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 | 1.9 | ||
Root | \(0.400970\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.400970 | 0.283529 | 0.141764 | − | 0.989900i | \(-0.454722\pi\) | ||||
0.141764 | + | 0.989900i | \(0.454722\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.83922 | −0.919611 | ||||||||
\(5\) | 2.30562 | 1.03110 | 0.515552 | − | 0.856858i | \(-0.327587\pi\) | ||||
0.515552 | + | 0.856858i | \(0.327587\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.53941 | −0.544265 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.924485 | 0.292348 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.49155 | −1.24573 | −0.622866 | − | 0.782329i | \(-0.714032\pi\) | ||||
−0.622866 | + | 0.782329i | \(0.714032\pi\) | |||||||
\(14\) | −0.400970 | −0.107164 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.06119 | 0.765297 | ||||||||
\(17\) | −7.46771 | −1.81119 | −0.905593 | − | 0.424148i | \(-0.860574\pi\) | ||||
−0.905593 | + | 0.424148i | \(0.860574\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.34729 | 0.309090 | 0.154545 | − | 0.987986i | \(-0.450609\pi\) | ||||
0.154545 | + | 0.987986i | \(0.450609\pi\) | |||||||
\(20\) | −4.24055 | −0.948216 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.27146 | −0.890661 | −0.445330 | − | 0.895366i | \(-0.646914\pi\) | ||||
−0.445330 | + | 0.895366i | \(0.646914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.315883 | 0.0631766 | ||||||||
\(26\) | −1.80098 | −0.353201 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.83922 | 0.347580 | ||||||||
\(29\) | −1.12589 | −0.209072 | −0.104536 | − | 0.994521i | \(-0.533336\pi\) | ||||
−0.104536 | + | 0.994521i | \(0.533336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.11240 | −1.45703 | −0.728515 | − | 0.685030i | \(-0.759789\pi\) | ||||
−0.728515 | + | 0.685030i | \(0.759789\pi\) | |||||||
\(32\) | 4.30627 | 0.761249 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.99433 | −0.513523 | ||||||||
\(35\) | −2.30562 | −0.389721 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0657 | 1.81920 | 0.909598 | − | 0.415490i | \(-0.136390\pi\) | ||||
0.909598 | + | 0.415490i | \(0.136390\pi\) | |||||||
\(38\) | 0.540224 | 0.0876359 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.54930 | −0.561194 | ||||||||
\(41\) | 1.16172 | 0.181430 | 0.0907152 | − | 0.995877i | \(-0.471085\pi\) | ||||
0.0907152 | + | 0.995877i | \(0.471085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.95451 | −1.51805 | −0.759024 | − | 0.651063i | \(-0.774324\pi\) | ||||
−0.759024 | + | 0.651063i | \(0.774324\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.71273 | −0.252528 | ||||||||
\(47\) | 12.8441 | 1.87350 | 0.936751 | − | 0.349998i | \(-0.113818\pi\) | ||||
0.936751 | + | 0.349998i | \(0.113818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.126660 | 0.0179124 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.26096 | 1.14559 | ||||||||
\(53\) | 11.7297 | 1.61120 | 0.805602 | − | 0.592457i | \(-0.201842\pi\) | ||||
0.805602 | + | 0.592457i | \(0.201842\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.53941 | 0.205713 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.451447 | −0.0592779 | ||||||||
\(59\) | −1.04893 | −0.136559 | −0.0682793 | − | 0.997666i | \(-0.521751\pi\) | ||||
−0.0682793 | + | 0.997666i | \(0.521751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.69637 | 0.857382 | 0.428691 | − | 0.903451i | \(-0.358975\pi\) | ||||
0.428691 | + | 0.903451i | \(0.358975\pi\) | |||||||
\(62\) | −3.25283 | −0.413110 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.39569 | −0.549461 | ||||||||
\(65\) | −10.3558 | −1.28448 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.46445 | −0.301080 | −0.150540 | − | 0.988604i | \(-0.548101\pi\) | ||||
−0.150540 | + | 0.988604i | \(0.548101\pi\) | |||||||
\(68\) | 13.7348 | 1.66559 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.924485 | −0.110497 | ||||||||
\(71\) | 8.42283 | 0.999606 | 0.499803 | − | 0.866139i | \(-0.333406\pi\) | ||||
0.499803 | + | 0.866139i | \(0.333406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7770 | 1.26135 | 0.630673 | − | 0.776048i | \(-0.282779\pi\) | ||||
0.630673 | + | 0.776048i | \(0.282779\pi\) | |||||||
\(74\) | 4.43703 | 0.515794 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.47797 | −0.284243 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.71147 | −0.305065 | −0.152532 | − | 0.988298i | \(-0.548743\pi\) | ||||
−0.152532 | + | 0.988298i | \(0.548743\pi\) | |||||||
\(80\) | 7.05793 | 0.789101 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.465816 | 0.0514407 | ||||||||
\(83\) | 9.12912 | 1.00205 | 0.501025 | − | 0.865433i | \(-0.332956\pi\) | ||||
0.501025 | + | 0.865433i | \(0.332956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.2177 | −1.86752 | ||||||||
\(86\) | −3.99146 | −0.430410 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.28542 | 0.560253 | 0.280126 | − | 0.959963i | \(-0.409624\pi\) | ||||
0.280126 | + | 0.959963i | \(0.409624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.49155 | 0.470842 | ||||||||
\(92\) | 7.85617 | 0.819062 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.15009 | 0.531191 | ||||||||
\(95\) | 3.10634 | 0.318704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.74601 | 0.583419 | 0.291709 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291709 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(98\) | 0.400970 | 0.0405041 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.580979 | −0.0580979 | ||||||||
\(101\) | −9.56357 | −0.951611 | −0.475805 | − | 0.879551i | \(-0.657843\pi\) | ||||
−0.475805 | + | 0.879551i | \(0.657843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.807595 | −0.0795747 | −0.0397873 | − | 0.999208i | \(-0.512668\pi\) | ||||
−0.0397873 | + | 0.999208i | \(0.512668\pi\) | |||||||
\(104\) | 6.91435 | 0.678008 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.70328 | 0.456823 | ||||||||
\(107\) | 16.8478 | 1.62874 | 0.814371 | − | 0.580345i | \(-0.197082\pi\) | ||||
0.814371 | + | 0.580345i | \(0.197082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.41870 | −0.902147 | −0.451074 | − | 0.892487i | \(-0.648959\pi\) | ||||
−0.451074 | + | 0.892487i | \(0.648959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.06119 | −0.289255 | ||||||||
