Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.69353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.74252 | −1.03658 | −0.518288 | − | 0.855206i | \(-0.673430\pi\) | ||||
−0.518288 | + | 0.855206i | \(0.673430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.76763 | 1.73901 | 0.869504 | − | 0.493927i | \(-0.164439\pi\) | ||||
0.869504 | + | 0.493927i | \(0.164439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.742521 | −0.180088 | −0.0900439 | − | 0.995938i | \(-0.528701\pi\) | ||||
−0.0900439 | + | 0.995938i | \(0.528701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.26394 | −0.519385 | −0.259692 | − | 0.965691i | \(-0.583621\pi\) | ||||
−0.259692 | + | 0.965691i | \(0.583621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.74252 | 0.598467 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.74252 | −0.571855 | −0.285928 | − | 0.958251i | \(-0.592302\pi\) | ||||
−0.285928 | + | 0.958251i | \(0.592302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.263945 | −0.0490133 | −0.0245067 | − | 0.999700i | \(-0.507801\pi\) | ||||
−0.0245067 | + | 0.999700i | \(0.507801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.76763 | −1.00402 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.74252 | −0.463571 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.76763 | 1.27699 | 0.638496 | − | 0.769625i | \(-0.279557\pi\) | ||||
0.638496 | + | 0.769625i | \(0.279557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.76763 | −0.588406 | −0.294203 | − | 0.955743i | \(-0.595054\pi\) | ||||
−0.294203 | + | 0.955743i | \(0.595054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.28906 | 0.806574 | 0.403287 | − | 0.915074i | \(-0.367868\pi\) | ||||
0.403287 | + | 0.915074i | \(0.367868\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.521423 | 0.0744891 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.742521 | 0.103974 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0567 | 1.79347 | 0.896737 | − | 0.442563i | \(-0.145931\pi\) | ||||
0.896737 | + | 0.442563i | \(0.145931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.76763 | 0.777708 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.26394 | 0.299867 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.0502 | −1.30843 | −0.654214 | − | 0.756309i | \(-0.727000\pi\) | ||||
−0.654214 | + | 0.756309i | \(0.727000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.2527 | 1.69683 | 0.848416 | − | 0.529330i | \(-0.177557\pi\) | ||||
0.848416 | + | 0.529330i | \(0.177557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.74252 | −0.345525 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2462 | −1.25177 | −0.625887 | − | 0.779914i | \(-0.715263\pi\) | ||||
−0.625887 | + | 0.779914i | \(0.715263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.74252 | 0.330161 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.5417 | 1.96314 | 0.981571 | − | 0.191096i | \(-0.0612041\pi\) | ||||
0.981571 | + | 0.191096i | \(0.0612041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.02511 | 1.05631 | 0.528155 | − | 0.849148i | \(-0.322884\pi\) | ||||
0.528155 | + | 0.849148i | \(0.322884\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.8179 | −1.80261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00647 | −0.113236 | −0.0566181 | − | 0.998396i | \(-0.518032\pi\) | ||||
−0.0566181 | + | 0.998396i | \(0.518032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.24621 | −0.685611 | −0.342805 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342805 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.742521 | −0.0805377 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.263945 | 0.0282979 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.993534 | 0.105314 | 0.0526572 | − | 0.998613i | \(-0.483231\pi\) | ||||
0.0526572 | + | 0.998613i | \(0.483231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.74252 | −0.287494 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.26394 | −0.232276 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.27041 | −0.535129 | −0.267565 | − | 0.963540i | \(-0.586219\pi\) | ||||
−0.267565 | + | 0.963540i | \(0.586219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.76763 | 0.579669 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.2843 | −1.71985 | −0.859924 | − | 0.510422i | \(-0.829489\pi\) | ||||
−0.859924 | + | 0.510422i | \(0.829489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.8243 | −1.65775 | −0.828875 | − | 0.559434i | \(-0.811019\pi\) | ||||
−0.828875 | + | 0.559434i | \(0.811019\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.74252 | 0.267643 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.2955 | −0.995306 | −0.497653 | − | 0.867376i | \(-0.665805\pi\) | ||||
−0.497653 | + | 0.867376i | \(0.665805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5102 | 1.00669 | 0.503345 | − | 0.864085i | \(-0.332102\pi\) | ||||
0.503345 | + | 0.864085i | \(0.332102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.76763 | −0.737271 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5231 | −1.17807 | −0.589037 | − | 0.808106i | \(-0.700493\pi\) | ||||
−0.589037 | + | 0.808106i | \(0.700493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.74252 | −0.255741 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.03638 | 0.186675 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.2656 | 2.02415 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.76763 | 0.339716 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.27613 | −0.290709 | −0.145355 | − | 0.989380i | \(-0.546432\pi\) | ||||
−0.145355 | + | 0.989380i | \(0.546432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.28906 | −0.465676 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.02511 | −0.264305 | −0.132153 | − | 0.991229i | \(-0.542189\pi\) | ||||
