) | 13.9874 | 1.08238 | 0.541188 | − | 0.840902i | \(-0.317975\pi\) | ||||
0.541188 | + | 0.840902i | \(0.317975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.0270 | 1.54054 | ||||||||
\(170\) | −11.8510 | −0.908932 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.7486 | 1.42957 | ||||||||
\(173\) | −3.50877 | −0.266767 | −0.133383 | − | 0.991065i | \(-0.542584\pi\) | ||||
−0.133383 | + | 0.991065i | \(0.542584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.22518 | 0.243801 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.9152 | −1.64261 | ||||||||
\(179\) | −2.22735 | −0.166480 | −0.0832399 | − | 0.996530i | \(-0.526527\pi\) | ||||
−0.0832399 | + | 0.996530i | \(0.526527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.11432 | 0.0828265 | 0.0414132 | − | 0.999142i | \(-0.486814\pi\) | ||||
0.0414132 | + | 0.999142i | \(0.486814\pi\) | |||||||
\(182\) | 11.9658 | 0.886963 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.786532 | −0.0579839 | ||||||||
\(185\) | 11.2269 | 0.825417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.52408 | 0.475818 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.450898 | 0.0327116 | ||||||||
\(191\) | −10.2314 | −0.740320 | −0.370160 | − | 0.928968i | \(-0.620697\pi\) | ||||
−0.370160 | + | 0.928968i | \(0.620697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9336 | 1.29089 | 0.645443 | − | 0.763808i | \(-0.276673\pi\) | ||||
0.645443 | + | 0.763808i | \(0.276673\pi\) | |||||||
\(194\) | 25.3213 | 1.81797 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.33525 | 0.166803 | ||||||||
\(197\) | 4.30284 | 0.306564 | 0.153282 | − | 0.988182i | \(-0.451016\pi\) | ||||
0.153282 | + | 0.988182i | \(0.451016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0560 | 1.56351 | 0.781753 | − | 0.623588i | \(-0.214326\pi\) | ||||
0.781753 | + | 0.623588i | \(0.214326\pi\) | |||||||
\(200\) | −2.25125 | −0.159188 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.16875 | 0.222952 | ||||||||
\(203\) | −9.83547 | −0.690315 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00449 | −0.419372 | ||||||||
\(206\) | 32.2031 | 2.24370 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.4885 | 1.28195 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8525 | 1.02249 | 0.511244 | − | 0.859435i | \(-0.329185\pi\) | ||||
0.511244 | + | 0.859435i | \(0.329185\pi\) | |||||||
\(212\) | 24.4927 | 1.68216 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.1784 | −1.17429 | ||||||||
\(215\) | −10.6958 | −0.729450 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.09480 | −0.617395 | ||||||||
\(218\) | −0.637011 | −0.0431438 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.5531 | −1.65162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.59782 | 0.374857 | 0.187429 | − | 0.982278i | \(-0.439985\pi\) | ||||
0.187429 | + | 0.982278i | \(0.439985\pi\) | |||||||
\(224\) | 8.09449 | 0.540836 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.1341 | −1.40582 | ||||||||
\(227\) | −7.52880 | −0.499704 | −0.249852 | − | 0.968284i | \(-0.580382\pi\) | ||||
−0.249852 | + | 0.968284i | \(0.580382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.2330 | −1.79961 | −0.899805 | − | 0.436292i | \(-0.856292\pi\) | ||||
−0.899805 | + | 0.436292i | \(0.856292\pi\) | |||||||
\(230\) | 3.12558 | 0.206094 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.86539 | 0.450735 | ||||||||
\(233\) | −5.48986 | −0.359653 | −0.179826 | − | 0.983698i | \(-0.557554\pi\) | ||||
−0.179826 | + | 0.983698i | \(0.557554\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.72189 | −0.242790 | ||||||||
\(236\) | 31.7885 | 2.06926 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.89567 | −0.576621 | ||||||||
\(239\) | −24.8413 | −1.60685 | −0.803426 | − | 0.595405i | \(-0.796992\pi\) | ||||
−0.803426 | + | 0.595405i | \(0.796992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.3238 | −1.11592 | −0.557961 | − | 0.829867i | \(-0.688416\pi\) | ||||
−0.557961 | + | 0.829867i | \(0.688416\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −18.8404 | −1.20613 | ||||||||
\(245\) | −1.33222 | −0.0851127 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.934176 | 0.0594402 | ||||||||
\(248\) | 6.34839 | 0.403123 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22.8155 | 1.44298 | ||||||||
\(251\) | 24.6655 | 1.55687 | 0.778436 | − | 0.627724i | \(-0.216013\pi\) | ||||
0.778436 | + | 0.627724i | \(0.216013\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7.92819 | −0.497459 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.37538 | 0.585961 | ||||||||
\(257\) | −3.87897 | −0.241964 | −0.120982 | − | 0.992655i | \(-0.538604\pi\) | ||||
−0.120982 | + | 0.992655i | \(0.538604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.42718 | 0.523639 | ||||||||
\(260\) | 17.8790 | 1.10881 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −30.5265 | −1.88593 | ||||||||
\(263\) | −5.19075 | −0.320075 | −0.160038 | − | 0.987111i | \(-0.551162\pi\) | ||||
−0.160038 | + | 0.987111i | \(0.551162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9727 | −0.858336 | ||||||||
\(266\) | 0.338455 | 0.0207520 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.2585 | 1.29857 | ||||||||
