Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 16x^{4} + 14x^{3} - 20x^{2} - 10x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.19009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.190092 | −0.134415 | −0.0672077 | − | 0.997739i | \(-0.521409\pi\) | ||||
−0.0672077 | + | 0.997739i | \(0.521409\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.96387 | −0.981933 | ||||||||
\(5\) | −2.28332 | −1.02113 | −0.510566 | − | 0.859838i | \(-0.670564\pi\) | ||||
−0.510566 | + | 0.859838i | \(0.670564\pi\) | |||||||
\(6\) | 0.190092 | 0.0776047 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.753499 | 0.266402 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.434041 | 0.137256 | ||||||||
\(11\) | 1.72995 | 0.521600 | 0.260800 | − | 0.965393i | \(-0.416014\pi\) | ||||
0.260800 | + | 0.965393i | \(0.416014\pi\) | |||||||
\(12\) | 1.96387 | 0.566919 | ||||||||
\(13\) | −1.61662 | −0.448370 | −0.224185 | − | 0.974547i | \(-0.571972\pi\) | ||||
−0.224185 | + | 0.974547i | \(0.571972\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.28332 | 0.589551 | ||||||||
\(16\) | 3.78450 | 0.946124 | ||||||||
\(17\) | 3.96707 | 0.962157 | 0.481079 | − | 0.876678i | \(-0.340245\pi\) | ||||
0.481079 | + | 0.876678i | \(0.340245\pi\) | |||||||
\(18\) | −0.190092 | −0.0448051 | ||||||||
\(19\) | −1.10774 | −0.254134 | −0.127067 | − | 0.991894i | \(-0.540556\pi\) | ||||
−0.127067 | + | 0.991894i | \(0.540556\pi\) | |||||||
\(20\) | 4.48414 | 1.00268 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.328850 | −0.0701111 | ||||||||
\(23\) | −2.20725 | −0.460243 | −0.230122 | − | 0.973162i | \(-0.573912\pi\) | ||||
−0.230122 | + | 0.973162i | \(0.573912\pi\) | |||||||
\(24\) | −0.753499 | −0.153807 | ||||||||
\(25\) | 0.213562 | 0.0427124 | ||||||||
\(26\) | 0.307306 | 0.0602678 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.83771 | 1.45543 | 0.727713 | − | 0.685882i | \(-0.240583\pi\) | ||||
0.727713 | + | 0.685882i | \(0.240583\pi\) | |||||||
\(30\) | −0.434041 | −0.0792447 | ||||||||
\(31\) | −3.24019 | −0.581955 | −0.290977 | − | 0.956730i | \(-0.593980\pi\) | ||||
−0.290977 | + | 0.956730i | \(0.593980\pi\) | |||||||
\(32\) | −2.22640 | −0.393576 | ||||||||
\(33\) | −1.72995 | −0.301146 | ||||||||
\(34\) | −0.754109 | −0.129329 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96387 | −0.327311 | ||||||||
\(37\) | 1.90046 | 0.312433 | 0.156217 | − | 0.987723i | \(-0.450070\pi\) | ||||
0.156217 | + | 0.987723i | \(0.450070\pi\) | |||||||
\(38\) | 0.210573 | 0.0341595 | ||||||||
\(39\) | 1.61662 | 0.258866 | ||||||||
\(40\) | −1.72048 | −0.272032 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.91253 | 0.444157 | 0.222078 | − | 0.975029i | \(-0.428716\pi\) | ||||
0.222078 | + | 0.975029i | \(0.428716\pi\) | |||||||
\(44\) | −3.39739 | −0.512176 | ||||||||
\(45\) | −2.28332 | −0.340378 | ||||||||
\(46\) | 0.419580 | 0.0618637 | ||||||||
\(47\) | −5.86193 | −0.855050 | −0.427525 | − | 0.904003i | \(-0.640614\pi\) | ||||
−0.427525 | + | 0.904003i | \(0.640614\pi\) | |||||||
\(48\) | −3.78450 | −0.546245 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0405965 | −0.00574121 | ||||||||
\(51\) | −3.96707 | −0.555502 | ||||||||
\(52\) | 3.17482 | 0.440269 | ||||||||
\(53\) | −2.97657 | −0.408864 | −0.204432 | − | 0.978881i | \(-0.565535\pi\) | ||||
−0.204432 | + | 0.978881i | \(0.565535\pi\) | |||||||
\(54\) | 0.190092 | 0.0258682 | ||||||||
\(55\) | −3.95004 | −0.532623 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.10774 | 0.146724 | ||||||||
\(58\) | −1.48989 | −0.195632 | ||||||||
\(59\) | −5.61410 | −0.730893 | −0.365447 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365447 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(60\) | −4.48414 | −0.578900 | ||||||||
\(61\) | −4.86425 | −0.622803 | −0.311401 | − | 0.950278i | \(-0.600798\pi\) | ||||
−0.311401 | + | 0.950278i | \(0.600798\pi\) | |||||||
\(62\) | 0.615934 | 0.0782237 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.14577 | −0.893221 | ||||||||
\(65\) | 3.69127 | 0.457845 | ||||||||
\(66\) | 0.328850 | 0.0404786 | ||||||||
\(67\) | −13.1894 | −1.61134 | −0.805672 | − | 0.592362i | \(-0.798195\pi\) | ||||
−0.805672 | + | 0.592362i | \(0.798195\pi\) | |||||||
\(68\) | −7.79080 | −0.944773 | ||||||||
\(69\) | 2.20725 | 0.265722 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1166 | 1.31930 | 0.659648 | − | 0.751575i | \(-0.270705\pi\) | ||||
0.659648 | + | 0.751575i | \(0.270705\pi\) | |||||||
\(72\) | 0.753499 | 0.0888007 | ||||||||
\(73\) | 0.406178 | 0.0475395 | 0.0237697 | − | 0.999717i | \(-0.492433\pi\) | ||||
0.0237697 | + | 0.999717i | \(0.492433\pi\) | |||||||
\(74\) | −0.361261 | −0.0419958 | ||||||||
\(75\) | −0.213562 | −0.0246600 | ||||||||
\(76\) | 2.17546 | 0.249542 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.307306 | −0.0347956 | ||||||||
\(79\) | −2.23080 | −0.250984 | −0.125492 | − | 0.992095i | \(-0.540051\pi\) | ||||
−0.125492 | + | 0.992095i | \(0.540051\pi\) | |||||||
\(80\) | −8.64123 | −0.966118 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.190092 | 0.0209921 | ||||||||
\(83\) | 1.25842 | 0.138129 | 0.0690646 | − | 0.997612i | \(-0.477999\pi\) | ||||
0.0690646 | + | 0.997612i | \(0.477999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.05811 | −0.982490 | ||||||||
\(86\) | −0.553649 | −0.0597015 | ||||||||
\(87\) | −7.83771 | −0.840291 | ||||||||
\(88\) | 1.30352 | 0.138955 | ||||||||
\(89\) | −8.84330 | −0.937388 | −0.468694 | − | 0.883361i | \(-0.655275\pi\) | ||||
−0.468694 | + | 0.883361i | \(0.655275\pi\) | |||||||
\(90\) | 0.434041 | 0.0457520 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.33474 | 0.451928 | ||||||||
\(93\) | 3.24019 | 0.335992 | ||||||||
\(94\) | 1.11431 | 0.114932 | ||||||||
\(95\) | 2.52934 | 0.259504 | ||||||||
\(96\) | 2.22640 | 0.227231 | ||||||||
\(97\) | 18.9259 | 1.92163 | 0.960816 | − | 0.277187i | \(-0.0894022\pi\) | ||||
0.960816 | + | 0.277187i | \(0.0894022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72995 | 0.173867 | ||||||||
\(100\) | −0.419407 | −0.0419407 | ||||||||
\(101\) | −2.37750 | −0.236570 | −0.118285 | − | 0.992980i | \(-0.537740\pi\) | ||||
−0.118285 | + | 0.992980i | \(0.537740\pi\) | |||||||
\(102\) | 0.754109 | 0.0746679 | ||||||||
\(103\) | −1.27186 | −0.125321 | −0.0626603 | − | 0.998035i | \(-0.519958\pi\) | ||||
−0.0626603 | + | 0.998035i | \(0.519958\pi\) | |||||||
\(104\) | −1.21812 | −0.119447 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.565823 | 0.0549576 | ||||||||
\(107\) | −15.4694 | −1.49548 | −0.747742 | − | 0.663989i | \(-0.768862\pi\) | ||||
−0.747742 | + | 0.663989i | \(0.768862\pi\) | |||||||
\(108\) | 1.96387 | 0.188973 | ||||||||
\(109\) | −5.96439 | −0.571285 | −0.285643 | − | 0.958336i | \(-0.592207\pi\) | ||||
−0.285643 | + | 0.958336i | \(0.592207\pi\) | |||||||
\(110\) | 0.750871 | 0.0715927 | ||||||||
\(111\) | −1.90046 | −0.180383 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.73825 | 0.916097 | 0.458049 | − | 0.888927i | \(-0.348549\pi\) | ||||