−0.132153 | + | 0.991229i | \(0.542189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.20892 | 0.538381 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.7741 | 1.09137 | 0.545683 | − | 0.837992i | \(-0.316270\pi\) | ||||
0.545683 | + | 0.837992i | \(0.316270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.78057 | 0.659939 | 0.329970 | − | 0.943992i | \(-0.392962\pi\) | ||||
0.329970 | + | 0.943992i | \(0.392962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.76763 | 0.482314 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.263945 | −0.0219194 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.521423 | −0.0430063 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.3458 | 1.50294 | 0.751471 | − | 0.659766i | \(-0.229345\pi\) | ||||
0.751471 | + | 0.659766i | \(0.229345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9701 | 0.892733 | 0.446366 | − | 0.894850i | \(-0.352718\pi\) | ||||
0.446366 | + | 0.894850i | \(0.352718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.742521 | −0.0600293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.19598 | 0.175259 | 0.0876293 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876293 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.0567 | −1.03546 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.52142 | 0.592771 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4915 | −0.821758 | −0.410879 | − | 0.911690i | \(-0.634778\pi\) | ||||
−0.410879 | + | 0.911690i | \(0.634778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.76763 | −0.449010 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.6283 | −1.28674 | −0.643370 | − | 0.765555i | \(-0.722464\pi\) | ||||
−0.643370 | + | 0.765555i | \(0.722464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.26394 | −0.173128 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.19598 | −0.166958 | −0.0834788 | − | 0.996510i | \(-0.526603\pi\) | ||||
−0.0834788 | + | 0.996510i | \(0.526603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.74252 | −0.207315 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0502 | 0.755421 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.01218 | 0.0756540 | 0.0378270 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378270 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3328 | 1.21401 | 0.607004 | − | 0.794698i | \(-0.292371\pi\) | ||||
0.607004 | + | 0.794698i | \(0.292371\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.2527 | −0.979666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.76763 | 0.571088 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.28259 | −0.313174 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.74252 | 0.199489 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.5054 | 1.62843 | 0.814215 | − | 0.580563i | \(-0.197168\pi\) | ||||
0.814215 | + | 0.580563i | \(0.197168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2778 | −0.883775 | −0.441887 | − | 0.897071i | \(-0.645691\pi\) | ||||
−0.441887 | + | 0.897071i | \(0.645691\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.80402 | 0.128531 | 0.0642654 | − | 0.997933i | \(-0.479530\pi\) | ||||
0.0642654 | + | 0.997933i | \(0.479530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.2163 | 1.78754 | 0.893768 | − | 0.448530i | \(-0.148052\pi\) | ||||
0.893768 | + | 0.448530i | \(0.148052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.2462 | 0.722712 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.723874 | 0.0508060 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.76763 | −0.263143 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.74252 | −0.190618 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.0576 | −0.903214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0705 | 1.31287 | 0.656435 | − | 0.754383i | \(-0.272064\pi\) | ||||
0.656435 | + | 0.754383i | \(0.272064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.5417 | −1.13342 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.28906 | 0.360711 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.02511 | −0.609861 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.742521 | −0.0499474 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6032 | 1.17880 | 0.589400 | − | 0.807842i | \(-0.299364\pi\) | ||||
0.589400 | + | 0.807842i | \(0.299364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.01293 | 0.399092 | 0.199546 | − | 0.979888i | \(-0.436053\pi\) | ||||
0.199546 | + | 0.979888i | \(0.436053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5305 | −1.02628 | −0.513141 | − | 0.858304i | \(-0.671518\pi\) | ||||
−0.513141 | + | 0.858304i | \(0.671518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.8179 | 1.04074 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.7628 | 1.42573 | 0.712865 | − | 0.701301i | \(-0.247397\pi\) | ||||
0.712865 | + | 0.701301i | \(0.247397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00647 | 0.0653770 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2955 | 1.44218 | 0.721089 | − | 0.692843i | \(-0.243642\pi\) | ||||
0.721089 | + | 0.692843i | \(0.243642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9572 | 0.705812 | 0.352906 | − | 0.935659i | \(-0.385193\pi\) | ||||
0.352906 | + | 0.935659i | \(0.385193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.521423 | 0.0333125 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.26394 | −0.144051 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.24621 | 0.395838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.9952 | 0.883369 | 0.441685 | − | 0.897170i | \(-0.354381\pi\) | ||||
0.441685 | + | 0.897170i | \(0.354381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.8179 | −0.994460 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.742521 | 0.0464985 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.6032 | 1.22282 | 0.611408 | − | 0.791316i | \(-0.290603\pi\) | ||||