\(269\) | 16.8397 | 1.02673 | 0.513366 | − | 0.858170i | \(-0.328398\pi\) | ||||
0.513366 | + | 0.858170i | \(0.328398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0214 | 0.851739 | 0.425870 | − | 0.904785i | \(-0.359968\pi\) | ||||
0.425870 | + | 0.904785i | \(0.359968\pi\) | |||||||
\(272\) | −13.7448 | −0.833402 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −35.0434 | −2.11705 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.945328 | −0.0567992 | −0.0283996 | − | 0.999597i | \(-0.509041\pi\) | ||||
−0.0283996 | + | 0.999597i | \(0.509041\pi\) | |||||||
\(278\) | 16.2295 | 0.973380 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.929924 | 0.0555736 | ||||||||
\(281\) | 4.03539 | 0.240731 | 0.120366 | − | 0.992730i | \(-0.461593\pi\) | ||||
0.120366 | + | 0.992730i | \(0.461593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.80601 | −0.285688 | −0.142844 | − | 0.989745i | \(-0.545625\pi\) | ||||
−0.142844 | + | 0.989745i | \(0.545625\pi\) | |||||||
\(284\) | −2.37971 | −0.141210 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.50712 | −0.266047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.25340 | 0.0737292 | ||||||||
\(290\) | −27.2822 | −1.60207 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.8605 | 1.04521 | ||||||||
\(293\) | −1.04668 | −0.0611474 | −0.0305737 | − | 0.999533i | \(-0.509733\pi\) | ||||
−0.0305737 | + | 0.999533i | \(0.509733\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.1349 | −1.05585 | ||||||||
\(296\) | −5.88237 | −0.341906 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.2380 | 1.17236 | ||||||||
\(299\) | 6.47561 | 0.374494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.02855 | −0.462758 | ||||||||
\(302\) | −21.0327 | −1.21029 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.522952 | 0.0299933 | ||||||||
\(305\) | 10.7482 | 0.615440 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.1929 | 1.49491 | 0.747455 | − | 0.664313i | \(-0.231276\pi\) | ||||
0.747455 | + | 0.664313i | \(0.231276\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25.2277 | −1.43284 | ||||||||
\(311\) | 22.0318 | 1.24931 | 0.624655 | − | 0.780901i | \(-0.285240\pi\) | ||||
0.624655 | + | 0.780901i | \(0.285240\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.4119 | 1.71898 | 0.859491 | − | 0.511151i | \(-0.170781\pi\) | ||||
0.859491 | + | 0.511151i | \(0.170781\pi\) | |||||||
\(314\) | −10.3047 | −0.581531 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0127801 | 0.000718938 0 | ||||||||
\(317\) | 19.0776 | 1.07151 | 0.535753 | − | 0.844374i | \(-0.320028\pi\) | ||||
0.535753 | + | 0.844374i | \(0.320028\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.8811 | 0.775978 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.34613 | 0.130745 | ||||||||
\(323\) | −0.694490 | −0.0386425 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.5348 | 1.02813 | ||||||||
\(326\) | 14.0189 | 0.776434 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.14608 | 0.173713 | ||||||||
\(329\) | −2.79374 | −0.154024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.61239 | 0.198555 | 0.0992774 | − | 0.995060i | \(-0.468347\pi\) | ||||
0.0992774 | + | 0.995060i | \(0.468347\pi\) | |||||||
\(332\) | 6.61418 | 0.363000 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.1235 | 1.59357 | ||||||||
\(335\) | −12.1277 | −0.662605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.67839 | 0.145901 | 0.0729507 | − | 0.997336i | \(-0.476758\pi\) | ||||
0.0729507 | + | 0.997336i | \(0.476758\pi\) | |||||||
\(338\) | 41.6987 | 2.26811 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.2917 | −0.720846 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.60412 | 0.302154 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.30570 | −0.392757 | ||||||||
\(347\) | −18.4546 | −0.990696 | −0.495348 | − | 0.868695i | \(-0.664959\pi\) | ||||
−0.495348 | + | 0.868695i | \(0.664959\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.3015 | −1.08672 | −0.543358 | − | 0.839501i | \(-0.682847\pi\) | ||||
−0.543358 | + | 0.839501i | \(0.682847\pi\) | |||||||
\(350\) | 6.71523 | 0.358944 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7771 | 0.680054 | 0.340027 | − | 0.940416i | \(-0.389564\pi\) | ||||
0.340027 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35759 | 0.0720533 | ||||||||
\(356\) | −24.5794 | −1.30270 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.63762 | −0.245106 | ||||||||
\(359\) | 10.2976 | 0.543486 | 0.271743 | − | 0.962370i | \(-0.412400\pi\) | ||||
0.271743 | + | 0.962370i | \(0.412400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9736 | −0.998609 | ||||||||
\(362\) | 2.32015 | 0.121944 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.4204 | 0.703423 | ||||||||
\(365\) | −10.1892 | −0.533325 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.65025 | 0.138342 | 0.0691710 | − | 0.997605i | \(-0.477965\pi\) | ||||
0.0691710 | + | 0.997605i | \(0.477965\pi\) | |||||||
\(368\) | 3.62504 | 0.188968 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 23.3758 | 1.21525 | ||||||||
\(371\) | −10.4883 | −0.544523 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.9030 | −1.70365 | −0.851827 | − | 0.523824i | \(-0.824505\pi\) | ||||