\(113\) | −4.35139 | −0.409344 | −0.204672 | − | 0.978831i | \(-0.565613\pi\) | ||||
−0.204672 | + | 0.978831i | \(0.565613\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.84836 | −0.918365 | ||||||||
\(116\) | 2.07076 | 0.192265 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.420588 | −0.0387183 | ||||||||
\(119\) | 7.46771 | 0.684564 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.68504 | 0.243093 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.9205 | 1.33990 | ||||||||
\(125\) | −10.7998 | −0.965963 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.34739 | 0.563240 | 0.281620 | − | 0.959526i | \(-0.409128\pi\) | ||||
0.281620 | + | 0.959526i | \(0.409128\pi\) | |||||||
\(128\) | −10.3751 | −0.917036 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.15237 | −0.364187 | ||||||||
\(131\) | 15.2292 | 1.33058 | 0.665290 | − | 0.746585i | \(-0.268308\pi\) | ||||
0.665290 | + | 0.746585i | \(0.268308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.34729 | −0.116825 | ||||||||
\(134\) | −0.988170 | −0.0853649 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.4959 | 0.985765 | ||||||||
\(137\) | −19.0993 | −1.63176 | −0.815880 | − | 0.578221i | \(-0.803747\pi\) | ||||
−0.815880 | + | 0.578221i | \(0.803747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.93905 | 0.334106 | 0.167053 | − | 0.985948i | \(-0.446575\pi\) | ||||
0.167053 | + | 0.985948i | \(0.446575\pi\) | |||||||
\(140\) | 4.24055 | 0.358392 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.37730 | 0.283417 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.59587 | −0.215575 | ||||||||
\(146\) | 4.32124 | 0.357628 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.3523 | −1.67295 | ||||||||
\(149\) | 20.3815 | 1.66972 | 0.834859 | − | 0.550464i | \(-0.185549\pi\) | ||||
0.834859 | + | 0.550464i | \(0.185549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.91718 | 0.400154 | 0.200077 | − | 0.979780i | \(-0.435881\pi\) | ||||
0.200077 | + | 0.979780i | \(0.435881\pi\) | |||||||
\(152\) | −2.07404 | −0.168227 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.7041 | −1.50235 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.24200 | 0.178931 | 0.0894653 | − | 0.995990i | \(-0.471484\pi\) | ||||
0.0894653 | + | 0.995990i | \(0.471484\pi\) | |||||||
\(158\) | −1.08722 | −0.0864946 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.92863 | 0.784927 | ||||||||
\(161\) | 4.27146 | 0.336638 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.83745 | −0.770529 | −0.385264 | − | 0.922806i | \(-0.625890\pi\) | ||||
−0.385264 | + | 0.922806i | \(0.625890\pi\) | |||||||
\(164\) | −2.13666 | −0.166845 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.66050 | 0.284110 | ||||||||
\(167\) | −8.64481 | −0.668955 | −0.334478 | − | 0.942404i | \(-0.608560\pi\) | ||||
−0.334478 | + | 0.942404i | \(0.608560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.17400 | 0.551847 | ||||||||
\(170\) | −6.90378 | −0.529496 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.3086 | 1.39601 | ||||||||
\(173\) | −15.9672 | −1.21397 | −0.606984 | − | 0.794714i | \(-0.707621\pi\) | ||||
−0.606984 | + | 0.794714i | \(0.707621\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.315883 | −0.0238785 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.11929 | 0.158848 | ||||||||
\(179\) | −17.5759 | −1.31368 | −0.656841 | − | 0.754029i | \(-0.728108\pi\) | ||||
−0.656841 | + | 0.754029i | \(0.728108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7645 | 1.54341 | 0.771707 | − | 0.635979i | \(-0.219403\pi\) | ||||
0.771707 | + | 0.635979i | \(0.219403\pi\) | |||||||
\(182\) | 1.80098 | 0.133497 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.57554 | 0.484756 | ||||||||
\(185\) | 25.5134 | 1.87578 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −23.6231 | −1.72289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.24555 | 0.0903618 | ||||||||
\(191\) | 10.5001 | 0.759762 | 0.379881 | − | 0.925035i | \(-0.375965\pi\) | ||||
0.379881 | + | 0.925035i | \(0.375965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9500 | 0.932164 | 0.466082 | − | 0.884742i | \(-0.345665\pi\) | ||||
0.466082 | + | 0.884742i | \(0.345665\pi\) | |||||||
\(194\) | 2.30398 | 0.165416 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.83922 | −0.131373 | ||||||||
\(197\) | −0.664214 | −0.0473233 | −0.0236617 | − | 0.999720i | \(-0.507532\pi\) | ||||
−0.0236617 | + | 0.999720i | \(0.507532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3550 | 0.946710 | 0.473355 | − | 0.880872i | \(-0.343043\pi\) | ||||
0.473355 | + | 0.880872i | \(0.343043\pi\) | |||||||
\(200\) | −0.486274 | −0.0343848 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.83470 | −0.269809 | ||||||||
\(203\) | 1.12589 | 0.0790218 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.67849 | 0.187074 | ||||||||
\(206\) | −0.323821 | −0.0225617 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.7495 | −0.953354 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0795 | −0.900428 | −0.450214 | − | 0.892921i | \(-0.648652\pi\) | ||||
−0.450214 | + | 0.892921i | \(0.648652\pi\) | |||||||
\(212\) | −21.5736 | −1.48168 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.75548 | 0.461795 | ||||||||
\(215\) | −22.9513 | −1.56527 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.11240 | 0.550706 | ||||||||
\(218\) | −3.77662 | −0.255785 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.5416 | 2.25625 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2293 | 0.685004 | 0.342502 | − | 0.939517i | \(-0.388726\pi\) | ||||
0.342502 | + | 0.939517i | \(0.388726\pi\) | |||||||
\(224\) | −4.30627 | −0.287725 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.74478 | −0.116061 | ||||||||
\(227\) | 2.98867 | 0.198365 | 0.0991824 | − | 0.995069i | \(-0.468377\pi\) | ||||
0.0991824 | + | 0.995069i | \(0.468377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1017 | 1.32836 | 0.664179 | − | 0.747574i | \(-0.268781\pi\) | ||||
0.664179 | + | 0.747574i | \(0.268781\pi\) | |||||||
\(230\) | −3.94890 | −0.260383 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.73321 | 0.113791 | ||||||||
\(233\) | 4.67052 | 0.305976 | 0.152988 | − | 0.988228i | \(-0.451110\pi\) | ||||
0.152988 | + | 0.988228i | \(0.451110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.6136 | 1.93178 | ||||||||