0.458049 | + | 0.888927i | \(0.348549\pi\) | |||||||
\(114\) | −0.210573 | −0.0197220 | ||||||||
\(115\) | 5.03986 | 0.469970 | ||||||||
\(116\) | −15.3922 | −1.42913 | ||||||||
\(117\) | −1.61662 | −0.149457 | ||||||||
\(118\) | 1.06719 | 0.0982432 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.72048 | 0.157058 | ||||||||
\(121\) | −8.00727 | −0.727933 | ||||||||
\(122\) | 0.924654 | 0.0837142 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 6.36329 | 0.571441 | ||||||||
\(125\) | 10.9290 | 0.977518 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.74582 | −0.421124 | −0.210562 | − | 0.977581i | \(-0.567529\pi\) | ||||
−0.210562 | + | 0.977581i | \(0.567529\pi\) | |||||||
\(128\) | 5.81115 | 0.513638 | ||||||||
\(129\) | −2.91253 | −0.256434 | ||||||||
\(130\) | −0.701680 | −0.0615414 | ||||||||
\(131\) | −3.47647 | −0.303740 | −0.151870 | − | 0.988400i | \(-0.548530\pi\) | ||||
−0.151870 | + | 0.988400i | \(0.548530\pi\) | |||||||
\(132\) | 3.39739 | 0.295705 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.50720 | 0.216589 | ||||||||
\(135\) | 2.28332 | 0.196517 | ||||||||
\(136\) | 2.98919 | 0.256321 | ||||||||
\(137\) | −8.28210 | −0.707587 | −0.353794 | − | 0.935324i | \(-0.615108\pi\) | ||||
−0.353794 | + | 0.935324i | \(0.615108\pi\) | |||||||
\(138\) | −0.419580 | −0.0357170 | ||||||||
\(139\) | 6.78978 | 0.575902 | 0.287951 | − | 0.957645i | \(-0.407026\pi\) | ||||
0.287951 | + | 0.957645i | \(0.407026\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.86193 | 0.493663 | ||||||||
\(142\) | −2.11317 | −0.177334 | ||||||||
\(143\) | −2.79668 | −0.233870 | ||||||||
\(144\) | 3.78450 | 0.315375 | ||||||||
\(145\) | −17.8960 | −1.48618 | ||||||||
\(146\) | −0.0772111 | −0.00639004 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.73224 | −0.306788 | ||||||||
\(149\) | −4.76826 | −0.390631 | −0.195316 | − | 0.980740i | \(-0.562573\pi\) | ||||
−0.195316 | + | 0.980740i | \(0.562573\pi\) | |||||||
\(150\) | 0.0405965 | 0.00331469 | ||||||||
\(151\) | −7.61766 | −0.619917 | −0.309958 | − | 0.950750i | \(-0.600315\pi\) | ||||
−0.309958 | + | 0.950750i | \(0.600315\pi\) | |||||||
\(152\) | −0.834683 | −0.0677017 | ||||||||
\(153\) | 3.96707 | 0.320719 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.39840 | 0.594253 | ||||||||
\(156\) | −3.17482 | −0.254189 | ||||||||
\(157\) | 12.4677 | 0.995031 | 0.497515 | − | 0.867455i | \(-0.334246\pi\) | ||||
0.497515 | + | 0.867455i | \(0.334246\pi\) | |||||||
\(158\) | 0.424056 | 0.0337361 | ||||||||
\(159\) | 2.97657 | 0.236058 | ||||||||
\(160\) | 5.08359 | 0.401893 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.190092 | −0.0149350 | ||||||||
\(163\) | 22.2666 | 1.74406 | 0.872028 | − | 0.489457i | \(-0.162805\pi\) | ||||
0.872028 | + | 0.489457i | \(0.162805\pi\) | |||||||
\(164\) | 1.96387 | 0.153352 | ||||||||
\(165\) | 3.95004 | 0.307510 | ||||||||
\(166\) | −0.239215 | −0.0185667 | ||||||||
\(167\) | −14.3144 | −1.10768 | −0.553842 | − | 0.832622i | \(-0.686839\pi\) | ||||
−0.553842 | + | 0.832622i | \(0.686839\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3865 | −0.798965 | ||||||||
\(170\) | 1.72187 | 0.132062 | ||||||||
\(171\) | −1.10774 | −0.0847112 | ||||||||
\(172\) | −5.71982 | −0.436132 | ||||||||
\(173\) | 8.70139 | 0.661554 | 0.330777 | − | 0.943709i | \(-0.392689\pi\) | ||||
0.330777 | + | 0.943709i | \(0.392689\pi\) | |||||||
\(174\) | 1.48989 | 0.112948 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.54700 | 0.493498 | ||||||||
\(177\) | 5.61410 | 0.421981 | ||||||||
\(178\) | 1.68104 | 0.125999 | ||||||||
\(179\) | −2.03988 | −0.152468 | −0.0762341 | − | 0.997090i | \(-0.524290\pi\) | ||||
−0.0762341 | + | 0.997090i | \(0.524290\pi\) | |||||||
\(180\) | 4.48414 | 0.334228 | ||||||||
\(181\) | 20.5069 | 1.52427 | 0.762133 | − | 0.647421i | \(-0.224152\pi\) | ||||
0.762133 | + | 0.647421i | \(0.224152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.86425 | 0.359575 | ||||||||
\(184\) | −1.66316 | −0.122610 | ||||||||
\(185\) | −4.33935 | −0.319036 | ||||||||
\(186\) | −0.615934 | −0.0451624 | ||||||||
\(187\) | 6.86285 | 0.501861 | ||||||||
\(188\) | 11.5120 | 0.839602 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.480806 | −0.0348813 | ||||||||
\(191\) | 10.2243 | 0.739803 | 0.369902 | − | 0.929071i | \(-0.379391\pi\) | ||||
0.369902 | + | 0.929071i | \(0.379391\pi\) | |||||||
\(192\) | 7.14577 | 0.515702 | ||||||||
\(193\) | 21.1438 | 1.52196 | 0.760982 | − | 0.648773i | \(-0.224718\pi\) | ||||
0.760982 | + | 0.648773i | \(0.224718\pi\) | |||||||
\(194\) | −3.59766 | −0.258297 | ||||||||
\(195\) | −3.69127 | −0.264337 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1685 | −1.08071 | −0.540355 | − | 0.841437i | \(-0.681710\pi\) | ||||
−0.540355 | + | 0.841437i | \(0.681710\pi\) | |||||||
\(198\) | −0.328850 | −0.0233704 | ||||||||
\(199\) | 7.99926 | 0.567053 | 0.283526 | − | 0.958964i | \(-0.408496\pi\) | ||||
0.283526 | + | 0.958964i | \(0.408496\pi\) | |||||||
\(200\) | 0.160919 | 0.0113787 | ||||||||
\(201\) | 13.1894 | 0.930310 | ||||||||
\(202\) | 0.451944 | 0.0317987 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.79080 | 0.545465 | ||||||||
\(205\) | 2.28332 | 0.159474 | ||||||||
\(206\) | 0.241771 | 0.0168450 | ||||||||
\(207\) | −2.20725 | −0.153414 | ||||||||
\(208\) | −6.11809 | −0.424213 | ||||||||
\(209\) | −1.91634 | −0.132556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1670 | −1.25067 | −0.625335 | − | 0.780356i | \(-0.715038\pi\) | ||||
−0.625335 | + | 0.780356i | \(0.715038\pi\) | |||||||
\(212\) | 5.84559 | 0.401477 | ||||||||
\(213\) | −11.1166 | −0.761696 | ||||||||
\(214\) | 2.94061 | 0.201016 | ||||||||
\(215\) | −6.65025 | −0.453543 | ||||||||
\(216\) | −0.753499 | −0.0512691 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.13378 | 0.0767895 | ||||||||
\(219\) | −0.406178 | −0.0274469 | ||||||||
\(220\) | 7.75734 | 0.523000 | ||||||||
\(221\) | −6.41325 | −0.431402 | ||||||||
\(222\) | 0.361261 | 0.0242463 | ||||||||
\(223\) | 15.1901 | 1.01720 | 0.508601 | − | 0.861002i | \(-0.330163\pi\) | ||||
0.508601 | + | 0.861002i | \(0.330163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.213562 | 0.0142375 | ||||||||
\(226\) | −1.85116 | −0.123138 | ||||||||
\(227\) | 11.3294 | 0.751958 | 0.375979 | − | 0.926628i | \(-0.377307\pi\) | ||||
0.375979 | + | 0.926628i | \(0.377307\pi\) | |||||||
\(228\) | −2.17546 | −0.144073 | ||||||||
\(229\) | 16.3760 | 1.08216 | 0.541079 | − | 0.840972i | \(-0.318016\pi\) | ||||
0.541079 | + | 0.840972i | \(0.318016\pi\) | |||||||
\(230\) | −0.958037 | −0.0631711 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.90570 | 0.387729 | ||||||||
\(233\) | −2.40958 | −0.157857 | −0.0789284 | − | 0.996880i | \(-0.525150\pi\) | ||||
−0.0789284 | + | 0.996880i | \(0.525150\pi\) | |||||||
\(234\) | 0.307306 | 0.0200893 | ||||||||
\(235\) | 13.3847 | 0.873120 | ||||||||
\(236\) | 11.0253 | 0.717688 | ||||||||