0.611408 | + | 0.791316i | \(0.290603\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.3029 | −1.32370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.263945 | −0.0163378 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.05503 | 0.250044 | 0.125022 | − | 0.992154i | \(-0.460100\pi\) | ||||
0.125022 | + | 0.992154i | \(0.460100\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0567 | 0.802066 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.993534 | −0.0608033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.34409 | −0.203893 | −0.101946 | − | 0.994790i | \(-0.532507\pi\) | ||||
−0.101946 | + | 0.994790i | \(0.532507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.565184 | −0.0343325 | −0.0171662 | − | 0.999853i | \(-0.505464\pi\) | ||||
−0.0171662 | + | 0.999853i | \(0.505464\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.74252 | 0.165985 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.76763 | 0.347801 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.81695 | −0.469675 | −0.234837 | − | 0.972035i | \(-0.575456\pi\) | ||||
−0.234837 | + | 0.972035i | \(0.575456\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2761 | 1.26923 | 0.634614 | − | 0.772830i | \(-0.281159\pi\) | ||||
0.634614 | + | 0.772830i | \(0.281159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2721 | −1.08616 | −0.543081 | − | 0.839680i | \(-0.682742\pi\) | ||||
−0.543081 | + | 0.839680i | \(0.682742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.26394 | 0.134105 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3328 | 0.609927 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4487 | −0.967568 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.27041 | 0.308957 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.81695 | −0.456671 | −0.228335 | − | 0.973583i | \(-0.573328\pi\) | ||||
−0.228335 | + | 0.973583i | \(0.573328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0502 | −0.585147 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.76763 | −0.334672 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.74252 | −0.158604 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.5054 | −0.836075 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.2843 | 0.992955 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.2527 | 0.758846 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.49889 | 0.542130 | 0.271065 | − | 0.962561i | \(-0.412624\pi\) | ||||
0.271065 | + | 0.962561i | \(0.412624\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.8243 | 0.957103 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.98707 | 0.339495 | 0.169748 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169748 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4422 | 0.929368 | 0.464684 | − | 0.885477i | \(-0.346168\pi\) | ||||
0.464684 | + | 0.885477i | \(0.346168\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.74252 | −0.154524 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.5781 | −0.706457 | −0.353229 | − | 0.935537i | \(-0.614916\pi\) | ||||
−0.353229 | + | 0.935537i | \(0.614916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.52234 | −0.0852345 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.2955 | 0.574640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.68103 | 0.0935349 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.5102 | −0.581213 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.706141 | 0.0388130 | 0.0194065 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194065 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.76763 | 0.425664 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2462 | −0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5984 | 0.740754 | 0.370377 | − | 0.928882i | \(-0.379229\pi\) | ||||
0.370377 | + | 0.928882i | \(0.379229\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5231 | 0.680161 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7676 | 0.959362 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.74252 | 0.147652 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.8810 | 1.92619 | 0.963097 | − | 0.269154i | \(-0.0867442\pi\) | ||||
0.963097 | + | 0.269154i | \(0.0867442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0753 | 1.02108 | 0.510540 | − | 0.859854i | \(-0.329446\pi\) | ||||
0.510540 | + | 0.859854i | \(0.329446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.8169 | 0.628953 | 0.314476 | − | 0.949265i | \(-0.398171\pi\) | ||||
0.314476 | + | 0.949265i | \(0.398171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.5417 | 0.877944 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.03638 | −0.107777 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.7538 | 0.725897 | 0.362949 | − | 0.931809i | \(-0.381770\pi\) | ||||
0.362949 | + | 0.931809i | \(0.381770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8746 | −0.730240 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.2656 | −1.16864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.02511 | 0.472396 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.81140 | 0.355552 | 0.177776 | − | 0.984071i | \(-0.443110\pi\) | ||||
0.177776 | + | 0.984071i | \(0.443110\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.76763 | −0.196135 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.8083 | −1.85907 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3522 | 1.62336 | 0.811678 | − | 0.584105i | \(-0.198554\pi\) | ||||
0.811678 | + | 0.584105i | \(0.198554\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.263945 | −0.0135938 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.6633 | −0.907302 | −0.453651 | − | 0.891179i | \(-0.649879\pi\) | ||||