\(236\) | 1.92921 | 0.125581 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.99433 | 0.194094 | ||||||||
\(239\) | −22.7673 | −1.47269 | −0.736347 | − | 0.676604i | \(-0.763451\pi\) | ||||
−0.736347 | + | 0.676604i | \(0.763451\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.83714 | 0.311587 | 0.155794 | − | 0.987790i | \(-0.450207\pi\) | ||||
0.155794 | + | 0.987790i | \(0.450207\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.3161 | −0.788459 | ||||||||
\(245\) | 2.30562 | 0.147301 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.05143 | −0.385043 | ||||||||
\(248\) | 12.4883 | 0.793011 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.33039 | −0.273878 | ||||||||
\(251\) | −16.0556 | −1.01342 | −0.506710 | − | 0.862117i | \(-0.669138\pi\) | ||||
−0.506710 | + | 0.862117i | \(0.669138\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.54512 | 0.159695 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.63128 | 0.289455 | ||||||||
\(257\) | 12.1743 | 0.759411 | 0.379706 | − | 0.925107i | \(-0.376025\pi\) | ||||
0.379706 | + | 0.925107i | \(0.376025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0657 | −0.687591 | ||||||||
\(260\) | 19.0466 | 1.18122 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.10645 | 0.377258 | ||||||||
\(263\) | 18.8786 | 1.16411 | 0.582053 | − | 0.813151i | \(-0.302250\pi\) | ||||
0.582053 | + | 0.813151i | \(0.302250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.0443 | 1.66132 | ||||||||
\(266\) | −0.540224 | −0.0331233 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.53267 | 0.276877 | ||||||||
\(269\) | −0.711037 | −0.0433527 | −0.0216763 | − | 0.999765i | \(-0.506900\pi\) | ||||
−0.0216763 | + | 0.999765i | \(0.506900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7238 | −0.894404 | −0.447202 | − | 0.894433i | \(-0.647580\pi\) | ||||
−0.447202 | + | 0.894433i | \(0.647580\pi\) | |||||||
\(272\) | −22.8601 | −1.38609 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.65823 | −0.462651 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.5829 | −1.05645 | −0.528227 | − | 0.849103i | \(-0.677143\pi\) | ||||
−0.528227 | + | 0.849103i | \(0.677143\pi\) | |||||||
\(278\) | 1.57944 | 0.0947286 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.54930 | 0.212111 | ||||||||
\(281\) | −14.9728 | −0.893200 | −0.446600 | − | 0.894734i | \(-0.647365\pi\) | ||||
−0.446600 | + | 0.894734i | \(0.647365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.4418 | −1.03681 | −0.518404 | − | 0.855136i | \(-0.673474\pi\) | ||||
−0.518404 | + | 0.855136i | \(0.673474\pi\) | |||||||
\(284\) | −15.4915 | −0.919249 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.16172 | −0.0685742 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7667 | 2.28039 | ||||||||
\(290\) | −1.04087 | −0.0611217 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −19.8212 | −1.15995 | ||||||||
\(293\) | 26.0123 | 1.51966 | 0.759828 | − | 0.650124i | \(-0.225283\pi\) | ||||
0.759828 | + | 0.650124i | \(0.225283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.41843 | −0.140806 | ||||||||
\(296\) | −17.0347 | −0.990124 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.17237 | 0.473413 | ||||||||
\(299\) | 19.1855 | 1.10952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.95451 | 0.573768 | ||||||||
\(302\) | 1.97164 | 0.113455 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.12431 | 0.236546 | ||||||||
\(305\) | 15.4393 | 0.884051 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5921 | 1.34647 | 0.673236 | − | 0.739428i | \(-0.264904\pi\) | ||||
0.673236 | + | 0.739428i | \(0.264904\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.49979 | −0.425960 | ||||||||
\(311\) | −4.55191 | −0.258115 | −0.129058 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129058 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1273 | −0.742000 | −0.371000 | − | 0.928633i | \(-0.620985\pi\) | ||||
−0.371000 | + | 0.928633i | \(0.620985\pi\) | |||||||
\(314\) | 0.898973 | 0.0507320 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.98700 | 0.280541 | ||||||||
\(317\) | 8.94352 | 0.502318 | 0.251159 | − | 0.967946i | \(-0.419188\pi\) | ||||
0.251159 | + | 0.967946i | \(0.419188\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.1348 | −0.566552 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.71273 | 0.0954466 | ||||||||
\(323\) | −10.0612 | −0.559820 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.41880 | −0.0787010 | ||||||||
\(326\) | −3.94453 | −0.218467 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.78837 | −0.0987462 | ||||||||
\(329\) | −12.8441 | −0.708117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9302 | 1.42525 | 0.712627 | − | 0.701543i | \(-0.247505\pi\) | ||||
0.712627 | + | 0.701543i | \(0.247505\pi\) | |||||||
\(332\) | −16.7905 | −0.921497 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.46631 | −0.189668 | ||||||||
\(335\) | −5.68208 | −0.310445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7560 | 0.858285 | 0.429142 | − | 0.903237i | \(-0.358816\pi\) | ||||
0.429142 | + | 0.903237i | \(0.358816\pi\) | |||||||
\(338\) | 2.87656 | 0.156464 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 31.6672 | 1.71739 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 15.3241 | 0.826220 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.40239 | −0.344195 | ||||||||
\(347\) | −2.22968 | −0.119696 | −0.0598478 | − | 0.998208i | \(-0.519062\pi\) | ||||
−0.0598478 | + | 0.998208i | \(0.519062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.61826 | −0.514854 | −0.257427 | − | 0.966298i | \(-0.582875\pi\) | ||||
−0.257427 | + | 0.966298i | \(0.582875\pi\) | |||||||
\(350\) | −0.126660 | −0.00677024 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.98576 | −0.531488 | −0.265744 | − | 0.964044i | \(-0.585618\pi\) | ||||
−0.265744 | + | 0.964044i | \(0.585618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4198 | 1.03070 | ||||||||
\(356\) | −9.72106 | −0.515215 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.04740 | −0.372466 | ||||||||
\(359\) | 10.2469 | 0.540808 | 0.270404 | − | 0.962747i | \(-0.412843\pi\) | ||||
0.270404 | + | 0.962747i | \(0.412843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1848 | −0.904463 | ||||||||
\(362\) | 8.32595 | 0.437602 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.26096 | −0.432992 | ||||||||