\(237\) | 2.23080 | 0.144906 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.04273 | 0.520241 | 0.260120 | − | 0.965576i | \(-0.416238\pi\) | ||||
0.260120 | + | 0.965576i | \(0.416238\pi\) | |||||||
\(240\) | 8.64123 | 0.557789 | ||||||||
\(241\) | 16.4724 | 1.06108 | 0.530541 | − | 0.847659i | \(-0.321989\pi\) | ||||
0.530541 | + | 0.847659i | \(0.321989\pi\) | |||||||
\(242\) | 1.52212 | 0.0978454 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.55272 | 0.611550 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.190092 | −0.0121198 | ||||||||
\(247\) | 1.79080 | 0.113946 | ||||||||
\(248\) | −2.44148 | −0.155034 | ||||||||
\(249\) | −1.25842 | −0.0797489 | ||||||||
\(250\) | −2.07751 | −0.131393 | ||||||||
\(251\) | 12.7762 | 0.806430 | 0.403215 | − | 0.915105i | \(-0.367893\pi\) | ||||
0.403215 | + | 0.915105i | \(0.367893\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81844 | −0.240063 | ||||||||
\(254\) | 0.902143 | 0.0566055 | ||||||||
\(255\) | 9.05811 | 0.567241 | ||||||||
\(256\) | 13.1869 | 0.824181 | ||||||||
\(257\) | −17.5803 | −1.09663 | −0.548315 | − | 0.836272i | \(-0.684731\pi\) | ||||
−0.548315 | + | 0.836272i | \(0.684731\pi\) | |||||||
\(258\) | 0.553649 | 0.0344687 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.24915 | −0.449573 | ||||||||
\(261\) | 7.83771 | 0.485142 | ||||||||
\(262\) | 0.660848 | 0.0408273 | ||||||||
\(263\) | 2.61090 | 0.160995 | 0.0804976 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804976 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(264\) | −1.30352 | −0.0802259 | ||||||||
\(265\) | 6.79648 | 0.417504 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.84330 | 0.541201 | ||||||||
\(268\) | 25.9022 | 1.58223 | ||||||||
\(269\) | 18.5601 | 1.13163 | 0.565816 | − | 0.824532i | \(-0.308561\pi\) | ||||
0.565816 | + | 0.824532i | \(0.308561\pi\) | |||||||
\(270\) | −0.434041 | −0.0264149 | ||||||||
\(271\) | −21.3817 | −1.29885 | −0.649423 | − | 0.760427i | \(-0.724990\pi\) | ||||
−0.649423 | + | 0.760427i | \(0.724990\pi\) | |||||||
\(272\) | 15.0134 | 0.910320 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.57436 | 0.0951105 | ||||||||
\(275\) | 0.369452 | 0.0222788 | ||||||||
\(276\) | −4.33474 | −0.260921 | ||||||||
\(277\) | 14.0879 | 0.846462 | 0.423231 | − | 0.906022i | \(-0.360896\pi\) | ||||
0.423231 | + | 0.906022i | \(0.360896\pi\) | |||||||
\(278\) | −1.29068 | −0.0774100 | ||||||||
\(279\) | −3.24019 | −0.193985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.3895 | −1.33565 | −0.667823 | − | 0.744320i | \(-0.732774\pi\) | ||||
−0.667823 | + | 0.744320i | \(0.732774\pi\) | |||||||
\(282\) | −1.11431 | −0.0663559 | ||||||||
\(283\) | 10.5639 | 0.627961 | 0.313980 | − | 0.949429i | \(-0.398337\pi\) | ||||
0.313980 | + | 0.949429i | \(0.398337\pi\) | |||||||
\(284\) | −21.8315 | −1.29546 | ||||||||
\(285\) | −2.52934 | −0.149825 | ||||||||
\(286\) | 0.531625 | 0.0314357 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.22640 | −0.131192 | ||||||||
\(289\) | −1.26232 | −0.0742539 | ||||||||
\(290\) | 3.40189 | 0.199766 | ||||||||
\(291\) | −18.9259 | −1.10945 | ||||||||
\(292\) | −0.797678 | −0.0466806 | ||||||||
\(293\) | 8.74247 | 0.510740 | 0.255370 | − | 0.966843i | \(-0.417803\pi\) | ||||
0.255370 | + | 0.966843i | \(0.417803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8188 | 0.746339 | ||||||||
\(296\) | 1.43199 | 0.0832328 | ||||||||
\(297\) | −1.72995 | −0.100382 | ||||||||
\(298\) | 0.906408 | 0.0525068 | ||||||||
\(299\) | 3.56828 | 0.206359 | ||||||||
\(300\) | 0.419407 | 0.0242145 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.44806 | 0.0833263 | ||||||||
\(303\) | 2.37750 | 0.136584 | ||||||||
\(304\) | −4.19225 | −0.240442 | ||||||||
\(305\) | 11.1066 | 0.635964 | ||||||||
\(306\) | −0.754109 | −0.0431095 | ||||||||
\(307\) | −7.97557 | −0.455190 | −0.227595 | − | 0.973756i | \(-0.573086\pi\) | ||||
−0.227595 | + | 0.973756i | \(0.573086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.27186 | 0.0723538 | ||||||||
\(310\) | −1.40638 | −0.0798767 | ||||||||
\(311\) | −14.1483 | −0.802276 | −0.401138 | − | 0.916018i | \(-0.631385\pi\) | ||||
−0.401138 | + | 0.916018i | \(0.631385\pi\) | |||||||
\(312\) | 1.21812 | 0.0689625 | ||||||||
\(313\) | 8.96795 | 0.506898 | 0.253449 | − | 0.967349i | \(-0.418435\pi\) | ||||
0.253449 | + | 0.967349i | \(0.418435\pi\) | |||||||
\(314\) | −2.37001 | −0.133747 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.38098 | 0.246449 | ||||||||
\(317\) | 8.04996 | 0.452131 | 0.226065 | − | 0.974112i | \(-0.427414\pi\) | ||||
0.226065 | + | 0.974112i | \(0.427414\pi\) | |||||||
\(318\) | −0.565823 | −0.0317298 | ||||||||
\(319\) | 13.5589 | 0.759151 | ||||||||
\(320\) | 16.3161 | 0.912098 | ||||||||
\(321\) | 15.4694 | 0.863419 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.39450 | −0.244517 | ||||||||
\(324\) | −1.96387 | −0.109104 | ||||||||
\(325\) | −0.345249 | −0.0191510 | ||||||||
\(326\) | −4.23270 | −0.234428 | ||||||||
\(327\) | 5.96439 | 0.329832 | ||||||||
\(328\) | −0.753499 | −0.0416050 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.750871 | −0.0413341 | ||||||||
\(331\) | 17.3497 | 0.953628 | 0.476814 | − | 0.879004i | \(-0.341792\pi\) | ||||
0.476814 | + | 0.879004i | \(0.341792\pi\) | |||||||
\(332\) | −2.47136 | −0.135634 | ||||||||
\(333\) | 1.90046 | 0.104144 | ||||||||
\(334\) | 2.72106 | 0.148890 | ||||||||
\(335\) | 30.1157 | 1.64540 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.8239 | −1.62461 | −0.812307 | − | 0.583230i | \(-0.801788\pi\) | ||||
−0.812307 | + | 0.583230i | \(0.801788\pi\) | |||||||
\(338\) | 1.97440 | 0.107393 | ||||||||
\(339\) | −9.73825 | −0.528909 | ||||||||
\(340\) | 17.7889 | 0.964739 | ||||||||
\(341\) | −5.60537 | −0.303548 | ||||||||
\(342\) | 0.210573 | 0.0113865 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.19459 | 0.118324 | ||||||||
\(345\) | −5.03986 | −0.271337 | ||||||||
\(346\) | −1.65406 | −0.0889230 | ||||||||
\(347\) | 18.3160 | 0.983255 | 0.491628 | − | 0.870805i | \(-0.336402\pi\) | ||||
0.491628 | + | 0.870805i | \(0.336402\pi\) | |||||||
\(348\) | 15.3922 | 0.825109 | ||||||||
\(349\) | 6.08069 | 0.325492 | 0.162746 | − | 0.986668i | \(-0.447965\pi\) | ||||
0.162746 | + | 0.986668i | \(0.447965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.61662 | 0.0862888 | ||||||||
\(352\) | −3.85157 | −0.205289 | ||||||||
\(353\) | 6.85088 | 0.364635 | 0.182318 | − | 0.983240i | \(-0.441640\pi\) | ||||
0.182318 | + | 0.983240i | \(0.441640\pi\) | |||||||
\(354\) | −1.06719 | −0.0567207 | ||||||||
\(355\) | −25.3827 | −1.34718 | ||||||||
\(356\) | 17.3670 | 0.920452 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.387766 | 0.0204940 | ||||||||
\(359\) | 0.354000 | 0.0186834 | 0.00934171 | − | 0.999956i | \(-0.497026\pi\) | ||||
0.00934171 | + | 0.999956i | \(0.497026\pi\) | |||||||
\(360\) | −1.72048 | −0.0906773 | ||||||||
\(361\) | −17.7729 | −0.935416 | ||||||||