−0.453651 | + | 0.891179i | \(0.649879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.27613 | 0.167841 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.54082 | −0.334220 | −0.167110 | − | 0.985938i | \(-0.553444\pi\) | ||||
−0.167110 | + | 0.985938i | \(0.553444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.8179 | −0.806153 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.28906 | 0.268858 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.31417 | −0.320141 | −0.160071 | − | 0.987106i | \(-0.551172\pi\) | ||||
−0.160071 | + | 0.987106i | \(0.551172\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.03638 | 0.102984 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.02511 | 0.152597 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00647 | −0.0506408 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2172 | −1.26562 | −0.632808 | − | 0.774309i | \(-0.718098\pi\) | ||||
−0.632808 | + | 0.774309i | \(0.718098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.20892 | −0.310835 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9199 | 0.545312 | 0.272656 | − | 0.962112i | \(-0.412098\pi\) | ||||
0.272656 | + | 0.962112i | \(0.412098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.8009 | 2.22070 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0074 | −0.643174 | −0.321587 | − | 0.946880i | \(-0.604216\pi\) | ||||
−0.321587 | + | 0.946880i | \(0.604216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.7741 | −0.630100 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.5630 | 1.35628 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.24621 | −0.306614 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.78057 | −0.381016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.0584 | 1.85927 | 0.929636 | − | 0.368479i | \(-0.120121\pi\) | ||||
0.929636 | + | 0.368479i | \(0.120121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.48984 | 0.462507 | 0.231253 | − | 0.972894i | \(-0.425717\pi\) | ||||
0.231253 | + | 0.972894i | \(0.425717\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.742521 | −0.0360176 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.3458 | −1.75889 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.76763 | −0.278464 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6487 | −1.23545 | −0.617726 | − | 0.786393i | \(-0.711946\pi\) | ||||
−0.617726 | + | 0.786393i | \(0.711946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0502 | −0.579097 | −0.289548 | − | 0.957163i | \(-0.593505\pi\) | ||||
−0.289548 | + | 0.957163i | \(0.593505\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.263945 | 0.0126552 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.20892 | 0.297013 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8049 | 0.849783 | 0.424891 | − | 0.905244i | \(-0.360312\pi\) | ||||
0.424891 | + | 0.905244i | \(0.360312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.521423 | 0.0248297 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3328 | 0.680973 | 0.340486 | − | 0.940249i | \(-0.389408\pi\) | ||||
0.340486 | + | 0.940249i | \(0.389408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.993534 | 0.0470980 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.3458 | −0.867724 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.9913 | 1.69853 | 0.849267 | − | 0.527963i | \(-0.177044\pi\) | ||||
0.849267 | + | 0.527963i | \(0.177044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.7303 | −1.02324 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.9701 | −0.515420 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.74252 | −0.128571 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.30033 | −0.107605 | −0.0538023 | − | 0.998552i | \(-0.517134\pi\) | ||||
−0.0538023 | + | 0.998552i | \(0.517134\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.742521 | 0.0346579 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.2804 | −1.55002 | −0.775011 | − | 0.631948i | \(-0.782256\pi\) | ||||
−0.775011 | + | 0.631948i | \(0.782256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.792748 | −0.0368421 | −0.0184211 | − | 0.999830i | \(-0.505864\pi\) | ||||
−0.0184211 | + | 0.999830i | \(0.505864\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.3103 | −1.49514 | −0.747571 | − | 0.664182i | \(-0.768780\pi\) | ||||
−0.747571 | + | 0.664182i | \(0.768780\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.1005 | 1.29756 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.19598 | −0.101186 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.5054 | 1.40264 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.26394 | −0.103877 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.0567 | 0.597825 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.2826 | 0.926735 | 0.463368 | − | 0.886166i | \(-0.346641\pi\) | ||||
0.463368 | + | 0.886166i | \(0.346641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.76763 | 0.354174 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.52142 | −0.342237 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.27041 | −0.239317 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.3709 | 0.877778 | 0.438889 | − | 0.898541i | \(-0.355372\pi\) | ||||
0.438889 | + | 0.898541i | \(0.355372\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.4915 | 0.474442 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.98227 | −0.179717 | −0.0898586 | − | 0.995955i | \(-0.528642\pi\) | ||||
−0.0898586 | + | 0.995955i | \(0.528642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.195985 | 0.00882670 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.76763 | 0.259236 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −45.3661 | −2.03495 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7619 | −0.795133 | −0.397566 | − | 0.917573i | \(-0.630145\pi\) | ||||