−0.851827 | + | 0.523824i | \(0.824505\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.95010 | 0.100569 | ||||||||
\(377\) | −56.5236 | −2.91111 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.2324 | −1.14200 | −0.571000 | − | 0.820950i | \(-0.693444\pi\) | ||||
−0.571000 | + | 0.820950i | \(0.693444\pi\) | |||||||
\(380\) | 0.505713 | 0.0259425 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.3031 | −1.08996 | ||||||||
\(383\) | −25.1289 | −1.28402 | −0.642012 | − | 0.766694i | \(-0.721900\pi\) | ||||
−0.642012 | + | 0.766694i | \(0.721900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37.3399 | 1.90055 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.3996 | 1.44177 | ||||||||
\(389\) | 23.0628 | 1.16933 | 0.584665 | − | 0.811275i | \(-0.301226\pi\) | ||||
0.584665 | + | 0.811275i | \(0.301226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.81413 | −0.243461 | ||||||||
\(392\) | 0.698024 | 0.0352555 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.95905 | 0.451350 | ||||||||
\(395\) | −0.00729087 | −0.000366844 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.78504 | −0.189966 | −0.0949828 | − | 0.995479i | \(-0.530280\pi\) | ||||
−0.0949828 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(398\) | 45.9233 | 2.30193 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.3758 | 0.518789 | ||||||||
\(401\) | 39.0596 | 1.95054 | 0.975271 | − | 0.221011i | \(-0.0709356\pi\) | ||||
0.975271 | + | 0.221011i | \(0.0709356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −52.2670 | −2.60361 | ||||||||
\(404\) | 3.55396 | 0.176816 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.4787 | −1.01634 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4034 | 1.45390 | 0.726952 | − | 0.686689i | \(-0.240936\pi\) | ||||
0.726952 | + | 0.686689i | \(0.240936\pi\) | |||||||
\(410\) | −12.5021 | −0.617435 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 36.1180 | 1.77941 | ||||||||
\(413\) | −13.6125 | −0.669828 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.77329 | −0.185224 | ||||||||
\(416\) | 46.5183 | 2.28075 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.5510 | −0.710863 | −0.355431 | − | 0.934702i | \(-0.615666\pi\) | ||||
−0.355431 | + | 0.934702i | \(0.615666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.7574 | 0.865443 | 0.432722 | − | 0.901528i | \(-0.357553\pi\) | ||||
0.432722 | + | 0.901528i | \(0.357553\pi\) | |||||||
\(422\) | 30.9248 | 1.50539 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.32105 | 0.355542 | ||||||||
\(425\) | −13.7793 | −0.668392 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.06786 | 0.390431 | ||||||||
\(428\) | −19.2668 | −0.931295 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −22.2701 | −1.07396 | ||||||||
\(431\) | −17.8382 | −0.859234 | −0.429617 | − | 0.903011i | \(-0.641351\pi\) | ||||
−0.429617 | + | 0.903011i | \(0.641351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4405 | 0.597851 | 0.298925 | − | 0.954276i | \(-0.403372\pi\) | ||||
0.298925 | + | 0.954276i | \(0.403372\pi\) | |||||||
\(434\) | −18.9365 | −0.908982 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.714451 | −0.0342160 | ||||||||
\(437\) | 0.183164 | 0.00876193 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.3740 | −0.781489 | −0.390744 | − | 0.920499i | \(-0.627782\pi\) | ||||
−0.390744 | + | 0.920499i | \(0.627782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −51.1226 | −2.43165 | ||||||||
\(443\) | −2.22725 | −0.105820 | −0.0529100 | − | 0.998599i | \(-0.516850\pi\) | ||||
−0.0529100 | + | 0.998599i | \(0.516850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0222 | 0.664715 | ||||||||
\(446\) | 11.6554 | 0.551897 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.4195 | 0.492276 | ||||||||
\(449\) | −31.9494 | −1.50779 | −0.753893 | − | 0.656997i | \(-0.771826\pi\) | ||||
−0.753893 | + | 0.656997i | \(0.771826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −23.7034 | −1.11491 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.6759 | −0.735707 | ||||||||
\(455\) | −7.65617 | −0.358927 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1342 | 1.03539 | 0.517697 | − | 0.855564i | \(-0.326790\pi\) | ||||
0.517697 | + | 0.855564i | \(0.326790\pi\) | |||||||
\(458\) | −56.7026 | −2.64954 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.50555 | 0.163447 | ||||||||
\(461\) | −14.9408 | −0.695865 | −0.347932 | − | 0.937520i | \(-0.613116\pi\) | ||||
−0.347932 | + | 0.937520i | \(0.613116\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.02953 | 0.233742 | 0.116871 | − | 0.993147i | \(-0.462714\pi\) | ||||
0.116871 | + | 0.993147i | \(0.462714\pi\) | |||||||
\(464\) | −31.6419 | −1.46894 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.4306 | −0.529512 | ||||||||
\(467\) | 32.1377 | 1.48716 | 0.743579 | − | 0.668649i | \(-0.233127\pi\) | ||||
0.743579 | + | 0.668649i | \(0.233127\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.10333 | −0.420353 | ||||||||
\(470\) | −7.74945 | −0.357455 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.50185 | 0.437358 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.524262 | 0.0240548 | ||||||||
\(476\) | −9.97710 | −0.457300 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −51.7228 | −2.36574 | ||||||||