\(362\) | −3.89820 | −0.204885 | ||||||||
\(363\) | 8.00727 | 0.420272 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.927435 | −0.0485441 | ||||||||
\(366\) | −0.924654 | −0.0483324 | ||||||||
\(367\) | 20.8456 | 1.08813 | 0.544065 | − | 0.839043i | \(-0.316884\pi\) | ||||
0.544065 | + | 0.839043i | \(0.316884\pi\) | |||||||
\(368\) | −8.35333 | −0.435447 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 0.824876 | 0.0428833 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.36329 | −0.329921 | ||||||||
\(373\) | 35.6438 | 1.84557 | 0.922783 | − | 0.385320i | \(-0.125909\pi\) | ||||
0.922783 | + | 0.385320i | \(0.125909\pi\) | |||||||
\(374\) | −1.30457 | −0.0674578 | ||||||||
\(375\) | −10.9290 | −0.564370 | ||||||||
\(376\) | −4.41696 | −0.227787 | ||||||||
\(377\) | −12.6706 | −0.652569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9661 | 0.820125 | 0.410063 | − | 0.912057i | \(-0.365507\pi\) | ||||
0.410063 | + | 0.912057i | \(0.365507\pi\) | |||||||
\(380\) | −4.96727 | −0.254816 | ||||||||
\(381\) | 4.74582 | 0.243136 | ||||||||
\(382\) | −1.94355 | −0.0994408 | ||||||||
\(383\) | 14.1502 | 0.723043 | 0.361521 | − | 0.932364i | \(-0.382257\pi\) | ||||
0.361521 | + | 0.932364i | \(0.382257\pi\) | |||||||
\(384\) | −5.81115 | −0.296549 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.01926 | −0.204575 | ||||||||
\(387\) | 2.91253 | 0.148052 | ||||||||
\(388\) | −37.1679 | −1.88691 | ||||||||
\(389\) | 9.66026 | 0.489795 | 0.244897 | − | 0.969549i | \(-0.421246\pi\) | ||||
0.244897 | + | 0.969549i | \(0.421246\pi\) | |||||||
\(390\) | 0.701680 | 0.0355309 | ||||||||
\(391\) | −8.75632 | −0.442826 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.47647 | 0.175365 | ||||||||
\(394\) | 2.88340 | 0.145264 | ||||||||
\(395\) | 5.09363 | 0.256288 | ||||||||
\(396\) | −3.39739 | −0.170725 | ||||||||
\(397\) | −9.54771 | −0.479186 | −0.239593 | − | 0.970873i | \(-0.577014\pi\) | ||||
−0.239593 | + | 0.970873i | \(0.577014\pi\) | |||||||
\(398\) | −1.52060 | −0.0762206 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.808225 | 0.0404113 | ||||||||
\(401\) | 34.5897 | 1.72733 | 0.863663 | − | 0.504070i | \(-0.168165\pi\) | ||||
0.863663 | + | 0.504070i | \(0.168165\pi\) | |||||||
\(402\) | −2.50720 | −0.125048 | ||||||||
\(403\) | 5.23815 | 0.260931 | ||||||||
\(404\) | 4.66909 | 0.232296 | ||||||||
\(405\) | −2.28332 | −0.113459 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.28770 | 0.162965 | ||||||||
\(408\) | −2.98919 | −0.147987 | ||||||||
\(409\) | −27.9927 | −1.38415 | −0.692074 | − | 0.721826i | \(-0.743303\pi\) | ||||
−0.692074 | + | 0.721826i | \(0.743303\pi\) | |||||||
\(410\) | −0.434041 | −0.0214358 | ||||||||
\(411\) | 8.28210 | 0.408526 | ||||||||
\(412\) | 2.49777 | 0.123056 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.419580 | 0.0206212 | ||||||||
\(415\) | −2.87337 | −0.141048 | ||||||||
\(416\) | 3.59924 | 0.176467 | ||||||||
\(417\) | −6.78978 | −0.332497 | ||||||||
\(418\) | 0.364281 | 0.0178176 | ||||||||
\(419\) | −20.1883 | −0.986263 | −0.493131 | − | 0.869955i | \(-0.664148\pi\) | ||||
−0.493131 | + | 0.869955i | \(0.664148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.88294 | 0.384191 | 0.192096 | − | 0.981376i | \(-0.438472\pi\) | ||||
0.192096 | + | 0.981376i | \(0.438472\pi\) | |||||||
\(422\) | 3.45341 | 0.168109 | ||||||||
\(423\) | −5.86193 | −0.285017 | ||||||||
\(424\) | −2.24285 | −0.108922 | ||||||||
\(425\) | 0.847217 | 0.0410961 | ||||||||
\(426\) | 2.11317 | 0.102384 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 30.3798 | 1.46847 | ||||||||
\(429\) | 2.79668 | 0.135025 | ||||||||
\(430\) | 1.26416 | 0.0609631 | ||||||||
\(431\) | −4.43615 | −0.213682 | −0.106841 | − | 0.994276i | \(-0.534074\pi\) | ||||
−0.106841 | + | 0.994276i | \(0.534074\pi\) | |||||||
\(432\) | −3.78450 | −0.182082 | ||||||||
\(433\) | 7.00079 | 0.336436 | 0.168218 | − | 0.985750i | \(-0.446199\pi\) | ||||
0.168218 | + | 0.985750i | \(0.446199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8960 | 0.858048 | ||||||||
\(436\) | 11.7133 | 0.560964 | ||||||||
\(437\) | 2.44507 | 0.116963 | ||||||||
\(438\) | 0.0772111 | 0.00368929 | ||||||||
\(439\) | 11.0416 | 0.526988 | 0.263494 | − | 0.964661i | \(-0.415125\pi\) | ||||
0.263494 | + | 0.964661i | \(0.415125\pi\) | |||||||
\(440\) | −2.97635 | −0.141892 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.21911 | 0.0579870 | ||||||||
\(443\) | −6.88937 | −0.327324 | −0.163662 | − | 0.986516i | \(-0.552331\pi\) | ||||
−0.163662 | + | 0.986516i | \(0.552331\pi\) | |||||||
\(444\) | 3.73224 | 0.177124 | ||||||||
\(445\) | 20.1921 | 0.957197 | ||||||||
\(446\) | −2.88751 | −0.136728 | ||||||||
\(447\) | 4.76826 | 0.225531 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.0247 | 1.27538 | 0.637688 | − | 0.770295i | \(-0.279891\pi\) | ||||
0.637688 | + | 0.770295i | \(0.279891\pi\) | |||||||
\(450\) | −0.0405965 | −0.00191374 | ||||||||
\(451\) | −1.72995 | −0.0814603 | ||||||||
\(452\) | −19.1246 | −0.899546 | ||||||||
\(453\) | 7.61766 | 0.357909 | ||||||||
\(454\) | −2.15362 | −0.101075 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.834683 | 0.0390876 | ||||||||
\(457\) | 2.39212 | 0.111899 | 0.0559494 | − | 0.998434i | \(-0.482181\pi\) | ||||
0.0559494 | + | 0.998434i | \(0.482181\pi\) | |||||||
\(458\) | −3.11295 | −0.145459 | ||||||||
\(459\) | −3.96707 | −0.185167 | ||||||||
\(460\) | −9.89761 | −0.461478 | ||||||||
\(461\) | −15.9987 | −0.745136 | −0.372568 | − | 0.928005i | \(-0.621523\pi\) | ||||
−0.372568 | + | 0.928005i | \(0.621523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3408 | 0.805893 | 0.402947 | − | 0.915224i | \(-0.367986\pi\) | ||||
0.402947 | + | 0.915224i | \(0.367986\pi\) | |||||||
\(464\) | 29.6618 | 1.37701 | ||||||||
\(465\) | −7.39840 | −0.343092 | ||||||||
\(466\) | 0.458042 | 0.0212184 | ||||||||
\(467\) | 31.7666 | 1.46998 | 0.734990 | − | 0.678078i | \(-0.237187\pi\) | ||||
0.734990 | + | 0.678078i | \(0.237187\pi\) | |||||||
\(468\) | 3.17482 | 0.146756 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.54432 | −0.117361 | ||||||||
\(471\) | −12.4677 | −0.574481 | ||||||||
\(472\) | −4.23022 | −0.194711 | ||||||||
\(473\) | 5.03854 | 0.231672 | ||||||||
\(474\) | −0.424056 | −0.0194776 | ||||||||
\(475\) | −0.236572 | −0.0108547 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.97657 | −0.136288 | ||||||||
\(478\) | −1.52886 | −0.0699283 | ||||||||
\(479\) | −12.5261 | −0.572331 | −0.286166 | − | 0.958180i | \(-0.592381\pi\) | ||||
−0.286166 | + | 0.958180i | \(0.592381\pi\) | |||||||
\(480\) | −5.08359 | −0.232033 | ||||||||
\(481\) | −3.07232 | −0.140086 | ||||||||
\(482\) | −3.13128 | −0.142626 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.7252 | 0.714781 | ||||||||
\(485\) | −43.2139 | −1.96224 | ||||||||
\(486\) | 0.190092 | 0.00862275 | ||||||||
\(487\) | 18.9271 | 0.857670 | 0.428835 | − | 0.903383i | \(-0.358924\pi\) | ||||
0.428835 | + | 0.903383i | \(0.358924\pi\) | |||||||