−0.397566 | + | 0.917573i | \(0.630145\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.6283 | 0.742900 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0454 | −0.715430 | −0.357715 | − | 0.933831i | \(-0.616444\pi\) | ||||
−0.357715 | + | 0.933831i | \(0.616444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.2843 | −0.769139 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7879 | 0.744113 | 0.372056 | − | 0.928210i | \(-0.378653\pi\) | ||||
0.372056 | + | 0.928210i | \(0.378653\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.7516 | −1.09494 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.26394 | 0.0999556 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.8243 | −0.741368 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.19598 | 0.0963930 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.5279 | 1.33745 | 0.668726 | − | 0.743509i | \(-0.266840\pi\) | ||||
0.668726 | + | 0.743509i | \(0.266840\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.0277 | −1.57538 | −0.787690 | − | 0.616071i | \(-0.788723\pi\) | ||||
−0.787690 | + | 0.616071i | \(0.788723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.74252 | 0.119693 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4786 | −0.672982 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0502 | −0.436143 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.76763 | −0.163194 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2955 | −0.445114 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.01218 | −0.0436788 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00738 | 0.129537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.04543 | −0.0879397 | −0.0439699 | − | 0.999033i | \(-0.514001\pi\) | ||||
−0.0439699 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.3328 | −0.700908 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5102 | 0.450206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.5183 | −1.21935 | −0.609677 | − | 0.792650i | \(-0.708701\pi\) | ||||
−0.609677 | + | 0.792650i | \(0.708701\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.2527 | 0.565610 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.597556 | 0.0254568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.76025 | 0.117378 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.76763 | −0.329718 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.0835 | 0.978078 | 0.489039 | − | 0.872262i | \(-0.337348\pi\) | ||||
0.489039 | + | 0.872262i | \(0.337348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.28906 | 0.223703 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.28259 | 0.180811 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6949 | 1.08291 | 0.541455 | − | 0.840730i | \(-0.317874\pi\) | ||||
0.541455 | + | 0.840730i | \(0.317874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.5231 | −0.526850 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.74252 | −0.115175 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0761 | −1.00932 | −0.504661 | − | 0.863318i | \(-0.668383\pi\) | ||||
−0.504661 | + | 0.863318i | \(0.668383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.82341 | 0.285551 | 0.142775 | − | 0.989755i | \(-0.454397\pi\) | ||||
0.142775 | + | 0.989755i | \(0.454397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.5054 | −0.940175 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.74252 | −0.114371 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.7126 | −0.820647 | −0.410323 | − | 0.911940i | \(-0.634584\pi\) | ||||
−0.410323 | + | 0.911940i | \(0.634584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.2778 | 0.510248 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1304 | 0.710687 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 75.3062 | 3.11887 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.50940 | 0.144849 | 0.0724243 | − | 0.997374i | \(-0.476926\pi\) | ||||
0.0724243 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.80402 | −0.0742073 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.2891 | 0.627846 | 0.313923 | − | 0.949448i | \(-0.398357\pi\) | ||||
0.313923 | + | 0.949448i | \(0.398357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.03638 | 0.0834835 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.2163 | −1.03203 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.07054 | −0.288894 | −0.144447 | − | 0.989513i | \(-0.546140\pi\) | ||||
−0.144447 | + | 0.989513i | \(0.546140\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.5620 | 1.45061 | 0.725303 | − | 0.688430i | \(-0.241700\pi\) | ||||
0.725303 | + | 0.688430i | \(0.241700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2462 | −0.417258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.2656 | 0.905226 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7409 | −0.638902 | −0.319451 | − | 0.947603i | \(-0.603498\pi\) | ||||
−0.319451 | + | 0.947603i | \(0.603498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.723874 | −0.0293329 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7676 | −0.475290 | −0.237645 | − | 0.971352i | \(-0.576376\pi\) | ||||
−0.237645 | + | 0.971352i | \(0.576376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.76763 | 0.151926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.7741 | −0.997368 | −0.498684 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498684 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.80882 | −0.0727025 | −0.0363512 | − | 0.999339i | \(-0.511574\pi\) | ||||
−0.0363512 | + | 0.999339i | \(0.511574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.74252 | 0.110054 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.72479 | −0.109166 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.0576 | 0.521471 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.76763 | −0.229971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.5685 | −1.53539 | −0.767694 | − | 0.640816i | \(-0.778596\pi\) | ||||