\(479\) | −13.1491 | −0.600798 | −0.300399 | − | 0.953814i | \(-0.597120\pi\) | ||||
−0.300399 | + | 0.953814i | \(0.597120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.4302 | 2.20823 | ||||||||
\(482\) | −36.0703 | −1.64296 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.2016 | −0.735675 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.05225 | 0.0476821 | 0.0238411 | − | 0.999716i | \(-0.492410\pi\) | ||||
0.0238411 | + | 0.999716i | \(0.492410\pi\) | |||||||
\(488\) | −5.63156 | −0.254929 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.77386 | −0.125310 | ||||||||
\(491\) | 27.3208 | 1.23297 | 0.616485 | − | 0.787367i | \(-0.288556\pi\) | ||||
0.616485 | + | 0.787367i | \(0.288556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.0211 | 1.89253 | ||||||||
\(494\) | 1.94507 | 0.0875129 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.2591 | −1.31377 | ||||||||
\(497\) | 1.01904 | 0.0457102 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.4585 | −1.05015 | −0.525073 | − | 0.851057i | \(-0.675962\pi\) | ||||
−0.525073 | + | 0.851057i | \(0.675962\pi\) | |||||||
\(500\) | 25.5891 | 1.14438 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 51.3567 | 2.29216 | ||||||||
\(503\) | −11.4795 | −0.511846 | −0.255923 | − | 0.966697i | \(-0.582379\pi\) | ||||
−0.255923 | + | 0.966697i | \(0.582379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.02749 | −0.0902219 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.89201 | −0.394519 | ||||||||
\(509\) | −1.40656 | −0.0623446 | −0.0311723 | − | 0.999514i | \(-0.509924\pi\) | ||||
−0.0311723 | + | 0.999514i | \(0.509924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.64824 | −0.338338 | ||||||||
\(512\) | 30.5322 | 1.34934 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.07651 | −0.356239 | ||||||||
\(515\) | −20.6048 | −0.907956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 17.5464 | 0.770946 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.34419 | 0.234358 | ||||||||
\(521\) | 18.5352 | 0.812041 | 0.406020 | − | 0.913864i | \(-0.366916\pi\) | ||||
0.406020 | + | 0.913864i | \(0.366916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.4670 | 1.59459 | 0.797295 | − | 0.603589i | \(-0.206263\pi\) | ||||
0.797295 | + | 0.603589i | \(0.206263\pi\) | |||||||
\(524\) | −34.2376 | −1.49568 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.8078 | −0.471242 | ||||||||
\(527\) | 38.8566 | 1.69262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7303 | −0.944797 | ||||||||
\(530\) | −29.0929 | −1.26372 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.379601 | 0.0164578 | ||||||||
\(533\) | −25.9020 | −1.12194 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9914 | 0.475200 | ||||||||
\(536\) | 6.35434 | 0.274466 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 35.0623 | 1.51164 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.1641 | −0.952910 | −0.476455 | − | 0.879199i | \(-0.658079\pi\) | ||||
−0.476455 | + | 0.879199i | \(0.658079\pi\) | |||||||
\(542\) | 29.1943 | 1.25400 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.5829 | −1.48273 | ||||||||
\(545\) | 0.407584 | 0.0174590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.5974 | 1.73582 | 0.867909 | − | 0.496723i | \(-0.165463\pi\) | ||||
0.867909 | + | 0.496723i | \(0.165463\pi\) | |||||||
\(548\) | −39.3036 | −1.67897 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.59878 | −0.0681105 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.00547271 | −0.000232723 0 | ||||||||
\(554\) | −1.96829 | −0.0836246 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.2025 | 0.771957 | ||||||||
\(557\) | 39.9780 | 1.69392 | 0.846961 | − | 0.531655i | \(-0.178430\pi\) | ||||
0.846961 | + | 0.531655i | \(0.178430\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.1394 | −1.95149 | ||||||||
\(560\) | −4.28592 | −0.181113 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.40219 | 0.354425 | ||||||||
\(563\) | −28.8313 | −1.21509 | −0.607546 | − | 0.794284i | \(-0.707846\pi\) | ||||
−0.607546 | + | 0.794284i | \(0.707846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.5224 | 0.568893 | ||||||||
\(566\) | −10.0067 | −0.420613 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.711314 | −0.0298461 | ||||||||
\(569\) | −18.0183 | −0.755365 | −0.377683 | − | 0.925935i | \(-0.623279\pi\) | ||||
−0.377683 | + | 0.925935i | \(0.623279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.2208 | −0.762515 | −0.381258 | − | 0.924469i | \(-0.624509\pi\) | ||||
−0.381258 | + | 0.924469i | \(0.624509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.38438 | −0.391697 | ||||||||
\(575\) | 3.63413 | 0.151554 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5299 | 0.438364 | 0.219182 | − | 0.975684i | \(-0.429661\pi\) | ||||
0.219182 | + | 0.975684i | \(0.429661\pi\) | |||||||
\(578\) | 2.60973 | 0.108550 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −30.5988 | −1.27055 | ||||||||
\(581\) | −2.83233 | −0.117505 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 5.33865 | 0.220915 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.17931 | −0.0900264 | ||||||||
\(587\) | 2.45140 | 0.101180 | 0.0505900 | − | 0.998720i | \(-0.483890\pi\) | ||||