\(365\) | 24.8475 | 1.30058 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.69263 | 0.192754 | 0.0963769 | − | 0.995345i | \(-0.469275\pi\) | ||||
0.0963769 | + | 0.995345i | \(0.469275\pi\) | |||||||
\(368\) | −13.0757 | −0.681620 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.2301 | 0.531838 | ||||||||
\(371\) | −11.7297 | −0.608978 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.2657 | −0.893986 | −0.446993 | − | 0.894538i | \(-0.647505\pi\) | ||||
−0.446993 | + | 0.894538i | \(0.647505\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.7723 | −1.01968 | ||||||||
\(377\) | 5.05697 | 0.260447 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.18952 | −0.266568 | −0.133284 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133284 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(380\) | −5.71326 | −0.293084 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.21023 | 0.215414 | ||||||||
\(383\) | −17.6212 | −0.900400 | −0.450200 | − | 0.892928i | \(-0.648647\pi\) | ||||
−0.450200 | + | 0.892928i | \(0.648647\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.19258 | 0.264295 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.5682 | −0.536519 | ||||||||
\(389\) | 10.6188 | 0.538396 | 0.269198 | − | 0.963085i | \(-0.413241\pi\) | ||||
0.269198 | + | 0.963085i | \(0.413241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.8980 | 1.61315 | ||||||||
\(392\) | −1.53941 | −0.0777521 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.266330 | −0.0134175 | ||||||||
\(395\) | −6.25163 | −0.314554 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6262 | 1.13557 | 0.567787 | − | 0.823175i | \(-0.307800\pi\) | ||||
0.567787 | + | 0.823175i | \(0.307800\pi\) | |||||||
\(398\) | 5.35495 | 0.268419 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.966976 | 0.0483488 | ||||||||
\(401\) | 4.60950 | 0.230187 | 0.115094 | − | 0.993355i | \(-0.463283\pi\) | ||||
0.115094 | + | 0.993355i | \(0.463283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.4372 | 1.81507 | ||||||||
\(404\) | 17.5895 | 0.875112 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.451447 | 0.0224049 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.0486 | −1.04079 | −0.520394 | − | 0.853926i | \(-0.674215\pi\) | ||||
−0.520394 | + | 0.853926i | \(0.674215\pi\) | |||||||
\(410\) | 1.07399 | 0.0530408 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.48535 | 0.0731778 | ||||||||
\(413\) | 1.04893 | 0.0516143 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.0483 | 1.03322 | ||||||||
\(416\) | −19.3418 | −0.948311 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.0827 | 0.687984 | 0.343992 | − | 0.938973i | \(-0.388221\pi\) | ||||
0.343992 | + | 0.938973i | \(0.388221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.5676 | 1.34356 | 0.671781 | − | 0.740750i | \(-0.265530\pi\) | ||||
0.671781 | + | 0.740750i | \(0.265530\pi\) | |||||||
\(422\) | −5.24448 | −0.255297 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0569 | −0.876922 | ||||||||
\(425\) | −2.35892 | −0.114424 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.69637 | −0.324060 | ||||||||
\(428\) | −30.9869 | −1.49781 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.20279 | −0.443798 | ||||||||
\(431\) | 34.4396 | 1.65890 | 0.829448 | − | 0.558584i | \(-0.188655\pi\) | ||||
0.829448 | + | 0.558584i | \(0.188655\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.1385 | 0.775564 | 0.387782 | − | 0.921751i | \(-0.373241\pi\) | ||||
0.387782 | + | 0.921751i | \(0.373241\pi\) | |||||||
\(434\) | 3.25283 | 0.156141 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.3231 | 0.829625 | ||||||||
\(437\) | −5.75491 | −0.275294 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3036 | −0.921309 | −0.460655 | − | 0.887580i | \(-0.652385\pi\) | ||||
−0.460655 | + | 0.887580i | \(0.652385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.4492 | 0.639712 | ||||||||
\(443\) | 13.1312 | 0.623880 | 0.311940 | − | 0.950102i | \(-0.399021\pi\) | ||||
0.311940 | + | 0.950102i | \(0.399021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.1862 | 0.577679 | ||||||||
\(446\) | 4.10164 | 0.194218 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.39569 | 0.207677 | ||||||||
\(449\) | −12.7511 | −0.601763 | −0.300882 | − | 0.953662i | \(-0.597281\pi\) | ||||
−0.300882 | + | 0.953662i | \(0.597281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.00317 | 0.376437 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.19837 | 0.0562421 | ||||||||
\(455\) | 10.3558 | 0.485488 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.19436 | 0.430094 | 0.215047 | − | 0.976604i | \(-0.431009\pi\) | ||||
0.215047 | + | 0.976604i | \(0.431009\pi\) | |||||||
\(458\) | 8.06018 | 0.376628 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.1133 | 0.844539 | ||||||||
\(461\) | −16.0714 | −0.748521 | −0.374260 | − | 0.927324i | \(-0.622103\pi\) | ||||
−0.374260 | + | 0.927324i | \(0.622103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.9203 | 1.52994 | 0.764968 | − | 0.644068i | \(-0.222755\pi\) | ||||
0.764968 | + | 0.644068i | \(0.222755\pi\) | |||||||
\(464\) | −3.44655 | −0.160002 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.87274 | 0.0867530 | ||||||||
\(467\) | −8.50986 | −0.393790 | −0.196895 | − | 0.980425i | \(-0.563086\pi\) | ||||
−0.196895 | + | 0.980425i | \(0.563086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.46445 | 0.113798 | ||||||||
\(470\) | 11.8742 | 0.547714 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.61473 | 0.0743240 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.425586 | 0.0195272 | ||||||||
\(476\) | −13.7348 | −0.629533 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.12901 | −0.417551 | ||||||||
\(479\) | 9.52240 | 0.435089 | 0.217545 | − | 0.976050i | \(-0.430195\pi\) | ||||
0.217545 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.7023 | −2.26623 | ||||||||
\(482\) | 1.93955 | 0.0883439 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.2481 | 0.601566 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.09438 | −0.0495910 | −0.0247955 | − | 0.999693i | \(-0.507893\pi\) | ||||
−0.0247955 | + | 0.999693i | \(0.507893\pi\) | |||||||
\(488\) | −10.3085 | −0.466643 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.924485 | 0.0417640 | ||||||||
\(491\) | −20.6684 | −0.932751 | −0.466375 | − | 0.884587i | \(-0.654440\pi\) | ||||