\(488\) | −3.66520 | −0.165916 | ||||||||
\(489\) | −22.2666 | −1.00693 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.3059 | 1.77385 | 0.886926 | − | 0.461912i | \(-0.152837\pi\) | ||||
0.886926 | + | 0.461912i | \(0.152837\pi\) | |||||||
\(492\) | −1.96387 | −0.0885379 | ||||||||
\(493\) | 31.0928 | 1.40035 | ||||||||
\(494\) | −0.340417 | −0.0153161 | ||||||||
\(495\) | −3.95004 | −0.177541 | ||||||||
\(496\) | −12.2625 | −0.550602 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.239215 | 0.0107195 | ||||||||
\(499\) | −0.0965158 | −0.00432064 | −0.00216032 | − | 0.999998i | \(-0.500688\pi\) | ||||
−0.00216032 | + | 0.999998i | \(0.500688\pi\) | |||||||
\(500\) | −21.4630 | −0.959857 | ||||||||
\(501\) | 14.3144 | 0.639521 | ||||||||
\(502\) | −2.42866 | −0.108396 | ||||||||
\(503\) | −35.7044 | −1.59198 | −0.795990 | − | 0.605310i | \(-0.793049\pi\) | ||||
−0.795990 | + | 0.605310i | \(0.793049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.42860 | 0.241570 | ||||||||
\(506\) | 0.725854 | 0.0322681 | ||||||||
\(507\) | 10.3865 | 0.461282 | ||||||||
\(508\) | 9.32016 | 0.413515 | ||||||||
\(509\) | −6.76202 | −0.299721 | −0.149861 | − | 0.988707i | \(-0.547883\pi\) | ||||
−0.149861 | + | 0.988707i | \(0.547883\pi\) | |||||||
\(510\) | −1.72187 | −0.0762459 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.1290 | −0.624421 | ||||||||
\(513\) | 1.10774 | 0.0489081 | ||||||||
\(514\) | 3.34188 | 0.147404 | ||||||||
\(515\) | 2.90408 | 0.127969 | ||||||||
\(516\) | 5.71982 | 0.251801 | ||||||||
\(517\) | −10.1409 | −0.445994 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.70139 | −0.381949 | ||||||||
\(520\) | 2.78136 | 0.121971 | ||||||||
\(521\) | 10.8582 | 0.475708 | 0.237854 | − | 0.971301i | \(-0.423556\pi\) | ||||
0.237854 | + | 0.971301i | \(0.423556\pi\) | |||||||
\(522\) | −1.48989 | −0.0652105 | ||||||||
\(523\) | 8.65423 | 0.378423 | 0.189212 | − | 0.981936i | \(-0.439407\pi\) | ||||
0.189212 | + | 0.981936i | \(0.439407\pi\) | |||||||
\(524\) | 6.82731 | 0.298252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.496312 | −0.0216402 | ||||||||
\(527\) | −12.8541 | −0.559932 | ||||||||
\(528\) | −6.54700 | −0.284921 | ||||||||
\(529\) | −18.1281 | −0.788176 | ||||||||
\(530\) | −1.29196 | −0.0561190 | ||||||||
\(531\) | −5.61410 | −0.243631 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.61662 | 0.0700236 | ||||||||
\(534\) | −1.68104 | −0.0727457 | ||||||||
\(535\) | 35.3217 | 1.52709 | ||||||||
\(536\) | −9.93821 | −0.429265 | ||||||||
\(537\) | 2.03988 | 0.0880275 | ||||||||
\(538\) | −3.52813 | −0.152109 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.48414 | −0.192967 | ||||||||
\(541\) | 34.5488 | 1.48537 | 0.742684 | − | 0.669642i | \(-0.233552\pi\) | ||||
0.742684 | + | 0.669642i | \(0.233552\pi\) | |||||||
\(542\) | 4.06449 | 0.174585 | ||||||||
\(543\) | −20.5069 | −0.880035 | ||||||||
\(544\) | −8.83229 | −0.378682 | ||||||||
\(545\) | 13.6186 | 0.583358 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.28734 | 0.268827 | 0.134414 | − | 0.990925i | \(-0.457085\pi\) | ||||
0.134414 | + | 0.990925i | \(0.457085\pi\) | |||||||
\(548\) | 16.2649 | 0.694803 | ||||||||
\(549\) | −4.86425 | −0.207601 | ||||||||
\(550\) | −0.0702299 | −0.00299461 | ||||||||
\(551\) | −8.68217 | −0.369873 | ||||||||
\(552\) | 1.66316 | 0.0707888 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.67800 | −0.113777 | ||||||||
\(555\) | 4.33935 | 0.184195 | ||||||||
\(556\) | −13.3342 | −0.565497 | ||||||||
\(557\) | −23.1197 | −0.979612 | −0.489806 | − | 0.871832i | \(-0.662932\pi\) | ||||
−0.489806 | + | 0.871832i | \(0.662932\pi\) | |||||||
\(558\) | 0.615934 | 0.0260746 | ||||||||
\(559\) | −4.70846 | −0.199146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.86285 | −0.289750 | ||||||||
\(562\) | 4.25606 | 0.179531 | ||||||||
\(563\) | −43.4261 | −1.83019 | −0.915095 | − | 0.403238i | \(-0.867885\pi\) | ||||
−0.915095 | + | 0.403238i | \(0.867885\pi\) | |||||||
\(564\) | −11.5120 | −0.484744 | ||||||||
\(565\) | −22.2356 | −0.935457 | ||||||||
\(566\) | −2.00812 | −0.0844076 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.37633 | 0.351463 | ||||||||
\(569\) | 0.0739827 | 0.00310152 | 0.00155076 | − | 0.999999i | \(-0.499506\pi\) | ||||
0.00155076 | + | 0.999999i | \(0.499506\pi\) | |||||||
\(570\) | 0.480806 | 0.0201388 | ||||||||
\(571\) | −5.95013 | −0.249005 | −0.124503 | − | 0.992219i | \(-0.539734\pi\) | ||||
−0.124503 | + | 0.992219i | \(0.539734\pi\) | |||||||
\(572\) | 5.49229 | 0.229644 | ||||||||
\(573\) | −10.2243 | −0.427125 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.471385 | −0.0196581 | ||||||||
\(576\) | −7.14577 | −0.297740 | ||||||||
\(577\) | 29.6618 | 1.23484 | 0.617418 | − | 0.786636i | \(-0.288179\pi\) | ||||
0.617418 | + | 0.786636i | \(0.288179\pi\) | |||||||
\(578\) | 0.239956 | 0.00998086 | ||||||||
\(579\) | −21.1438 | −0.878706 | ||||||||
\(580\) | 35.1454 | 1.45933 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.59766 | 0.149128 | ||||||||
\(583\) | −5.14933 | −0.213264 | ||||||||
\(584\) | 0.306054 | 0.0126646 | ||||||||
\(585\) | 3.69127 | 0.152615 | ||||||||
\(586\) | −1.66187 | −0.0686513 | ||||||||
\(587\) | 1.71541 | 0.0708025 | 0.0354012 | − | 0.999373i | \(-0.488729\pi\) | ||||
0.0354012 | + | 0.999373i | \(0.488729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.58930 | 0.147894 | ||||||||
\(590\) | −2.43675 | −0.100319 | ||||||||
\(591\) | 15.1685 | 0.623948 | ||||||||
\(592\) | 7.19227 | 0.295600 | ||||||||
\(593\) | −3.69486 | −0.151730 | −0.0758650 | − | 0.997118i | \(-0.524172\pi\) | ||||
−0.0758650 | + | 0.997118i | \(0.524172\pi\) | |||||||
\(594\) | 0.328850 | 0.0134929 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.36422 | 0.383573 | ||||||||
\(597\) | −7.99926 | −0.327388 | ||||||||
\(598\) | −0.678302 | −0.0277378 | ||||||||
\(599\) | −23.5445 | −0.962002 | −0.481001 | − | 0.876720i | \(-0.659727\pi\) | ||||
−0.481001 | + | 0.876720i | \(0.659727\pi\) | |||||||
\(600\) | −0.160919 | −0.00656949 | ||||||||
\(601\) | 9.90791 | 0.404152 | 0.202076 | − | 0.979370i | \(-0.435231\pi\) | ||||
0.202076 | + | 0.979370i | \(0.435231\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.1894 | −0.537115 | ||||||||
\(604\) | 14.9601 | 0.608716 | ||||||||
\(605\) | 18.2832 | 0.743317 | ||||||||
\(606\) | −0.451944 | −0.0183590 | ||||||||
\(607\) | 27.9949 | 1.13628 | 0.568139 | − | 0.822933i | \(-0.307664\pi\) | ||||
0.568139 | + | 0.822933i | \(0.307664\pi\) | |||||||
\(608\) | 2.46628 | 0.100021 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.11128 | −0.0854833 | ||||||||
\(611\) | 9.47651 | 0.383379 | ||||||||
\(612\) | −7.79080 | −0.314924 | ||||||||
\(613\) | −12.2122 | −0.493245 | −0.246622 | − | 0.969112i | \(-0.579321\pi\) | ||||
−0.246622 | + | 0.969112i | \(0.579321\pi\) | |||||||
\(614\) | 1.51609 | 0.0611845 | ||||||||
\(615\) | −2.28332 | −0.0920725 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.44647 | 0.138750 | 0.0693748 | − | 0.997591i | \(-0.477900\pi\) | ||||