0.0505900 | + | 0.998720i | \(0.483890\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47839 | −0.0609158 | ||||||||
\(590\) | −37.7591 | −1.55452 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.1112 | 1.11426 | ||||||||
\(593\) | 27.7941 | 1.14137 | 0.570684 | − | 0.821170i | \(-0.306678\pi\) | ||||
0.570684 | + | 0.821170i | \(0.306678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.69179 | 0.233341 | ||||||||
\(596\) | 22.6983 | 0.929760 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.4830 | 0.551362 | ||||||||
\(599\) | −0.747037 | −0.0305231 | −0.0152616 | − | 0.999884i | \(-0.504858\pi\) | ||||
−0.0152616 | + | 0.999884i | \(0.504858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0794 | 0.615103 | 0.307551 | − | 0.951531i | \(-0.400490\pi\) | ||||
0.307551 | + | 0.951531i | \(0.400490\pi\) | |||||||
\(602\) | −16.7165 | −0.681312 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −23.5896 | −0.959846 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.16609 | 0.169096 | 0.0845481 | − | 0.996419i | \(-0.473055\pi\) | ||||
0.0845481 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(608\) | 1.31578 | 0.0533620 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.3791 | 0.906102 | ||||||||
\(611\) | −16.0554 | −0.649532 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.7033 | −1.48243 | −0.741216 | − | 0.671266i | \(-0.765751\pi\) | ||||
−0.741216 | + | 0.671266i | \(0.765751\pi\) | |||||||
\(614\) | 54.5370 | 2.20093 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8780 | 0.921035 | 0.460518 | − | 0.887651i | \(-0.347664\pi\) | ||||
0.460518 | + | 0.887651i | \(0.347664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.59442 | −0.104279 | −0.0521393 | − | 0.998640i | \(-0.516604\pi\) | ||||
−0.0521393 | + | 0.998640i | \(0.516604\pi\) | |||||||
\(620\) | −28.2946 | −1.13634 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 45.8730 | 1.83934 | ||||||||
\(623\) | 10.5254 | 0.421691 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.52768 | 0.0611071 | ||||||||
\(626\) | 63.3214 | 2.53083 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.5575 | −0.461194 | ||||||||
\(629\) | −36.0043 | −1.43558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.7938 | 1.18607 | 0.593036 | − | 0.805176i | \(-0.297929\pi\) | ||||
0.593036 | + | 0.805176i | \(0.297929\pi\) | |||||||
\(632\) | 0.00382008 | 0.000151955 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39.7220 | 1.57756 | ||||||||
\(635\) | 5.07276 | 0.201306 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.74691 | −0.227701 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.33488 | 0.289937 | ||||||||
\(641\) | −32.9695 | −1.30222 | −0.651108 | − | 0.758985i | \(-0.725695\pi\) | ||||
−0.651108 | + | 0.758985i | \(0.725695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9257 | 0.825229 | 0.412614 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412614 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(644\) | 2.63135 | 0.103690 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.44602 | −0.0568927 | ||||||||
\(647\) | 12.9654 | 0.509722 | 0.254861 | − | 0.966978i | \(-0.417970\pi\) | ||||
0.254861 | + | 0.966978i | \(0.417970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 38.5918 | 1.51370 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.7231 | 0.615765 | ||||||||
\(653\) | −4.59805 | −0.179936 | −0.0899678 | − | 0.995945i | \(-0.528676\pi\) | ||||
−0.0899678 | + | 0.995945i | \(0.528676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5320 | 0.763180 | ||||||||
\(656\) | −14.4999 | −0.566127 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.81693 | −0.226767 | ||||||||
\(659\) | −27.8639 | −1.08542 | −0.542712 | − | 0.839919i | \(-0.682602\pi\) | ||||
−0.542712 | + | 0.839919i | \(0.682602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.2151 | 1.40861 | 0.704303 | − | 0.709900i | \(-0.251260\pi\) | ||||
0.704303 | + | 0.709900i | \(0.251260\pi\) | |||||||
\(662\) | 7.52144 | 0.292329 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.97703 | 0.0767237 | ||||||||
\(665\) | −0.216557 | −0.00839771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0826 | −0.429120 | ||||||||
\(668\) | 32.6640 | 1.26381 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.2513 | −0.975544 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.97277 | 0.268781 | 0.134390 | − | 0.990928i | \(-0.457092\pi\) | ||||
0.134390 | + | 0.990928i | \(0.457092\pi\) | |||||||
\(674\) | 5.57675 | 0.214808 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 46.7679 | 1.79876 | ||||||||
\(677\) | −21.9071 | −0.841958 | −0.420979 | − | 0.907070i | \(-0.638313\pi\) | ||||
−0.420979 | + | 0.907070i | \(0.638313\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.1613 | −0.466708 | ||||||||
\(680\) | −3.97301 | −0.152358 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.9585 | 1.87334 | 0.936672 | − | 0.350208i | \(-0.113889\pi\) | ||||
0.936672 | + | 0.350208i | \(0.113889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.4221 | 0.856706 | ||||||||
\(686\) | −2.08213 | −0.0794959 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.8288 | −0.984714 | ||||||||