−0.767694 | + | 0.640816i | \(0.778596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0705 | −0.757986 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.27613 | −0.130009 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.521423 | 0.0206595 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.5417 | 0.654381 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1263 | −0.873937 | −0.436969 | − | 0.899477i | \(-0.643948\pi\) | ||||
−0.436969 | + | 0.899477i | \(0.643948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.0770 | 1.10725 | 0.553624 | − | 0.832766i | \(-0.313244\pi\) | ||||
0.553624 | + | 0.832766i | \(0.313244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.28906 | −0.208256 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.2981 | −0.915943 | −0.457971 | − | 0.888967i | \(-0.651424\pi\) | ||||
−0.457971 | + | 0.888967i | \(0.651424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.9660 | −2.27537 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.82433 | 0.267057 | 0.133528 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133528 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.02511 | −0.118201 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.02511 | 0.352103 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.5733 | −0.957240 | −0.478620 | − | 0.878022i | \(-0.658863\pi\) | ||||
−0.478620 | + | 0.878022i | \(0.658863\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.9653 | 1.35999 | 0.679996 | − | 0.733216i | \(-0.261982\pi\) | ||||
0.679996 | + | 0.733216i | \(0.261982\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.742521 | 0.0288371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.20892 | 0.240771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.723874 | 0.0280285 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.6032 | −0.680580 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 76.4366 | 2.95080 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0576 | −1.04299 | −0.521497 | − | 0.853253i | \(-0.674626\pi\) | ||||
−0.521497 | + | 0.853253i | \(0.674626\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.42835 | 0.170195 | 0.0850977 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850977 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.4542 | 0.554702 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.01293 | −0.230416 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.8373 | 0.414676 | 0.207338 | − | 0.978269i | \(-0.433520\pi\) | ||||
0.207338 | + | 0.978269i | \(0.433520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.7741 | 0.488073 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.5305 | 0.592524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.0567 | 0.497420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7863 | −0.752706 | −0.376353 | − | 0.926476i | \(-0.622822\pi\) | ||||
−0.376353 | + | 0.926476i | \(0.622822\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.8179 | −0.600871 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.78057 | 0.295134 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.79755 | 0.105965 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.7628 | −0.823146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.2041 | 0.687560 | 0.343780 | − | 0.939050i | \(-0.388293\pi\) | ||||
0.343780 | + | 0.939050i | \(0.388293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.5855 | −0.663250 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.4024 | 1.78275 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5305 | −0.583259 | −0.291629 | − | 0.956531i | \(-0.594197\pi\) | ||||
−0.291629 | + | 0.956531i | \(0.594197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00647 | −0.0377454 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.76763 | 0.215697 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.2955 | −0.832642 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.9904 | 1.93891 | 0.969457 | − | 0.245260i | \(-0.0788733\pi\) | ||||
0.969457 | + | 0.245260i | \(0.0788733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.1411 | 1.71838 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9572 | −0.407501 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.263945 | −0.00980266 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3094 | 0.530705 | 0.265353 | − | 0.964151i | \(-0.414512\pi\) | ||||
0.265353 | + | 0.964151i | \(0.414512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.92724 | −0.145254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.3605 | 1.78624 | 0.893118 | − | 0.449822i | \(-0.148513\pi\) | ||||
0.893118 | + | 0.449822i | \(0.148513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.521423 | −0.0192330 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −59.0964 | −2.17684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.1986 | −1.36837 | −0.684186 | − | 0.729308i | \(-0.739842\pi\) | ||||
−0.684186 | + | 0.729308i | \(0.739842\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.26394 | 0.0831681 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0632 | 1.17628 | 0.588142 | − | 0.808758i | \(-0.299860\pi\) | ||||
0.588142 | + | 0.808758i | \(0.299860\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.3458 | 0.672136 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.24621 | −0.228537 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.2357 | 1.03171 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.6875 | −0.681916 | −0.340958 | − | 0.940078i | \(-0.610751\pi\) | ||||