0.0693748 | + | 0.997591i | \(0.477900\pi\) | |||||||
\(618\) | −0.241771 | −0.00972546 | ||||||||
\(619\) | 19.3249 | 0.776734 | 0.388367 | − | 0.921505i | \(-0.373039\pi\) | ||||
0.388367 | + | 0.921505i | \(0.373039\pi\) | |||||||
\(620\) | −14.5294 | −0.583517 | ||||||||
\(621\) | 2.20725 | 0.0885739 | ||||||||
\(622\) | 2.68948 | 0.107838 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.11809 | 0.244920 | ||||||||
\(625\) | −26.0222 | −1.04089 | ||||||||
\(626\) | −1.70473 | −0.0681349 | ||||||||
\(627\) | 1.91634 | 0.0765314 | ||||||||
\(628\) | −24.4849 | −0.977053 | ||||||||
\(629\) | 7.53925 | 0.300610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9587 | 0.476068 | 0.238034 | − | 0.971257i | \(-0.423497\pi\) | ||||
0.238034 | + | 0.971257i | \(0.423497\pi\) | |||||||
\(632\) | −1.68090 | −0.0668627 | ||||||||
\(633\) | 18.1670 | 0.722075 | ||||||||
\(634\) | −1.53023 | −0.0607733 | ||||||||
\(635\) | 10.8362 | 0.430023 | ||||||||
\(636\) | −5.84559 | −0.231793 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.57743 | −0.102041 | ||||||||
\(639\) | 11.1166 | 0.439765 | ||||||||
\(640\) | −13.2687 | −0.524493 | ||||||||
\(641\) | −46.6531 | −1.84269 | −0.921343 | − | 0.388751i | \(-0.872907\pi\) | ||||
−0.921343 | + | 0.388751i | \(0.872907\pi\) | |||||||
\(642\) | −2.94061 | −0.116057 | ||||||||
\(643\) | 7.35668 | 0.290119 | 0.145059 | − | 0.989423i | \(-0.453663\pi\) | ||||
0.145059 | + | 0.989423i | \(0.453663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.65025 | 0.261853 | ||||||||
\(646\) | 0.835359 | 0.0328668 | ||||||||
\(647\) | −2.57068 | −0.101064 | −0.0505320 | − | 0.998722i | \(-0.516092\pi\) | ||||
−0.0505320 | + | 0.998722i | \(0.516092\pi\) | |||||||
\(648\) | 0.753499 | 0.0296002 | ||||||||
\(649\) | −9.71212 | −0.381234 | ||||||||
\(650\) | 0.0656290 | 0.00257418 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.7286 | −1.71254 | ||||||||
\(653\) | −31.3911 | −1.22843 | −0.614215 | − | 0.789139i | \(-0.710527\pi\) | ||||
−0.614215 | + | 0.789139i | \(0.710527\pi\) | |||||||
\(654\) | −1.13378 | −0.0443344 | ||||||||
\(655\) | 7.93789 | 0.310159 | ||||||||
\(656\) | −3.78450 | −0.147760 | ||||||||
\(657\) | 0.406178 | 0.0158465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.55964 | 0.0997094 | 0.0498547 | − | 0.998756i | \(-0.484124\pi\) | ||||
0.0498547 | + | 0.998756i | \(0.484124\pi\) | |||||||
\(660\) | −7.75734 | −0.301954 | ||||||||
\(661\) | 19.6281 | 0.763445 | 0.381723 | − | 0.924277i | \(-0.375331\pi\) | ||||
0.381723 | + | 0.924277i | \(0.375331\pi\) | |||||||
\(662\) | −3.29805 | −0.128182 | ||||||||
\(663\) | 6.41325 | 0.249070 | ||||||||
\(664\) | 0.948216 | 0.0367979 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.361261 | −0.0139986 | ||||||||
\(667\) | −17.2998 | −0.669850 | ||||||||
\(668\) | 28.1116 | 1.08767 | ||||||||
\(669\) | −15.1901 | −0.587282 | ||||||||
\(670\) | −5.72475 | −0.221166 | ||||||||
\(671\) | −8.41491 | −0.324854 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.9831 | 0.693198 | 0.346599 | − | 0.938013i | \(-0.387337\pi\) | ||||
0.346599 | + | 0.938013i | \(0.387337\pi\) | |||||||
\(674\) | 5.66929 | 0.218373 | ||||||||
\(675\) | −0.213562 | −0.00822001 | ||||||||
\(676\) | 20.3978 | 0.784529 | ||||||||
\(677\) | 49.9993 | 1.92163 | 0.960815 | − | 0.277189i | \(-0.0894029\pi\) | ||||
0.960815 | + | 0.277189i | \(0.0894029\pi\) | |||||||
\(678\) | 1.85116 | 0.0710935 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.82528 | −0.261737 | ||||||||
\(681\) | −11.3294 | −0.434143 | ||||||||
\(682\) | 1.06554 | 0.0408015 | ||||||||
\(683\) | −0.152907 | −0.00585081 | −0.00292541 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292541 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(684\) | 2.17546 | 0.0831807 | ||||||||
\(685\) | 18.9107 | 0.722541 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3760 | −0.624784 | ||||||||
\(688\) | 11.0225 | 0.420227 | ||||||||
\(689\) | 4.81199 | 0.183322 | ||||||||
\(690\) | 0.958037 | 0.0364719 | ||||||||
\(691\) | 5.74600 | 0.218588 | 0.109294 | − | 0.994009i | \(-0.465141\pi\) | ||||
0.109294 | + | 0.994009i | \(0.465141\pi\) | |||||||
\(692\) | −17.0884 | −0.649602 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.48173 | −0.132165 | ||||||||
\(695\) | −15.5033 | −0.588072 | ||||||||
\(696\) | −5.90570 | −0.223855 | ||||||||
\(697\) | −3.96707 | −0.150264 | ||||||||
\(698\) | −1.15589 | −0.0437511 | ||||||||
\(699\) | 2.40958 | 0.0911387 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.6654 | −1.30929 | −0.654647 | − | 0.755934i | \(-0.727183\pi\) | ||||
−0.654647 | + | 0.755934i | \(0.727183\pi\) | |||||||
\(702\) | −0.307306 | −0.0115985 | ||||||||
\(703\) | −2.10522 | −0.0793998 | ||||||||
\(704\) | −12.3618 | −0.465904 | ||||||||
\(705\) | −13.3847 | −0.504096 | ||||||||
\(706\) | −1.30230 | −0.0490126 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.0253 | −0.414357 | ||||||||
\(709\) | −12.1602 | −0.456684 | −0.228342 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228342 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(710\) | 4.82506 | 0.181081 | ||||||||
\(711\) | −2.23080 | −0.0836614 | ||||||||
\(712\) | −6.66341 | −0.249722 | ||||||||
\(713\) | 7.15190 | 0.267841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.38571 | 0.238812 | ||||||||
\(716\) | 4.00606 | 0.149713 | ||||||||
\(717\) | −8.04273 | −0.300361 | ||||||||
\(718\) | −0.0672926 | −0.00251134 | ||||||||
\(719\) | −15.6701 | −0.584396 | −0.292198 | − | 0.956358i | \(-0.594387\pi\) | ||||
−0.292198 | + | 0.956358i | \(0.594387\pi\) | |||||||
\(720\) | −8.64123 | −0.322039 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.37849 | 0.125734 | ||||||||
\(723\) | −16.4724 | −0.612616 | ||||||||
\(724\) | −40.2728 | −1.49673 | ||||||||
\(725\) | 1.67384 | 0.0621648 | ||||||||
\(726\) | −1.52212 | −0.0564910 | ||||||||
\(727\) | −5.01300 | −0.185922 | −0.0929609 | − | 0.995670i | \(-0.529633\pi\) | ||||
−0.0929609 | + | 0.995670i | \(0.529633\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.176298 | 0.00652508 | ||||||||
\(731\) | 11.5542 | 0.427349 | ||||||||
\(732\) | −9.55272 | −0.353079 | ||||||||
\(733\) | −8.01404 | −0.296005 | −0.148003 | − | 0.988987i | \(-0.547284\pi\) | ||||
−0.148003 | + | 0.988987i | \(0.547284\pi\) | |||||||
\(734\) | −3.96258 | −0.146261 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.91422 | 0.181141 | ||||||||
\(737\) | −22.8171 | −0.840477 | ||||||||
\(738\) | 0.190092 | 0.00699738 | ||||||||
\(739\) | 0.161151 | 0.00592802 | 0.00296401 | − | 0.999996i | \(-0.499057\pi\) | ||||
0.00296401 | + | 0.999996i | \(0.499057\pi\) | |||||||
\(740\) | 8.52191 | 0.313272 | ||||||||
\(741\) | −1.79080 | −0.0657867 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.1913 | −0.373884 | −0.186942 | − | 0.982371i | \(-0.559858\pi\) | ||||
−0.186942 | + | 0.982371i | \(0.559858\pi\) | |||||||