\(689\) | −60.2751 | −2.29630 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8751 | −1.82126 | −0.910628 | − | 0.413227i | \(-0.864402\pi\) | ||||
−0.910628 | + | 0.413227i | \(0.864402\pi\) | |||||||
\(692\) | −8.19384 | −0.311483 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.4248 | −1.45859 | ||||||||
\(695\) | −10.3842 | −0.393897 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.2562 | 0.729381 | ||||||||
\(698\) | −42.2703 | −1.59995 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.53159 | 0.284667 | ||||||||
\(701\) | 6.95807 | 0.262803 | 0.131401 | − | 0.991329i | \(-0.458052\pi\) | ||||
0.131401 | + | 0.991329i | \(0.458052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.36986 | 0.0516653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.6034 | 1.00123 | ||||||||
\(707\) | −1.52188 | −0.0572362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.3838 | −0.765531 | −0.382766 | − | 0.923845i | \(-0.625028\pi\) | ||||
−0.382766 | + | 0.923845i | \(0.625028\pi\) | |||||||
\(710\) | 2.82667 | 0.106083 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.34698 | −0.275340 | ||||||||
\(713\) | −10.2480 | −0.383791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.20141 | −0.194386 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.4409 | 0.800166 | ||||||||
\(719\) | 36.9536 | 1.37814 | 0.689068 | − | 0.724697i | \(-0.258020\pi\) | ||||
0.689068 | + | 0.724697i | \(0.258020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4665 | −0.576002 | ||||||||
\(722\) | −39.5054 | −1.47024 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.60220 | 0.0967101 | ||||||||
\(725\) | −31.7212 | −1.17809 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.8565 | 1.51528 | 0.757641 | − | 0.652671i | \(-0.226352\pi\) | ||||
0.757641 | + | 0.652671i | \(0.226352\pi\) | |||||||
\(728\) | 4.01148 | 0.148675 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.2151 | −0.785207 | ||||||||
\(731\) | 34.3012 | 1.26868 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.9728 | 0.663839 | 0.331920 | − | 0.943308i | \(-0.392304\pi\) | ||||
0.331920 | + | 0.943308i | \(0.392304\pi\) | |||||||
\(734\) | 5.51815 | 0.203679 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.12086 | 0.336199 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.34892 | 0.0864064 | 0.0432032 | − | 0.999066i | \(-0.486244\pi\) | ||||
0.0432032 | + | 0.999066i | \(0.486244\pi\) | |||||||
\(740\) | 26.2175 | 0.963776 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −21.8379 | −0.801693 | ||||||||
\(743\) | −38.2722 | −1.40407 | −0.702036 | − | 0.712141i | \(-0.747726\pi\) | ||||
−0.702036 | + | 0.712141i | \(0.747726\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.9491 | −0.474417 | ||||||||
\(746\) | −68.5082 | −2.50826 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.25043 | 0.301464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.89080 | −0.105487 | −0.0527434 | − | 0.998608i | \(-0.516797\pi\) | ||||
−0.0527434 | + | 0.998608i | \(0.516797\pi\) | |||||||
\(752\) | −8.98781 | −0.327752 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −117.689 | −4.28599 | ||||||||
\(755\) | 13.4575 | 0.489769 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1721 | 0.878551 | 0.439275 | − | 0.898353i | \(-0.355235\pi\) | ||||
0.439275 | + | 0.898353i | \(0.355235\pi\) | |||||||
\(758\) | −46.2906 | −1.68135 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.151162 | 0.00548321 | ||||||||
\(761\) | −24.7044 | −0.895533 | −0.447766 | − | 0.894151i | \(-0.647780\pi\) | ||||
−0.447766 | + | 0.894151i | \(0.647780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.305943 | 0.0110759 | ||||||||
\(764\) | −23.8929 | −0.864415 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −52.3214 | −1.89045 | ||||||||
\(767\) | −78.2298 | −2.82472 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.8939 | 0.464967 | 0.232483 | − | 0.972600i | \(-0.425315\pi\) | ||||
0.232483 | + | 0.972600i | \(0.425315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 41.8793 | 1.50727 | ||||||||
\(773\) | 32.4616 | 1.16756 | 0.583780 | − | 0.811912i | \(-0.301573\pi\) | ||||
0.583780 | + | 0.811912i | \(0.301573\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.3324 | −1.05365 | ||||||||
\(776\) | 8.48887 | 0.304733 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.0196 | 1.72159 | ||||||||
\(779\) | −0.732645 | −0.0262497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −10.0236 | −0.358444 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.21712 | −0.114897 | ||||||||
\(785\) | 6.59338 | 0.235328 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.1909 | −1.00490 | −0.502448 | − | 0.864607i | \(-0.667567\pi\) | ||||
−0.502448 | + | 0.864607i | \(0.667567\pi\) | |||||||
\(788\) | 10.0482 | 0.357952 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.0151805 | −0.000540098 0 | ||||||||
\(791\) | 10.1503 | 0.360902 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.3652 | 1.64648 | ||||||||
\(794\) | −7.88093 | −0.279684 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 51.5061 | 1.82559 | ||||||||
\(797\) | −42.5723 | −1.50799 | −0.753995 | − | 0.656881i | \(-0.771876\pi\) | ||||
−0.753995 | + | 0.656881i | \(0.771876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.9360 | 0.422265 | ||||||||