−0.340958 | + | 0.940078i | \(0.610751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.9952 | −0.510013 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.9701 | 0.399242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.4496 | 0.416142 | 0.208071 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208071 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.8179 | 0.574152 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.9199 | 0.975844 | 0.487922 | − | 0.872887i | \(-0.337755\pi\) | ||||
0.487922 | + | 0.872887i | \(0.337755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.8243 | −1.04351 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.742521 | −0.0268459 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.0502 | −0.362893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.5223 | −1.42521 | −0.712606 | − | 0.701564i | \(-0.752485\pi\) | ||||
−0.712606 | + | 0.701564i | \(0.752485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.6032 | −0.705993 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.2237 | −1.08707 | −0.543535 | − | 0.839386i | \(-0.682915\pi\) | ||||
−0.543535 | + | 0.839386i | \(0.682915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.3029 | 0.764237 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.52972 | 0.305609 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 95.4067 | 3.41392 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.263945 | 0.00943262 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.19598 | 0.0783781 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8040 | −0.705937 | −0.352968 | − | 0.935635i | \(-0.614828\pi\) | ||||
−0.352968 | + | 0.935635i | \(0.614828\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.05503 | −0.144363 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.3448 | 1.22116 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.2527 | 0.470616 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.0567 | −0.463073 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.4487 | −1.18481 | −0.592406 | − | 0.805639i | \(-0.701822\pi\) | ||||
−0.592406 | + | 0.805639i | \(0.701822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.993534 | 0.0351048 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 52.0536 | 1.83693 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.52142 | 0.265095 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.34409 | 0.117717 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.9848 | −1.65190 | −0.825950 | − | 0.563744i | \(-0.809360\pi\) | ||||
−0.825950 | + | 0.563744i | \(0.809360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.8720 | −0.627570 | −0.313785 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313785 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.565184 | 0.0198219 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.4915 | −0.367502 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.9741 | −0.418922 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.74252 | −0.0958315 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.82746 | −0.203380 | −0.101690 | − | 0.994816i | \(-0.532425\pi\) | ||||
−0.101690 | + | 0.994816i | \(0.532425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.7386 | 1.21091 | 0.605456 | − | 0.795879i | \(-0.292991\pi\) | ||||
0.605456 | + | 0.795879i | \(0.292991\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.76763 | −0.200803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7685 | 0.548326 | 0.274163 | − | 0.961683i | \(-0.411599\pi\) | ||||
0.274163 | + | 0.961683i | \(0.411599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5781 | −0.714708 | −0.357354 | − | 0.933969i | \(-0.616321\pi\) | ||||
−0.357354 | + | 0.933969i | \(0.616321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.81695 | 0.271167 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.387168 | −0.0134146 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6283 | −0.575448 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.6018 | 1.12554 | 0.562770 | − | 0.826614i | \(-0.309736\pi\) | ||||
0.562770 | + | 0.826614i | \(0.309736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9303 | −0.997598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.2761 | −0.732789 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −61.0639 | −2.09818 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.2721 | 0.627096 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.3029 | −0.730254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.59442 | 0.260028 | 0.130014 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130014 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.26394 | −0.0774253 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.7499 | −1.08456 | −0.542278 | − | 0.840199i | \(-0.682438\pi\) | ||||
−0.542278 | + | 0.840199i | \(0.682438\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.74510 | 0.264259 | 0.132130 | − | 0.991232i | \(-0.457818\pi\) | ||||
0.132130 | + | 0.991232i | \(0.457818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.3328 | −0.352142 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.9476 | 1.53003 | 0.765016 | − | 0.644011i | \(-0.222731\pi\) | ||||
0.765016 | + | 0.644011i | \(0.222731\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.19598 | −0.0746657 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.4487 | 0.558626 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.80493 | −0.196919 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2462 | −0.347180 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.27041 | −0.178376 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.74252 | −0.0927141 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1263 | 0.477012 | 0.238506 | − | 0.971141i | \(-0.423342\pi\) | ||||