\(744\) | 2.44148 | 0.0895089 | ||||||||
\(745\) | 10.8875 | 0.398886 | ||||||||
\(746\) | −6.77560 | −0.248072 | ||||||||
\(747\) | 1.25842 | 0.0460431 | ||||||||
\(748\) | −13.4777 | −0.492794 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.07751 | 0.0758600 | ||||||||
\(751\) | −5.99474 | −0.218751 | −0.109376 | − | 0.994000i | \(-0.534885\pi\) | ||||
−0.109376 | + | 0.994000i | \(0.534885\pi\) | |||||||
\(752\) | −22.1844 | −0.808983 | ||||||||
\(753\) | −12.7762 | −0.465592 | ||||||||
\(754\) | 2.40858 | 0.0877153 | ||||||||
\(755\) | 17.3936 | 0.633017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.7296 | −1.66207 | −0.831035 | − | 0.556220i | \(-0.812251\pi\) | ||||
−0.831035 | + | 0.556220i | \(0.812251\pi\) | |||||||
\(758\) | −3.03503 | −0.110237 | ||||||||
\(759\) | 3.81844 | 0.138600 | ||||||||
\(760\) | 1.90585 | 0.0691325 | ||||||||
\(761\) | −5.82408 | −0.211123 | −0.105561 | − | 0.994413i | \(-0.533664\pi\) | ||||
−0.105561 | + | 0.994413i | \(0.533664\pi\) | |||||||
\(762\) | −0.902143 | −0.0326812 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.0791 | −0.726437 | ||||||||
\(765\) | −9.05811 | −0.327497 | ||||||||
\(766\) | −2.68984 | −0.0971880 | ||||||||
\(767\) | 9.07586 | 0.327710 | ||||||||
\(768\) | −13.1869 | −0.475841 | ||||||||
\(769\) | −18.0668 | −0.651506 | −0.325753 | − | 0.945455i | \(-0.605618\pi\) | ||||
−0.325753 | + | 0.945455i | \(0.605618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.5803 | 0.633140 | ||||||||
\(772\) | −41.5235 | −1.49447 | ||||||||
\(773\) | −6.14546 | −0.221037 | −0.110518 | − | 0.993874i | \(-0.535251\pi\) | ||||
−0.110518 | + | 0.993874i | \(0.535251\pi\) | |||||||
\(774\) | −0.553649 | −0.0199005 | ||||||||
\(775\) | −0.691982 | −0.0248567 | ||||||||
\(776\) | 14.2606 | 0.511927 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.83634 | −0.0658359 | ||||||||
\(779\) | 1.10774 | 0.0396890 | ||||||||
\(780\) | 7.24915 | 0.259561 | ||||||||
\(781\) | 19.2312 | 0.688145 | ||||||||
\(782\) | 1.66451 | 0.0595226 | ||||||||
\(783\) | −7.83771 | −0.280097 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.4678 | −1.01606 | ||||||||
\(786\) | −0.660848 | −0.0235717 | ||||||||
\(787\) | −42.5487 | −1.51670 | −0.758349 | − | 0.651849i | \(-0.773993\pi\) | ||||
−0.758349 | + | 0.651849i | \(0.773993\pi\) | |||||||
\(788\) | 29.7888 | 1.06118 | ||||||||
\(789\) | −2.61090 | −0.0929506 | ||||||||
\(790\) | −0.968257 | −0.0344491 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.30352 | 0.0463185 | ||||||||
\(793\) | 7.86364 | 0.279246 | ||||||||
\(794\) | 1.81494 | 0.0644099 | ||||||||
\(795\) | −6.79648 | −0.241046 | ||||||||
\(796\) | −15.7095 | −0.556808 | ||||||||
\(797\) | −40.4705 | −1.43354 | −0.716770 | − | 0.697310i | \(-0.754380\pi\) | ||||
−0.716770 | + | 0.697310i | \(0.754380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.2547 | −0.822692 | ||||||||
\(800\) | −0.475475 | −0.0168106 | ||||||||
\(801\) | −8.84330 | −0.312463 | ||||||||
\(802\) | −6.57522 | −0.232179 | ||||||||
\(803\) | 0.702668 | 0.0247966 | ||||||||
\(804\) | −25.9022 | −0.913501 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.995731 | −0.0350731 | ||||||||
\(807\) | −18.5601 | −0.653348 | ||||||||
\(808\) | −1.79144 | −0.0630228 | ||||||||
\(809\) | 52.1135 | 1.83221 | 0.916107 | − | 0.400934i | \(-0.131314\pi\) | ||||
0.916107 | + | 0.400934i | \(0.131314\pi\) | |||||||
\(810\) | 0.434041 | 0.0152507 | ||||||||
\(811\) | −15.9764 | −0.561006 | −0.280503 | − | 0.959853i | \(-0.590501\pi\) | ||||
−0.280503 | + | 0.959853i | \(0.590501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.3817 | 0.749889 | ||||||||
\(814\) | −0.624965 | −0.0219050 | ||||||||
\(815\) | −50.8418 | −1.78091 | ||||||||
\(816\) | −15.0134 | −0.525573 | ||||||||
\(817\) | −3.22634 | −0.112875 | ||||||||
\(818\) | 5.32118 | 0.186051 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.48414 | −0.156593 | ||||||||
\(821\) | 23.4163 | 0.817235 | 0.408617 | − | 0.912706i | \(-0.366011\pi\) | ||||
0.408617 | + | 0.912706i | \(0.366011\pi\) | |||||||
\(822\) | −1.57436 | −0.0549121 | ||||||||
\(823\) | 50.2024 | 1.74994 | 0.874972 | − | 0.484173i | \(-0.160880\pi\) | ||||
0.874972 | + | 0.484173i | \(0.160880\pi\) | |||||||
\(824\) | −0.958348 | −0.0333856 | ||||||||
\(825\) | −0.369452 | −0.0128627 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.03629 | −0.140355 | −0.0701777 | − | 0.997535i | \(-0.522357\pi\) | ||||
−0.0701777 | + | 0.997535i | \(0.522357\pi\) | |||||||
\(828\) | 4.33474 | 0.150643 | ||||||||
\(829\) | 49.7726 | 1.72867 | 0.864337 | − | 0.502913i | \(-0.167738\pi\) | ||||
0.864337 | + | 0.502913i | \(0.167738\pi\) | |||||||
\(830\) | 0.546205 | 0.0189590 | ||||||||
\(831\) | −14.0879 | −0.488705 | ||||||||
\(832\) | 11.5520 | 0.400493 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.29068 | 0.0446927 | ||||||||
\(835\) | 32.6845 | 1.13109 | ||||||||
\(836\) | 3.76344 | 0.130161 | ||||||||
\(837\) | 3.24019 | 0.111997 | ||||||||
\(838\) | 3.83763 | 0.132569 | ||||||||
\(839\) | 7.36072 | 0.254120 | 0.127060 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127060 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.4297 | 1.11827 | ||||||||
\(842\) | −1.49848 | −0.0516412 | ||||||||
\(843\) | 22.3895 | 0.771135 | ||||||||
\(844\) | 35.6776 | 1.22807 | ||||||||
\(845\) | 23.7158 | 0.815849 | ||||||||
\(846\) | 1.11431 | 0.0383106 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.2648 | −0.386836 | ||||||||
\(849\) | −10.5639 | −0.362553 | ||||||||
\(850\) | −0.161049 | −0.00552394 | ||||||||
\(851\) | −4.19478 | −0.143795 | ||||||||
\(852\) | 21.8315 | 0.747934 | ||||||||
\(853\) | −12.6755 | −0.434001 | −0.217001 | − | 0.976171i | \(-0.569627\pi\) | ||||
−0.217001 | + | 0.976171i | \(0.569627\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.52934 | 0.0865014 | ||||||||
\(856\) | −11.6562 | −0.398400 | ||||||||
\(857\) | −14.3118 | −0.488883 | −0.244442 | − | 0.969664i | \(-0.578605\pi\) | ||||
−0.244442 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(858\) | −0.531625 | −0.0181494 | ||||||||
\(859\) | −12.6064 | −0.430126 | −0.215063 | − | 0.976600i | \(-0.568996\pi\) | ||||
−0.215063 | + | 0.976600i | \(0.568996\pi\) | |||||||
\(860\) | 13.0602 | 0.445349 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.843276 | 0.0287221 | ||||||||
\(863\) | −2.85848 | −0.0973037 | −0.0486518 | − | 0.998816i | \(-0.515492\pi\) | ||||
−0.0486518 | + | 0.998816i | \(0.515492\pi\) | |||||||
\(864\) | 2.22640 | 0.0757437 | ||||||||
\(865\) | −19.8681 | −0.675535 | ||||||||
\(866\) | −1.33079 | −0.0452222 | ||||||||
\(867\) | 1.26232 | 0.0428705 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.85917 | −0.130913 | ||||||||
\(870\) | −3.40189 | −0.115335 | ||||||||
\(871\) | 21.3223 | 0.722478 | ||||||||
\(872\) | −4.49416 | −0.152192 | ||||||||
\(873\) | 18.9259 | 0.640544 | ||||||||
\(874\) | −0.464787 | −0.0157217 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.797678 | 0.0269510 | ||||||||