\(800\) | 26.1062 | 0.922993 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 81.3270 | 2.87175 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.50115 | −0.0529085 | ||||||||
\(806\) | −108.826 | −3.83325 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.06231 | 0.0373719 | ||||||||
\(809\) | −14.1894 | −0.498873 | −0.249437 | − | 0.968391i | \(-0.580245\pi\) | ||||
−0.249437 | + | 0.968391i | \(0.580245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.58292 | −0.0906987 | −0.0453494 | − | 0.998971i | \(-0.514440\pi\) | ||||
−0.0453494 | + | 0.998971i | \(0.514440\pi\) | |||||||
\(812\) | −22.9682 | −0.806027 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.96982 | −0.314199 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.30506 | −0.0456584 | ||||||||
\(818\) | 61.2215 | 2.14056 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.0220 | −0.489668 | ||||||||
\(821\) | −52.5523 | −1.83409 | −0.917043 | − | 0.398787i | \(-0.869431\pi\) | ||||
−0.917043 | + | 0.398787i | \(0.869431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6509 | 0.510699 | 0.255349 | − | 0.966849i | \(-0.417809\pi\) | ||||
0.255349 | + | 0.966849i | \(0.417809\pi\) | |||||||
\(824\) | 10.7960 | 0.376095 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.3429 | −0.986177 | ||||||||
\(827\) | 15.1928 | 0.528304 | 0.264152 | − | 0.964481i | \(-0.414908\pi\) | ||||
0.264152 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.6162 | −1.44539 | −0.722695 | − | 0.691167i | \(-0.757097\pi\) | ||||
−0.722695 | + | 0.691167i | \(0.757097\pi\) | |||||||
\(830\) | −7.85647 | −0.272702 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 59.8800 | 2.07596 | ||||||||
\(833\) | 4.27240 | 0.148030 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.6343 | −0.644867 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.2970 | −1.04659 | ||||||||
\(839\) | −21.8835 | −0.755503 | −0.377752 | − | 0.925907i | \(-0.623303\pi\) | ||||
−0.377752 | + | 0.925907i | \(0.623303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 67.7365 | 2.33574 | ||||||||
\(842\) | 36.9732 | 1.27418 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 34.6842 | 1.19388 | ||||||||
\(845\) | −26.6804 | −0.917834 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −33.7420 | −1.15870 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28.6901 | −0.984063 | ||||||||
\(851\) | 9.49572 | 0.325509 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2054 | 0.760299 | 0.380149 | − | 0.924925i | \(-0.375873\pi\) | ||||
0.380149 | + | 0.924925i | \(0.375873\pi\) | |||||||
\(854\) | 16.7983 | 0.574826 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.75899 | −0.196838 | ||||||||
\(857\) | 24.6876 | 0.843311 | 0.421656 | − | 0.906756i | \(-0.361449\pi\) | ||||
0.421656 | + | 0.906756i | \(0.361449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3940 | 0.354639 | 0.177320 | − | 0.984153i | \(-0.443257\pi\) | ||||
0.177320 | + | 0.984153i | \(0.443257\pi\) | |||||||
\(860\) | −24.9774 | −0.851722 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.1413 | −1.26504 | ||||||||
\(863\) | 45.9179 | 1.56306 | 0.781532 | − | 0.623865i | \(-0.214439\pi\) | ||||
0.781532 | + | 0.623865i | \(0.214439\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.67447 | 0.158937 | ||||||||
\(866\) | 25.9026 | 0.880207 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −21.2386 | −0.720885 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.3160 | −1.77266 | ||||||||
\(872\) | −0.213555 | −0.00723189 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.381371 | 0.0129001 | ||||||||
\(875\) | −10.9578 | −0.370441 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.8872 | −1.17806 | −0.589029 | − | 0.808112i | \(-0.700490\pi\) | ||||
−0.589029 | + | 0.808112i | \(0.700490\pi\) | |||||||
\(878\) | −34.0927 | −1.15057 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.85305 | 0.298267 | 0.149133 | − | 0.988817i | \(-0.452352\pi\) | ||||
0.149133 | + | 0.988817i | \(0.452352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3511 | 0.583910 | 0.291955 | − | 0.956432i | \(-0.405694\pi\) | ||||
0.291955 | + | 0.956432i | \(0.405694\pi\) | |||||||
\(884\) | −57.3375 | −1.92847 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.63742 | −0.155797 | ||||||||
\(887\) | −38.0505 | −1.27761 | −0.638806 | − | 0.769368i | \(-0.720571\pi\) | ||||
−0.638806 | + | 0.769368i | \(0.720571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.80774 | 0.127707 | ||||||||
\(890\) | 29.1959 | 0.978650 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.0723 | 0.437692 | ||||||||
\(893\) | −0.454131 | −0.0151969 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.96733 | 0.0991868 | ||||||||
\(896\) | 5.50574 | 0.183934 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −66.5227 | −2.21989 | ||||||||
\(899\) | 89.4517 | 2.98338 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.8100 | 1.49284 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.08513 | −0.235648 | ||||||||
\(905\) | −1.48452 | −0.0493471 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.1082 | −0.468455 | −0.234227 | − | 0.972182i | \(-0.575256\pi\) | ||||
−0.234227 | + | 0.972182i | \(0.575256\pi\) | |||||||