−0.466375 | + | 0.884587i | \(0.654440\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.40780 | 0.378668 | ||||||||
\(494\) | −2.42644 | −0.109171 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.8336 | −1.11506 | ||||||||
\(497\) | −8.42283 | −0.377816 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8350 | 1.06700 | 0.533500 | − | 0.845800i | \(-0.320876\pi\) | ||||
0.533500 | + | 0.845800i | \(0.320876\pi\) | |||||||
\(500\) | 19.8632 | 0.888311 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.43781 | −0.287333 | ||||||||
\(503\) | −15.1096 | −0.673706 | −0.336853 | − | 0.941557i | \(-0.609362\pi\) | ||||
−0.336853 | + | 0.941557i | \(0.609362\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.0500 | −0.981210 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.6743 | −0.517962 | ||||||||
\(509\) | 1.67629 | 0.0743004 | 0.0371502 | − | 0.999310i | \(-0.488172\pi\) | ||||
0.0371502 | + | 0.999310i | \(0.488172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7770 | −0.476744 | ||||||||
\(512\) | 22.6072 | 0.999105 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.88152 | 0.215315 | ||||||||
\(515\) | −1.86201 | −0.0820498 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.43703 | −0.194952 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.9419 | 0.699097 | ||||||||
\(521\) | −35.9717 | −1.57595 | −0.787974 | − | 0.615709i | \(-0.788870\pi\) | ||||
−0.787974 | + | 0.615709i | \(0.788870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9612 | 0.697933 | 0.348967 | − | 0.937135i | \(-0.386533\pi\) | ||||
0.348967 | + | 0.937135i | \(0.386533\pi\) | |||||||
\(524\) | −28.0099 | −1.22362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.56976 | 0.330057 | ||||||||
\(527\) | 60.5811 | 2.63895 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.75463 | −0.206723 | ||||||||
\(530\) | 10.8440 | 0.471032 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.47797 | 0.107434 | ||||||||
\(533\) | −5.21793 | −0.226014 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.8447 | 1.67940 | ||||||||
\(536\) | 3.79380 | 0.163867 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.285104 | −0.0122917 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.68655 | 0.330471 | 0.165235 | − | 0.986254i | \(-0.447162\pi\) | ||||
0.165235 | + | 0.986254i | \(0.447162\pi\) | |||||||
\(542\) | −5.90379 | −0.253589 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.1580 | −1.37876 | ||||||||
\(545\) | −21.7159 | −0.930208 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.2442 | −0.651794 | −0.325897 | − | 0.945405i | \(-0.605666\pi\) | ||||
−0.325897 | + | 0.945405i | \(0.605666\pi\) | |||||||
\(548\) | 35.1278 | 1.50058 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.51690 | −0.0646221 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.71147 | 0.115304 | ||||||||
\(554\) | −7.05022 | −0.299535 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.24479 | −0.307248 | ||||||||
\(557\) | 2.09493 | 0.0887649 | 0.0443825 | − | 0.999015i | \(-0.485868\pi\) | ||||
0.0443825 | + | 0.999015i | \(0.485868\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.7112 | 1.89108 | ||||||||
\(560\) | −7.05793 | −0.298252 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00363 | −0.253248 | ||||||||
\(563\) | −9.86821 | −0.415895 | −0.207948 | − | 0.978140i | \(-0.566678\pi\) | ||||
−0.207948 | + | 0.978140i | \(0.566678\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0326 | −0.422077 | ||||||||
\(566\) | −6.99365 | −0.293965 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.9662 | −0.544051 | ||||||||
\(569\) | −15.2708 | −0.640186 | −0.320093 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320093 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5400 | 0.859573 | 0.429787 | − | 0.902930i | \(-0.358589\pi\) | ||||
0.429787 | + | 0.902930i | \(0.358589\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.465816 | −0.0194428 | ||||||||
\(575\) | −1.34928 | −0.0562689 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.2582 | 1.84249 | 0.921246 | − | 0.388980i | \(-0.127172\pi\) | ||||
0.921246 | + | 0.388980i | \(0.127172\pi\) | |||||||
\(578\) | 15.5443 | 0.646557 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.77438 | 0.198245 | ||||||||
\(581\) | −9.12912 | −0.378740 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −16.5902 | −0.686507 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.4302 | 0.430866 | ||||||||
\(587\) | 3.56942 | 0.147326 | 0.0736628 | − | 0.997283i | \(-0.476531\pi\) | ||||
0.0736628 | + | 0.997283i | \(0.476531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.9298 | −0.450354 | ||||||||
\(590\) | −0.969716 | −0.0399226 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.8743 | 1.39222 | ||||||||
\(593\) | −11.2563 | −0.462240 | −0.231120 | − | 0.972925i | \(-0.574239\pi\) | ||||
−0.231120 | + | 0.972925i | \(0.574239\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.2177 | 0.705857 | ||||||||
\(596\) | −37.4861 | −1.53549 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.69280 | 0.314582 | ||||||||
\(599\) | −43.6263 | −1.78252 | −0.891262 | − | 0.453488i | \(-0.850179\pi\) | ||||
−0.891262 | + | 0.453488i | \(0.850179\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.7286 | 0.723166 | 0.361583 | − | 0.932340i | \(-0.382236\pi\) | ||||
0.361583 | + | 0.932340i | \(0.382236\pi\) | |||||||
\(602\) | 3.99146 | 0.162680 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.04378 | −0.367986 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.16734 | 0.290913 | 0.145457 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145457 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(608\) | 5.80181 | 0.235294 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.19069 | 0.250654 | ||||||||
\(611\) | −57.6898 | −2.33388 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3784 | 0.499957 | 0.249979 | − | 0.968251i | \(-0.419576\pi\) | ||||
0.249979 | + | 0.968251i | \(0.419576\pi\) | |||||||
\(614\) | 9.45972 | 0.381763 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.11777 | 0.246292 | 0.123146 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123146 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.8234 | 1.56045 | 0.780223 | − | 0.625501i | \(-0.215106\pi\) | ||||
0.780223 | + | 0.625501i | \(0.215106\pi\) | |||||||