0.238506 | + | 0.971141i | \(0.423342\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.81695 | 0.263659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.0033 | 1.88680 | 0.943400 | − | 0.331657i | \(-0.107608\pi\) | ||||
0.943400 | + | 0.331657i | \(0.107608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.5183 | 1.22894 | 0.614469 | − | 0.788941i | \(-0.289370\pi\) | ||||
0.614469 | + | 0.788941i | \(0.289370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.0502 | 0.337835 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.21463 | 0.208667 | 0.104333 | − | 0.994542i | \(-0.466729\pi\) | ||||
0.104333 | + | 0.994542i | \(0.466729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.98485 | 0.301342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.76763 | 0.193223 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.01218 | 0.0338335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.74252 | 0.0915701 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.69487 | −0.322983 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.5054 | 0.482708 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.3328 | 0.542921 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.9230 | 1.35882 | 0.679412 | − | 0.733757i | \(-0.262235\pi\) | ||||
0.679412 | + | 0.733757i | \(0.262235\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.2843 | −0.573283 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.00738 | 0.232165 | 0.116082 | − | 0.993240i | \(-0.462966\pi\) | ||||
0.116082 | + | 0.993240i | \(0.462966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0259 | −1.19228 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.2527 | −0.438120 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.29644 | 0.273973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.8027 | 1.47790 | 0.738952 | − | 0.673758i | \(-0.235321\pi\) | ||||
0.738952 | + | 0.673758i | \(0.235321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.49889 | −0.312999 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5417 | 0.544478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.76763 | 0.255398 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.8243 | −0.552583 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.11985 | 0.299213 | 0.149606 | − | 0.988746i | \(-0.452199\pi\) | ||||
0.149606 | + | 0.988746i | \(0.452199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.18047 | −0.0386885 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.98707 | −0.196008 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.28259 | −0.140056 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.37904 | −0.143057 | −0.0715285 | − | 0.997439i | \(-0.522788\pi\) | ||||
−0.0715285 | + | 0.997439i | \(0.522788\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.4422 | −0.536571 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.8212 | −1.29813 | −0.649067 | − | 0.760731i | \(-0.724840\pi\) | ||||
−0.649067 | + | 0.760731i | \(0.724840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3328 | 0.336483 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.74252 | 0.0892142 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.8949 | 1.55637 | 0.778187 | − | 0.628033i | \(-0.216140\pi\) | ||||
0.778187 | + | 0.628033i | \(0.216140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.02511 | 0.292968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.5781 | 0.407873 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.22018 | −0.233885 | −0.116942 | − | 0.993139i | \(-0.537309\pi\) | ||||
−0.116942 | + | 0.993139i | \(0.537309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.5054 | 0.728256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.52234 | 0.0492102 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.0332 | −1.13128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.2955 | −0.331769 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.2778 | −0.395236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.16103 | 0.101652 | 0.0508260 | − | 0.998708i | \(-0.483815\pi\) | ||||
0.0508260 | + | 0.998708i | \(0.483815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.68103 | −0.0540024 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.9280 | −0.928343 | −0.464172 | − | 0.885745i | \(-0.653648\pi\) | ||||
−0.464172 | + | 0.885745i | \(0.653648\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.3384 | −0.684077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.79441 | 0.185380 | 0.0926898 | − | 0.995695i | \(-0.470453\pi\) | ||||
0.0926898 | + | 0.995695i | \(0.470453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.73034 | 0.183142 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5102 | 0.335563 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.2471 | −1.44316 | −0.721579 | − | 0.692332i | \(-0.756583\pi\) | ||||
−0.721579 | + | 0.692332i | \(0.756583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.80402 | 0.0574807 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5054 | −0.461243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.5118 | −1.25513 | −0.627567 | − | 0.778562i | \(-0.715949\pi\) | ||||
−0.627567 | + | 0.778562i | \(0.715949\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.706141 | −0.0224087 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.2163 | 0.799410 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.2495 | 1.21138 | 0.605688 | − | 0.795703i | \(-0.292898\pi\) | ||||
0.605688 | + | 0.795703i | \(0.292898\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.76763 | −0.245757 |
(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 | 6240.2.a.ce.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 6240.2.a.cf.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.ce.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6240.2.a.cf.1.3 | yes | 4 | 4.3 | odd | 2 |