\(877\) | −18.9915 | −0.641297 | −0.320648 | − | 0.947198i | \(-0.603901\pi\) | ||||
−0.320648 | + | 0.947198i | \(0.603901\pi\) | |||||||
\(878\) | −2.09893 | −0.0708353 | ||||||||
\(879\) | −8.74247 | −0.294876 | ||||||||
\(880\) | −14.9489 | −0.503928 | ||||||||
\(881\) | 4.63709 | 0.156228 | 0.0781138 | − | 0.996944i | \(-0.475110\pi\) | ||||
0.0781138 | + | 0.996944i | \(0.475110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5951 | 1.50074 | 0.750372 | − | 0.661016i | \(-0.229874\pi\) | ||||
0.750372 | + | 0.661016i | \(0.229874\pi\) | |||||||
\(884\) | 12.5948 | 0.423608 | ||||||||
\(885\) | −12.8188 | −0.430899 | ||||||||
\(886\) | 1.30961 | 0.0439973 | ||||||||
\(887\) | 56.2119 | 1.88741 | 0.943706 | − | 0.330785i | \(-0.107313\pi\) | ||||
0.943706 | + | 0.330785i | \(0.107313\pi\) | |||||||
\(888\) | −1.43199 | −0.0480545 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.83836 | −0.128662 | ||||||||
\(891\) | 1.72995 | 0.0579556 | ||||||||
\(892\) | −29.8312 | −0.998824 | ||||||||
\(893\) | 6.49351 | 0.217297 | ||||||||
\(894\) | −0.906408 | −0.0303148 | ||||||||
\(895\) | 4.65771 | 0.155690 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.56828 | −0.119142 | ||||||||
\(898\) | −5.13718 | −0.171430 | ||||||||
\(899\) | −25.3957 | −0.846992 | ||||||||
\(900\) | −0.419407 | −0.0139802 | ||||||||
\(901\) | −11.8083 | −0.393391 | ||||||||
\(902\) | 0.328850 | 0.0109495 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.33776 | 0.244050 | ||||||||
\(905\) | −46.8239 | −1.55648 | ||||||||
\(906\) | −1.44806 | −0.0481085 | ||||||||
\(907\) | −21.4550 | −0.712403 | −0.356201 | − | 0.934409i | \(-0.615928\pi\) | ||||
−0.356201 | + | 0.934409i | \(0.615928\pi\) | |||||||
\(908\) | −22.2494 | −0.738372 | ||||||||
\(909\) | −2.37750 | −0.0788567 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3499 | 0.707354 | 0.353677 | − | 0.935368i | \(-0.384931\pi\) | ||||
0.353677 | + | 0.935368i | \(0.384931\pi\) | |||||||
\(912\) | 4.19225 | 0.138819 | ||||||||
\(913\) | 2.17700 | 0.0720482 | ||||||||
\(914\) | −0.454723 | −0.0150409 | ||||||||
\(915\) | −11.1066 | −0.367174 | ||||||||
\(916\) | −32.1603 | −1.06261 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.754109 | 0.0248893 | ||||||||
\(919\) | −12.4136 | −0.409487 | −0.204744 | − | 0.978816i | \(-0.565636\pi\) | ||||
−0.204744 | + | 0.978816i | \(0.565636\pi\) | |||||||
\(920\) | 3.79753 | 0.125201 | ||||||||
\(921\) | 7.97557 | 0.262804 | ||||||||
\(922\) | 3.04123 | 0.100158 | ||||||||
\(923\) | −17.9713 | −0.591532 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.405866 | 0.0133448 | ||||||||
\(926\) | −3.29634 | −0.108324 | ||||||||
\(927\) | −1.27186 | −0.0417735 | ||||||||
\(928\) | −17.4499 | −0.572820 | ||||||||
\(929\) | −12.7962 | −0.419829 | −0.209914 | − | 0.977720i | \(-0.567319\pi\) | ||||
−0.209914 | + | 0.977720i | \(0.567319\pi\) | |||||||
\(930\) | 1.40638 | 0.0461169 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.73209 | 0.155005 | ||||||||
\(933\) | 14.1483 | 0.463194 | ||||||||
\(934\) | −6.03857 | −0.197588 | ||||||||
\(935\) | −15.6701 | −0.512467 | ||||||||
\(936\) | −1.21812 | −0.0398155 | ||||||||
\(937\) | 40.7436 | 1.33104 | 0.665518 | − | 0.746382i | \(-0.268211\pi\) | ||||
0.665518 | + | 0.746382i | \(0.268211\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.96795 | −0.292658 | ||||||||
\(940\) | −26.2857 | −0.857345 | ||||||||
\(941\) | 37.3259 | 1.21679 | 0.608395 | − | 0.793634i | \(-0.291814\pi\) | ||||
0.608395 | + | 0.793634i | \(0.291814\pi\) | |||||||
\(942\) | 2.37001 | 0.0772191 | ||||||||
\(943\) | 2.20725 | 0.0718779 | ||||||||
\(944\) | −21.2465 | −0.691516 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.957786 | −0.0311403 | ||||||||
\(947\) | −3.95826 | −0.128626 | −0.0643131 | − | 0.997930i | \(-0.520486\pi\) | ||||
−0.0643131 | + | 0.997930i | \(0.520486\pi\) | |||||||
\(948\) | −4.38098 | −0.142288 | ||||||||
\(949\) | −0.656635 | −0.0213153 | ||||||||
\(950\) | 0.0449704 | 0.00145903 | ||||||||
\(951\) | −8.04996 | −0.261038 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.5625 | −0.406940 | −0.203470 | − | 0.979081i | \(-0.565222\pi\) | ||||
−0.203470 | + | 0.979081i | \(0.565222\pi\) | |||||||
\(954\) | 0.565823 | 0.0183192 | ||||||||
\(955\) | −23.3453 | −0.755437 | ||||||||
\(956\) | −15.7948 | −0.510841 | ||||||||
\(957\) | −13.5589 | −0.438296 | ||||||||
\(958\) | 2.38111 | 0.0769301 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.3161 | −0.526600 | ||||||||
\(961\) | −20.5012 | −0.661328 | ||||||||
\(962\) | 0.584023 | 0.0188296 | ||||||||
\(963\) | −15.4694 | −0.498495 | ||||||||
\(964\) | −32.3496 | −1.04191 | ||||||||
\(965\) | −48.2781 | −1.55413 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.4422 | 1.13974 | 0.569871 | − | 0.821734i | \(-0.306993\pi\) | ||||
0.569871 | + | 0.821734i | \(0.306993\pi\) | |||||||
\(968\) | −6.03346 | −0.193923 | ||||||||
\(969\) | 4.39450 | 0.141172 | ||||||||
\(970\) | 8.21461 | 0.263755 | ||||||||
\(971\) | −28.0134 | −0.898994 | −0.449497 | − | 0.893282i | \(-0.648397\pi\) | ||||
−0.449497 | + | 0.893282i | \(0.648397\pi\) | |||||||
\(972\) | 1.96387 | 0.0629910 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.59790 | −0.115284 | ||||||||
\(975\) | 0.345249 | 0.0110568 | ||||||||
\(976\) | −18.4087 | −0.589249 | ||||||||
\(977\) | 6.84262 | 0.218915 | 0.109457 | − | 0.993991i | \(-0.465089\pi\) | ||||
0.109457 | + | 0.993991i | \(0.465089\pi\) | |||||||
\(978\) | 4.23270 | 0.135347 | ||||||||
\(979\) | −15.2985 | −0.488942 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.96439 | −0.190428 | ||||||||
\(982\) | −7.47174 | −0.238433 | ||||||||
\(983\) | 35.9377 | 1.14623 | 0.573117 | − | 0.819474i | \(-0.305734\pi\) | ||||
0.573117 | + | 0.819474i | \(0.305734\pi\) | |||||||
\(984\) | 0.753499 | 0.0240207 | ||||||||
\(985\) | 34.6345 | 1.10355 | ||||||||
\(986\) | −5.91049 | −0.188228 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.51689 | −0.111887 | ||||||||
\(989\) | −6.42868 | −0.204420 | ||||||||
\(990\) | 0.750871 | 0.0238642 | ||||||||
\(991\) | 49.4628 | 1.57124 | 0.785619 | − | 0.618710i | \(-0.212345\pi\) | ||||
0.785619 | + | 0.618710i | \(0.212345\pi\) | |||||||
\(992\) | 7.21395 | 0.229043 | ||||||||
\(993\) | −17.3497 | −0.550577 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.2649 | −0.579036 | ||||||||
\(996\) | 2.47136 | 0.0783081 | ||||||||
\(997\) | 47.1017 | 1.49173 | 0.745864 | − | 0.666099i | \(-0.232037\pi\) | ||||
0.745864 | + | 0.666099i | \(0.232037\pi\) | |||||||
\(998\) | 0.0183469 | 0.000580760 0 | ||||||||
\(999\) | −1.90046 | −0.0601278 |
(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 | 6027.2.a.y.1.3 | 7 | ||
7.6 | odd | 2 | 861.2.a.m.1.3 | ✓ | 7 | ||
21.20 | even | 2 | 2583.2.a.u.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.m.1.3 | ✓ | 7 | 7.6 | odd | 2 | ||
2583.2.a.u.1.5 | 7 | 21.20 | even | 2 | |||
6027.2.a.y.1.3 | 7 | 1.1 | even | 1 | trivial |