\(620\) | 34.4010 | 1.38158 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.82518 | −0.0731831 | ||||||||
\(623\) | −5.28542 | −0.211756 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4796 | −1.05919 | ||||||||
\(626\) | −5.26366 | −0.210378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.12353 | −0.164547 | ||||||||
\(629\) | −82.6357 | −3.29490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.70799 | −0.386469 | −0.193234 | − | 0.981153i | \(-0.561898\pi\) | ||||
−0.193234 | + | 0.981153i | \(0.561898\pi\) | |||||||
\(632\) | 4.17408 | 0.166036 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.58609 | 0.142422 | ||||||||
\(635\) | 14.6347 | 0.580759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.49155 | −0.177962 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.9210 | −0.945560 | ||||||||
\(641\) | −14.8483 | −0.586473 | −0.293236 | − | 0.956040i | \(-0.594732\pi\) | ||||
−0.293236 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.05956 | −0.0417851 | −0.0208926 | − | 0.999782i | \(-0.506651\pi\) | ||||
−0.0208926 | + | 0.999782i | \(0.506651\pi\) | |||||||
\(644\) | −7.85617 | −0.309576 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.03424 | −0.158725 | ||||||||
\(647\) | −12.5622 | −0.493872 | −0.246936 | − | 0.969032i | \(-0.579424\pi\) | ||||
−0.246936 | + | 0.969032i | \(0.579424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.568898 | −0.0223140 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.0933 | 0.708587 | ||||||||
\(653\) | 29.6143 | 1.15890 | 0.579449 | − | 0.815009i | \(-0.303268\pi\) | ||||
0.579449 | + | 0.815009i | \(0.303268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.1127 | 1.37197 | ||||||||
\(656\) | 3.55625 | 0.138848 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.15009 | −0.200771 | ||||||||
\(659\) | 9.45208 | 0.368201 | 0.184100 | − | 0.982907i | \(-0.441063\pi\) | ||||
0.184100 | + | 0.982907i | \(0.441063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.94284 | −0.347836 | −0.173918 | − | 0.984760i | \(-0.555643\pi\) | ||||
−0.173918 | + | 0.984760i | \(0.555643\pi\) | |||||||
\(662\) | 10.3972 | 0.404100 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.0535 | −0.545381 | ||||||||
\(665\) | −3.10634 | −0.120459 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.80918 | 0.186212 | ||||||||
\(668\) | 15.8997 | 0.615179 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.27834 | −0.0880201 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.68207 | −0.296122 | −0.148061 | − | 0.988978i | \(-0.547303\pi\) | ||||
−0.148061 | + | 0.988978i | \(0.547303\pi\) | |||||||
\(674\) | 6.31769 | 0.243348 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.1946 | −0.507484 | ||||||||
\(677\) | 35.0474 | 1.34698 | 0.673490 | − | 0.739197i | \(-0.264795\pi\) | ||||
0.673490 | + | 0.739197i | \(0.264795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.74601 | −0.220512 | ||||||||
\(680\) | 26.5052 | 1.01643 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.5098 | −0.899577 | −0.449789 | − | 0.893135i | \(-0.648501\pi\) | ||||
−0.449789 | + | 0.893135i | \(0.648501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.0356 | −1.68251 | ||||||||
\(686\) | −0.400970 | −0.0153091 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.4726 | −1.16176 | ||||||||
\(689\) | −52.6847 | −2.00713 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.2445 | −0.617968 | −0.308984 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308984 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(692\) | 29.3673 | 1.11638 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.894036 | −0.0339371 | ||||||||
\(695\) | 9.08195 | 0.344498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.67540 | −0.328604 | ||||||||
\(698\) | −3.85664 | −0.145976 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.580979 | 0.0219589 | ||||||||
\(701\) | 22.5424 | 0.851413 | 0.425706 | − | 0.904861i | \(-0.360026\pi\) | ||||
0.425706 | + | 0.904861i | \(0.360026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.9088 | 0.562295 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00399 | −0.150692 | ||||||||
\(707\) | 9.56357 | 0.359675 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.1185 | 0.905791 | 0.452896 | − | 0.891564i | \(-0.350391\pi\) | ||||
0.452896 | + | 0.891564i | \(0.350391\pi\) | |||||||
\(710\) | 7.78678 | 0.292233 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.13644 | −0.304926 | ||||||||
\(713\) | 34.6518 | 1.29772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.3259 | 1.20808 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.10868 | 0.153335 | ||||||||
\(719\) | 32.2087 | 1.20118 | 0.600591 | − | 0.799557i | \(-0.294932\pi\) | ||||
0.600591 | + | 0.799557i | \(0.294932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.807595 | 0.0300764 | ||||||||
\(722\) | −6.89059 | −0.256441 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.1906 | −1.41934 | ||||||||
\(725\) | −0.355648 | −0.0132084 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.29214 | 0.270450 | 0.135225 | − | 0.990815i | \(-0.456824\pi\) | ||||
0.135225 | + | 0.990815i | \(0.456824\pi\) | |||||||
\(728\) | −6.91435 | −0.256263 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.96313 | 0.368752 | ||||||||
\(731\) | 74.3374 | 2.74947 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.81868 | −0.214918 | −0.107459 | − | 0.994210i | \(-0.534271\pi\) | ||||
−0.107459 | + | 0.994210i | \(0.534271\pi\) | |||||||
\(734\) | 1.48063 | 0.0546512 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.3941 | −0.678014 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1113 | 0.519093 | 0.259546 | − | 0.965731i | \(-0.416427\pi\) | ||||
0.259546 | + | 0.965731i | \(0.416427\pi\) | |||||||
\(740\) | −46.9248 | −1.72499 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.70328 | −0.172663 | ||||||||
\(743\) | −2.28107 | −0.0836843 | −0.0418422 | − | 0.999124i | \(-0.513323\pi\) | ||||
−0.0418422 | + | 0.999124i | \(0.513323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.9920 | 1.72165 | ||||||||
\(746\) | −6.92304 | −0.253471 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.8478 | −0.615607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4870 | −0.930033 | −0.465016 | − | 0.885302i | \(-0.653952\pi\) | ||||
−0.465016 | + | 0.885302i | \(0.653952\pi\) | |||||||