\(908\) | −17.5816 | −0.583466 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.9411 | −0.528443 | ||||||||
\(911\) | −29.1703 | −0.966457 | −0.483228 | − | 0.875494i | \(-0.660536\pi\) | ||||
−0.483228 | + | 0.875494i | \(0.660536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 46.0861 | 1.52439 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −63.5959 | −2.10127 | ||||||||
\(917\) | 14.6612 | 0.484156 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.84247 | −0.126751 | −0.0633757 | − | 0.997990i | \(-0.520187\pi\) | ||||
−0.0633757 | + | 0.997990i | \(0.520187\pi\) | |||||||
\(920\) | 1.04784 | 0.0345461 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −31.1087 | −1.02451 | ||||||||
\(923\) | 5.85633 | 0.192763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.1792 | 0.893645 | ||||||||
\(926\) | 10.4721 | 0.344135 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −79.6131 | −2.61343 | ||||||||
\(929\) | −11.2254 | −0.368295 | −0.184147 | − | 0.982899i | \(-0.558952\pi\) | ||||
−0.184147 | + | 0.982899i | \(0.558952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.162553 | −0.00532745 | ||||||||
\(932\) | −12.8202 | −0.419939 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 66.9148 | 2.18952 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9651 | −0.358213 | −0.179106 | − | 0.983830i | \(-0.557321\pi\) | ||||
−0.179106 | + | 0.983830i | \(0.557321\pi\) | |||||||
\(938\) | −18.9543 | −0.618879 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.69154 | −0.283487 | ||||||||
\(941\) | −60.7290 | −1.97971 | −0.989855 | − | 0.142083i | \(-0.954620\pi\) | ||||
−0.989855 | + | 0.142083i | \(0.954620\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.07861 | −0.165382 | ||||||||
\(944\) | −43.7930 | −1.42534 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.2278 | 1.46971 | 0.734854 | − | 0.678226i | \(-0.237251\pi\) | ||||
0.734854 | + | 0.678226i | \(0.237251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.9537 | −1.42680 | ||||||||
\(950\) | 1.09158 | 0.0354155 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.98224 | −0.0966548 | ||||||||
\(953\) | −1.48140 | −0.0479872 | −0.0239936 | − | 0.999712i | \(-0.507638\pi\) | ||||
−0.0239936 | + | 0.999712i | \(0.507638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.6306 | 0.441074 | ||||||||
\(956\) | −58.0106 | −1.87620 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.3781 | −0.884545 | ||||||||
\(959\) | 16.8306 | 0.543489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.7155 | 1.66824 | ||||||||
\(962\) | 100.838 | 3.25114 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40.4553 | −1.30298 | ||||||||
\(965\) | −23.8915 | −0.769095 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.8504 | 0.606187 | 0.303094 | − | 0.952961i | \(-0.401981\pi\) | ||||
0.303094 | + | 0.952961i | \(0.401981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −33.7337 | −1.08312 | ||||||||
\(971\) | −58.9217 | −1.89089 | −0.945444 | − | 0.325785i | \(-0.894371\pi\) | ||||
−0.945444 | + | 0.325785i | \(0.894371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.79467 | −0.249886 | ||||||||
\(974\) | 2.19092 | 0.0702017 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.9552 | 0.830807 | ||||||||
\(977\) | 43.0633 | 1.37772 | 0.688858 | − | 0.724896i | \(-0.258112\pi\) | ||||
0.688858 | + | 0.724896i | \(0.258112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.11107 | −0.0993795 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.8853 | 1.81528 | ||||||||
\(983\) | −13.2499 | −0.422605 | −0.211303 | − | 0.977421i | \(-0.567771\pi\) | ||||
−0.211303 | + | 0.977421i | \(0.567771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.73234 | −0.182648 | ||||||||
\(986\) | 87.4931 | 2.78635 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.18153 | 0.0694037 | ||||||||
\(989\) | −9.04656 | −0.287664 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.1260 | 0.448728 | 0.224364 | − | 0.974505i | \(-0.427970\pi\) | ||||
0.224364 | + | 0.974505i | \(0.427970\pi\) | |||||||
\(992\) | −73.6178 | −2.33737 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.12177 | 0.0672984 | ||||||||
\(995\) | −29.3835 | −0.931519 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.3911 | −0.424100 | −0.212050 | − | 0.977259i | \(-0.568014\pi\) | ||||
−0.212050 | + | 0.977259i | \(0.568014\pi\) | |||||||
\(998\) | −48.8435 | −1.54611 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7623.2.a.db.1.13 | 16 | ||
3.2 | odd | 2 | inner | 7623.2.a.db.1.4 | 16 | ||
11.7 | odd | 10 | 693.2.m.k.379.2 | yes | 32 | ||
11.8 | odd | 10 | 693.2.m.k.64.2 | ✓ | 32 | ||
11.10 | odd | 2 | 7623.2.a.dc.1.4 | 16 | |||
33.8 | even | 10 | 693.2.m.k.64.7 | yes | 32 | ||
33.29 | even | 10 | 693.2.m.k.379.7 | yes | 32 | ||
33.32 | even | 2 | 7623.2.a.dc.1.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.k.64.2 | ✓ | 32 | 11.8 | odd | 10 | ||
693.2.m.k.64.7 | yes | 32 | 33.8 | even | 10 | ||
693.2.m.k.379.2 | yes | 32 | 11.7 | odd | 10 | ||
693.2.m.k.379.7 | yes | 32 | 33.29 | even | 10 | ||
7623.2.a.db.1.4 | 16 | 3.2 | odd | 2 | inner | ||
7623.2.a.db.1.13 | 16 | 1.1 | even | 1 | trivial | ||
7623.2.a.dc.1.4 | 16 | 11.10 | odd | 2 | |||
7623.2.a.dc.1.13 | 16 | 33.32 | even | 2 |