\(752\) | 39.3181 | 1.43378 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.02770 | 0.0738443 | ||||||||
\(755\) | 11.3371 | 0.412601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1462 | 0.913953 | 0.456976 | − | 0.889479i | \(-0.348932\pi\) | ||||
0.456976 | + | 0.889479i | \(0.348932\pi\) | |||||||
\(758\) | −2.08084 | −0.0755796 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.78195 | −0.173460 | ||||||||
\(761\) | −28.4523 | −1.03139 | −0.515697 | − | 0.856771i | \(-0.672467\pi\) | ||||
−0.515697 | + | 0.856771i | \(0.672467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.41870 | 0.340980 | ||||||||
\(764\) | −19.3120 | −0.698685 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.06556 | −0.255289 | ||||||||
\(767\) | 4.71130 | 0.170115 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.0119 | 1.62317 | 0.811586 | − | 0.584233i | \(-0.198605\pi\) | ||||
0.811586 | + | 0.584233i | \(0.198605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.8180 | −0.857229 | ||||||||
\(773\) | 30.8653 | 1.11015 | 0.555074 | − | 0.831801i | \(-0.312690\pi\) | ||||
0.555074 | + | 0.831801i | \(0.312690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.56257 | −0.0920502 | ||||||||
\(776\) | −8.84548 | −0.317534 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.25783 | 0.152651 | ||||||||
\(779\) | 1.56518 | 0.0560783 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.7902 | 0.457375 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.06119 | 0.109328 | ||||||||
\(785\) | 5.16919 | 0.184496 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.6535 | 1.27091 | 0.635456 | − | 0.772137i | \(-0.280812\pi\) | ||||
0.635456 | + | 0.772137i | \(0.280812\pi\) | |||||||
\(788\) | 1.22164 | 0.0435191 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.50672 | −0.0891850 | ||||||||
\(791\) | 4.35139 | 0.154718 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.0771 | −1.06807 | ||||||||
\(794\) | 9.07241 | 0.321968 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.5628 | −0.870605 | ||||||||
\(797\) | 44.3444 | 1.57076 | 0.785379 | − | 0.619015i | \(-0.212468\pi\) | ||||
0.785379 | + | 0.619015i | \(0.212468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −95.9158 | −3.39326 | ||||||||
\(800\) | 1.36028 | 0.0480931 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.84827 | 0.0652647 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.84836 | 0.347109 | ||||||||
\(806\) | 14.6102 | 0.514624 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.7223 | 0.517928 | ||||||||
\(809\) | −6.41321 | −0.225476 | −0.112738 | − | 0.993625i | \(-0.535962\pi\) | ||||
−0.112738 | + | 0.993625i | \(0.535962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.5913 | −1.21466 | −0.607332 | − | 0.794448i | \(-0.707760\pi\) | ||||
−0.607332 | + | 0.794448i | \(0.707760\pi\) | |||||||
\(812\) | −2.07076 | −0.0726693 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.6814 | −0.794496 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.4116 | −0.469214 | ||||||||
\(818\) | −8.43987 | −0.295093 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.92634 | −0.172035 | ||||||||
\(821\) | 13.8043 | 0.481772 | 0.240886 | − | 0.970553i | \(-0.422562\pi\) | ||||
0.240886 | + | 0.970553i | \(0.422562\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −56.7973 | −1.97983 | −0.989915 | − | 0.141666i | \(-0.954754\pi\) | ||||
−0.989915 | + | 0.141666i | \(0.954754\pi\) | |||||||
\(824\) | 1.24322 | 0.0433097 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.420588 | 0.0146341 | ||||||||
\(827\) | −5.29390 | −0.184087 | −0.0920434 | − | 0.995755i | \(-0.529340\pi\) | ||||
−0.0920434 | + | 0.995755i | \(0.529340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.6618 | 1.06493 | 0.532463 | − | 0.846453i | \(-0.321266\pi\) | ||||
0.532463 | + | 0.846453i | \(0.321266\pi\) | |||||||
\(830\) | 8.43973 | 0.292947 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.7434 | 0.684481 | ||||||||
\(833\) | −7.46771 | −0.258741 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.9316 | −0.689763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.64673 | 0.195063 | ||||||||
\(839\) | −15.4714 | −0.534133 | −0.267067 | − | 0.963678i | \(-0.586054\pi\) | ||||
−0.267067 | + | 0.963678i | \(0.586054\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7324 | −0.956289 | ||||||||
\(842\) | 11.0538 | 0.380938 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.0561 | 0.828044 | ||||||||
\(845\) | 16.5405 | 0.569011 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 35.9069 | 1.23305 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.945857 | −0.0324426 | ||||||||
\(851\) | −47.2668 | −1.62029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.3631 | 1.24505 | 0.622524 | − | 0.782600i | \(-0.286107\pi\) | ||||
0.622524 | + | 0.782600i | \(0.286107\pi\) | |||||||
\(854\) | −2.68504 | −0.0918803 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.9358 | −0.886467 | ||||||||
\(857\) | −17.0833 | −0.583554 | −0.291777 | − | 0.956486i | \(-0.594246\pi\) | ||||
−0.291777 | + | 0.956486i | \(0.594246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.3315 | 0.727822 | 0.363911 | − | 0.931434i | \(-0.381441\pi\) | ||||
0.363911 | + | 0.931434i | \(0.381441\pi\) | |||||||
\(860\) | 42.2126 | 1.43944 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.8092 | 0.470345 | ||||||||
\(863\) | 14.9495 | 0.508887 | 0.254443 | − | 0.967088i | \(-0.418108\pi\) | ||||
0.254443 | + | 0.967088i | \(0.418108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.8144 | −1.25173 | ||||||||
\(866\) | 6.47104 | 0.219895 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.9205 | −0.506435 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.0692 | 0.375065 | ||||||||
\(872\) | 14.4993 | 0.491007 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.30755 | −0.0780539 | ||||||||
\(875\) | 10.7998 | 0.365100 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.2499 | −0.582488 | −0.291244 | − | 0.956649i | \(-0.594069\pi\) | ||||
−0.291244 | + | 0.956649i | \(0.594069\pi\) | |||||||
\(878\) | −7.74015 | −0.261218 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.58251 | −0.0870069 | −0.0435035 | − | 0.999053i | \(-0.513852\pi\) | ||||
−0.0435035 | + | 0.999053i | \(0.513852\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.2072 | 1.21847 | 0.609234 | − | 0.792990i | \(-0.291477\pi\) | ||||
0.609234 | + | 0.792990i | \(0.291477\pi\) | |||||||
\(884\) | −61.6904 | −2.07487 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.26520 | 0.176888 | ||||||||
\(887\) | −53.1757 | −1.78546 | −0.892732 | − | 0.450587i | \(-0.851215\pi\) | ||||
−0.892732 | + | 0.450587i | \(0.851215\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.34739 | −0.212885 | ||||||||
\(890\) | 4.88629 | 0.163789 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.8140 | −0.629938 | ||||||||
\(893\) | 17.3047 | 0.579081 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.5233 | −1.35454 | ||||||||
\(896\) | 10.3751 | 0.346607 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.11282 | −0.170617 | ||||||||
\(899\) | 9.13365 | 0.304624 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −87.5943 | −2.91819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.69858 | 0.222792 | ||||||||
\(905\) | 47.8751 | 1.59142 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.9616 | 1.62574 | 0.812872 | − | 0.582443i | \(-0.197903\pi\) | ||||
0.812872 | + | 0.582443i | \(0.197903\pi\) | |||||||
\(908\) | −5.49682 | −0.182418 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.15237 | 0.137650 | ||||||||
\(911\) | 0.998096 | 0.0330684 | 0.0165342 | − | 0.999863i | \(-0.494737\pi\) | ||||
0.0165342 | + | 0.999863i | \(0.494737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.68667 | 0.121944 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.9715 | −1.22157 | ||||||||
\(917\) | −15.2292 | −0.502912 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.3533 | −1.75996 | −0.879982 | − | 0.475008i | \(-0.842445\pi\) | ||||
−0.879982 | + | 0.475008i | \(0.842445\pi\) | |||||||
\(920\) | 15.1607 | 0.499834 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.44416 | −0.212227 | ||||||||
\(923\) | −37.8315 | −1.24524 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.49547 | 0.114930 | ||||||||
\(926\) | 13.2001 | 0.433781 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.84837 | −0.159156 | ||||||||
\(929\) | 2.72724 | 0.0894778 | 0.0447389 | − | 0.998999i | \(-0.485754\pi\) | ||||
0.0447389 | + | 0.998999i | \(0.485754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.34729 | 0.0441557 | ||||||||
\(932\) | −8.59013 | −0.281379 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.41220 | −0.111651 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.6735 | −0.414024 | −0.207012 | − | 0.978338i | \(-0.566374\pi\) | ||||
−0.207012 | + | 0.978338i | \(0.566374\pi\) | |||||||
\(938\) | 0.988170 | 0.0322649 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −54.4659 | −1.77648 | ||||||||
\(941\) | 6.00255 | 0.195678 | 0.0978388 | − | 0.995202i | \(-0.468807\pi\) | ||||
0.0978388 | + | 0.995202i | \(0.468807\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.96225 | −0.161593 | ||||||||
\(944\) | −3.21096 | −0.104508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.2935 | −0.659450 | −0.329725 | − | 0.944077i | \(-0.606956\pi\) | ||||
−0.329725 | + | 0.944077i | \(0.606956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.4052 | −1.57130 | ||||||||
\(950\) | 0.170647 | 0.00553653 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.4959 | −0.372584 | ||||||||
\(953\) | 25.6882 | 0.832122 | 0.416061 | − | 0.909337i | \(-0.363410\pi\) | ||||
0.416061 | + | 0.909337i | \(0.363410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.2093 | 0.783394 | ||||||||
\(956\) | 41.8741 | 1.35431 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.81820 | 0.123360 | ||||||||
\(959\) | 19.0993 | 0.616747 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.8111 | 1.12294 | ||||||||
\(962\) | −19.9291 | −0.642541 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.89657 | −0.286539 | ||||||||
\(965\) | 29.8579 | 0.961158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.86788 | 0.124383 | 0.0621914 | − | 0.998064i | \(-0.480191\pi\) | ||||
0.0621914 | + | 0.998064i | \(0.480191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.31210 | 0.170561 | ||||||||
\(971\) | −25.8216 | −0.828656 | −0.414328 | − | 0.910128i | \(-0.635983\pi\) | ||||
−0.414328 | + | 0.910128i | \(0.635983\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.93905 | −0.126280 | ||||||||
\(974\) | −0.438813 | −0.0140605 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.4988 | 0.656152 | ||||||||
\(977\) | −52.2227 | −1.67075 | −0.835376 | − | 0.549679i | \(-0.814750\pi\) | ||||
−0.835376 | + | 0.549679i | \(0.814750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.24055 | −0.135459 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.28740 | −0.264462 | ||||||||
\(983\) | −32.4955 | −1.03645 | −0.518223 | − | 0.855246i | \(-0.673406\pi\) | ||||
−0.518223 | + | 0.855246i | \(0.673406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.53143 | −0.0487953 | ||||||||
\(986\) | 3.37128 | 0.107363 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.1299 | 0.354090 | ||||||||
\(989\) | 42.5203 | 1.35207 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.37062 | 0.0435391 | 0.0217695 | − | 0.999763i | \(-0.493070\pi\) | ||||
0.0217695 | + | 0.999763i | \(0.493070\pi\) | |||||||
\(992\) | −34.9342 | −1.10916 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.37730 | −0.107122 | ||||||||
\(995\) | 30.7915 | 0.976157 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.64360 | −0.273746 | −0.136873 | − | 0.990589i | \(-0.543705\pi\) | ||||
−0.136873 | + | 0.990589i | \(0.543705\pi\) | |||||||
\(998\) | 9.55712 | 0.302525 | ||||||||
\(999\) | 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.1.9 | 16 | ||
3.2 | odd | 2 | inner | 7623.2.a.db.1.8 | 16 | ||
11.7 | odd | 10 | 693.2.m.k.379.4 | yes | 32 | ||
11.8 | odd | 10 | 693.2.m.k.64.4 | ✓ | 32 | ||
11.10 | odd | 2 | 7623.2.a.dc.1.8 | 16 | |||
33.8 | even | 10 | 693.2.m.k.64.5 | yes | 32 | ||
33.29 | even | 10 | 693.2.m.k.379.5 | yes | 32 | ||
33.32 | even | 2 | 7623.2.a.dc.1.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.k.64.4 | ✓ | 32 | 11.8 | odd | 10 | ||
693.2.m.k.64.5 | yes | 32 | 33.8 | even | 10 | ||
693.2.m.k.379.4 | yes | 32 | 11.7 | odd | 10 | ||
693.2.m.k.379.5 | yes | 32 | 33.29 | even | 10 | ||
7623.2.a.db.1.8 | 16 | 3.2 | odd | 2 | inner | ||
7623.2.a.db.1.9 | 16 | 1.1 | even | 1 | trivial | ||
7623.2.a.dc.1.8 | 16 | 11.10 | odd | 2 | |||
7623.2.a.dc.1.9 | 16 | 33.32 | even | 2 |